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El tío Petros y la conjetura de Goldbach
“Toda familia tiene su ovejas negra; en la nuestra era el tío Petros”. Así lo afirma el sobrino favorito de Petros Papachristos-y narrador de las peripecias de su tío-, en esta novela de Apostolos Doxiadis.
El anciano tío Petros vive retirado de la vida social y familiar, entregado al cuidado de su jardín y a la práctica del ajedrez. Su sobrino, sin embargo, descubre por azar que su tío Petros fue un matemático eminente, profesor en Alemania e Inglaterra, niño prodigio en esta disciplina y estudioso totalmente absorto en sus investigaciones científicas.
La vida de Petros Papachristos ha girado durante años en torno a la demostración de la famosa Conjetura de Goldbach, un problema en apariencia sencillo y que cualquier estudiante de secundaria puede entender, pero que durante más de dos siglos nadie ha sabido resolver: “Todo número par superior a dos se puede escribir como suma de dos números primos”.
La forma de plantearse el problema en la novela es, sencillamente, magnífica. El sobrino quiere estudiar matemáticas y pide consejo a su tío Petros. Este no sabe como hacer desaparecer esa idea de la cabeza de su sobrino, así que le propone un reto bien sencillo en apariencia: demostrar en el verano que cualquier número par mayor que dos es suma de dos primos. El sobrino, por supuesto, no consigue lo que nadie ha conseguido aún y abandona las matemáticas hasta que meses después su compañero le explica la trampa que le tendió su tío.
A partir de aquí Apostolos Doxiadis nos abre las puertas de una extraordinaria aventura personal inscrita en el ámbito de las matemáticas, donde personajes ficticios conversan con algunos delos mejores matemáticos de este siglo pasado como Hardy, Ramanujan, Turing y Gödel. Describe el esfuerzo y el sufrimiento de un científico por resolver un enigma y refleja la lucha del ser humano por conquistar lo imposible.
El anciano tío Petros vive retirado de la vida social y familiar, entregado al cuidado de su jardín y a la práctica del ajedrez. Su sobrino, sin embargo, descubre por azar que su tío Petros fue un matemático eminente, profesor en Alemania e Inglaterra, niño prodigio en esta disciplina y estudioso totalmente absorto en sus investigaciones científicas.
La vida de Petros Papachristos ha girado durante años en torno a la demostración de la famosa Conjetura de Goldbach, un problema en apariencia sencillo y que cualquier estudiante de secundaria puede entender, pero que durante más de dos siglos nadie ha sabido resolver: “Todo número par superior a dos se puede escribir como suma de dos números primos”.
La forma de plantearse el problema en la novela es, sencillamente, magnífica. El sobrino quiere estudiar matemáticas y pide consejo a su tío Petros. Este no sabe como hacer desaparecer esa idea de la cabeza de su sobrino, así que le propone un reto bien sencillo en apariencia: demostrar en el verano que cualquier número par mayor que dos es suma de dos primos. El sobrino, por supuesto, no consigue lo que nadie ha conseguido aún y abandona las matemáticas hasta que meses después su compañero le explica la trampa que le tendió su tío.
A partir de aquí Apostolos Doxiadis nos abre las puertas de una extraordinaria aventura personal inscrita en el ámbito de las matemáticas, donde personajes ficticios conversan con algunos delos mejores matemáticos de este siglo pasado como Hardy, Ramanujan, Turing y Gödel. Describe el esfuerzo y el sufrimiento de un científico por resolver un enigma y refleja la lucha del ser humano por conquistar lo imposible.
4 pages, Paperback
First published January 1, 1992
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About the author
Apostolos Doxiadis
6 books277 followersApostolos Doxiadis (Greek: Απόστολος Δοξιάδης) was born in Brisbane, Australia in 1953, and grew up in Greece.
Although interested in fiction and the arts from his youngest years, a sudden and totally unexpected love affair with mathematics led him to New York's Columbia University at the age of fifteen. He did graduate work in Applied Mathematics at the École Pratique des Hautes Études in Paris, working on mathematical models for the nervous system.
After his studies, Apostolos returned to Greece and his adolescent loves of writing, cinema and the theater. For some years he directed professionally for the theater, and in 1983 made his first film Underground Passage (in Greek). His second film, Terirem (1986) won the prize of the International Center for Artistic Cinema (CICAE) at the 1988 Berlin International Film Festival.
Since the mid-eighties, most of Apostolos' work has been in fiction. He has published four novels in Greek, Parallel Life (1985), Makavettas (1988), Uncle Petros and Goldbach's Conjecture (1992) and Three Little Men (1997). His translation of Uncle Petros was published internationally in 2000, to great critical acclaim, and has since been translated into over thirty languages. Apostolos now writes in both Greek and English.
Apart from his work in fiction, Apostolos has written two plays. In 1999, he wrote and directed the musical shadow puppet play "The Tragical History of Jackson Pollock, Abstract Expressionist", accompanied by a volume of texts and images, Paralipomena. In 2006, his play Seventeenth Night had a year-long run in an Athens theatre. The play is a fictional recreation of the last days in the life of the great logician, and father of the incompleteness theorem, Kurt Gödel.
In autumn 2008, Apostolos, completed the graphic novel Logicomix, co-authored with Christos H. Papadimitriou, with art by Alecos Papadatos and Annie di Donna. The book's story is based on the epic quest for the foundations of mathematics. Logicomix was published in Autumn 2009 by Bloomsbury in the U.S. and the U.K.
Apart from his work in the various modes of storytelling, in the past few years, Apostolos has been studying the relationship between mathematics and narrative. He is currently editing a volume on mathematics and narrative with mathematician Barry Mazur, of Harvard University, due to be published in 2010.
Apostolos lives in Athens with his wife, the novelist Dorina Papaliou, and their children.
Although interested in fiction and the arts from his youngest years, a sudden and totally unexpected love affair with mathematics led him to New York's Columbia University at the age of fifteen. He did graduate work in Applied Mathematics at the École Pratique des Hautes Études in Paris, working on mathematical models for the nervous system.
After his studies, Apostolos returned to Greece and his adolescent loves of writing, cinema and the theater. For some years he directed professionally for the theater, and in 1983 made his first film Underground Passage (in Greek). His second film, Terirem (1986) won the prize of the International Center for Artistic Cinema (CICAE) at the 1988 Berlin International Film Festival.
Since the mid-eighties, most of Apostolos' work has been in fiction. He has published four novels in Greek, Parallel Life (1985), Makavettas (1988), Uncle Petros and Goldbach's Conjecture (1992) and Three Little Men (1997). His translation of Uncle Petros was published internationally in 2000, to great critical acclaim, and has since been translated into over thirty languages. Apostolos now writes in both Greek and English.
Apart from his work in fiction, Apostolos has written two plays. In 1999, he wrote and directed the musical shadow puppet play "The Tragical History of Jackson Pollock, Abstract Expressionist", accompanied by a volume of texts and images, Paralipomena. In 2006, his play Seventeenth Night had a year-long run in an Athens theatre. The play is a fictional recreation of the last days in the life of the great logician, and father of the incompleteness theorem, Kurt Gödel.
In autumn 2008, Apostolos, completed the graphic novel Logicomix, co-authored with Christos H. Papadimitriou, with art by Alecos Papadatos and Annie di Donna. The book's story is based on the epic quest for the foundations of mathematics. Logicomix was published in Autumn 2009 by Bloomsbury in the U.S. and the U.K.
Apart from his work in the various modes of storytelling, in the past few years, Apostolos has been studying the relationship between mathematics and narrative. He is currently editing a volume on mathematics and narrative with mathematician Barry Mazur, of Harvard University, due to be published in 2010.
Apostolos lives in Athens with his wife, the novelist Dorina Papaliou, and their children.
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June 30, 2020
Trust the Young
Number theory has nothing to do with the real world, unless you happen to be a number theorist. Then it is the real world; everything else is illusory. Number theory has no application to anything except... well, numbers. It eschews other branches of mathematics as pedestrian. Physics, engineering, and even geometry, although they use numbers, are simply diversions for the less talented, that is to say inferior, intellect. Mere calculation is trivial even if it is arduous and complex. Number theory’s only concern is with the relationship of numbers to each other. It seeks the hidden, often mysterious, connections that exist, and have always existed, among these most abstract of all ideas. Since numbers are eternal, infinite, and everywhere, they are easily taken for divine (For more on the significance and literary import of number theory, see: https://www.goodreads.com/review/show...).
And who knows? Numbers may well be divine. Among other reasons because the fundamental logic of numbers is as elusive as the theology of God. Apparently, just like any other believers, mathematicians make an act of faith every time they form an hypothesis, attempt a proof, or demonstrate a theorem. The reason that faith is necessary is that when the foundations of mathematics are probed far enough, they are shown to be, not built on sand, but entirely absent. All of mathematics, including number theory, floats above an intellectual void known as Godel’s Incompleteness Theorem. Kurt Godel showed in the 1930’s that no logical system, of which basic arithmetic is one, can contain the axioms necessary to ensure its own reliability. The consequences of Godel’s discovery are even more profound for mathematics than the discovery of Quantum Uncertainty is for physics.
So Incompleteness raises some important issues which Doxiadis uses as the substrate of his story. If mathematics is suspect, what hope is there for any other science? Or for human thought in general? The Incompleteness Theorem seems to suggest that everything is relative, that intellectual discipline is a fraud, that science is some kind of con game which we pretend to take seriously. And yet, mathematicians, scientists, engineers, and the check-out assistants in the supermarket continue to work away with numbers as if nothing were amiss. Is their apparent faith different from that of Christians, Jews, Muslims, and Mormons who also create doctrines, liturgies, and ethics over an abyss empty of ultimate reason and without sufficient reasons they can articulate?
Uncle Petros introduces these issues implicitly in his concern with the so-called Goldbach Conjecture, an hypothesis first formulated by an 18th century mathematician: “Every number greater than 2 can be written as a sum of two primes.” When he started his career, Uncle Petros was unaware of the Conjecture’s relation to the Incompleteness Theorem since the latter had yet to be formulated. But he had a certain faith, not just in his own mathematical ability but, more importantly, in the power of mathematics to ultimately prove or disprove what was Goldbach’s intuitive guess. One could accurately call this ‘blind’ faith but not as a reproach and not in the manner of religious faith, which when it is blind is often dangerous.
The first difference between religious and mathematical faith, of course, is that mathematical hypotheses such as that of Goldbach are based on empirical observation; mathematics is very much an empirical discipline. Every specific number greater than two which has been analysed can be shown to be the sum of two primes. But such empirical proof is inadequate for mathematics no matter how often it is observed. There could be some number among the infinity of numbers for which this general rule doesn’t apply. Hence the importance of the Conjecture if it can be proven abstractly as an invariable condition for any number at all and not just specific numbers.
This is where the mathematician’s second difference with religious believers comes into play. Mathematical logic works backwards from an hypothesis to discover the logic by which the hypothesis can be derived from communally accepted axioms. This logic can be both positive - if X, then Y etc. - or it can be negative - if not X, then Y or not Y etc. This latter form is that of a logical reductio ad absurdam, a contradiction which both affirms and denies a conclusion. Almost everything about religious faith is subject to a reductio ad absurdam. For example the proposition to reject the religious claim that ‘God created everything’ is compatible with both the axioms ‘the world is inherently good’ and ‘there is tremendous evil in the world.’ Creation is both good and not good with or without a divine origin. Mathematicians would view such a theological conclusion therefore as meaningless.*
The final difference in matters of faith concerns the fundamental axioms and their status in mathematics and religion. The difference here is somewhat surprising. Theology relies on fixed axioms from which it the derives its conclusions. These axioms are given the status of revealed truth and are the dogmatic focus of religious faith. Mathematicians since Godel on the other hand know that the fundamental axioms of their science are somewhat arbitrary. Euclid’s axioms of three dimensional space, for example, can be replaced by the n-dimensional space of Riemannian geometry with no loss of logical rigor. Euclid is not proven wrong but merely shown to be a special case of the more general conditions of Riemann.
This is an illustration as well of a crucial difference in method. Mathematics seeks to continuously extend the generality of its conclusions by discovering more and more inclusive axioms from which to work. Religious faith seeks to fix the axioms in order to preserve, limit and restrict doctrinal conclusions. Put another way: mathematics looks into the abyss of the Incompleteness Theorem and considers it an horizon to be striven toward painfully, incrementally, and with ho chance of complete success. This takes intellectual and, dare one say it, moral courage. The theologian looks into a similar abyss and considers that the horizon has arrived at his location. There is nothing to explore, nothing to find beyond the axioms which have been set by tradition. This sort of faith isn’t one of courage but stubbornness. It ramifies ‘conclusive’ conclusions because it takes its axioms for granted.
So the faith of the mathematician is not the faith of the religious believer. The faith required to attack the apparent intractability if the Goldbach Conjecture has nothing to do with the faith that proclaims One God or a religious ethic of forgiveness, or retribution, or community. The mathematician must have perseverance; the theologian merely persistence. The mathematician is concerned about expanding the world we know, the theologian with limiting what we know of the world. One requires genuine creative faith; the other futile insistence. Doxiadis quotes the 19th century mathematician, David Hilbert: “We must know, we shall know! In mathematics there is no ignorabimus!" Compare that with the commitment of religious faith by the first Christian theologian, Paul of Tarsus: “But if there be no resurrection of the dead, then is Christ not risen: and if Christ be not risen, then is our preaching vain, and your faith is also vain.”**
Both mathematicians and theologians tend to be obsessives. Both types are probably born not made. But mathematicians reach their intellectual peak in their relative youth. The best theologians are usually old men. I suspect the reason for this has to do with the paradoxical character of experiential wisdom. Young mathematicians have an intuitive grasp of reality unsullied by too much knowledge of what others call the world; while old theologians have been pickled in cultural history and traditions of thought that distort much of reality.
Uncle Petros himself tends to slide into quasi-theological reverie about mathematics in his dotage after suffering the slings and arrows of family as a failed mathematical prodigy, and especially after the publication of Godel’s Incompleteness Theorem. In a sense he has lost his faith in mathematics and replaced it with an entirely different kind of faithful resignation to cultural inevitability. This is why Petros loves chess: as in theology, its axioms are fixed, its rules invariably traditional.
It takes his nephew to help Uncle Petros understand that Godel freed mathematics from theological pretensions. There is no firm foundation for mathematics. Even David Hilbert thought there was but he was wrong; and so was Uncle Petros if he thought that firm intellectual foundations were necessary for his continuing commitment to mathematics. As Doxiadis has Alan Turing say, “Truth is not not always provable.” But this doesn’t invalidate mathematics or its method. Unlike theology, the commitment to mathematics is to an entirely unknown, and unnamed, future state of knowing. The content of that state is not, and cannot be, specified much less proven. Doxiadis compares it to being in love.
This is an important message from a young mathematician to an old one about a very different sort of tradition and a very different sort of faith, one that does away with “attainable goals.” And it is a message that makes Doxiadis’s little book a lot bigger than its size.
———————————————————————————————————-
*Neil Gaiman, in his American Gods captures the character of the reductio in theology rather well: “I believe in a personal god who cares about me and worries and oversees everything I do. I believe in an impersonal god who set the universe in motion and went off to hang with her girlfriends and doesn't even know that I'm alive. I believe in an empty and godless universe of causal chaos, background noise, and sheer blind luck.”
** For those who have forgotten their school Latin ‘ignorabimus’ is future tense: “we will be ignorant.” St. Paul, significantly, is concerned solely about the present but only in terms of the past in his exhortation.
Number theory has nothing to do with the real world, unless you happen to be a number theorist. Then it is the real world; everything else is illusory. Number theory has no application to anything except... well, numbers. It eschews other branches of mathematics as pedestrian. Physics, engineering, and even geometry, although they use numbers, are simply diversions for the less talented, that is to say inferior, intellect. Mere calculation is trivial even if it is arduous and complex. Number theory’s only concern is with the relationship of numbers to each other. It seeks the hidden, often mysterious, connections that exist, and have always existed, among these most abstract of all ideas. Since numbers are eternal, infinite, and everywhere, they are easily taken for divine (For more on the significance and literary import of number theory, see: https://www.goodreads.com/review/show...).
And who knows? Numbers may well be divine. Among other reasons because the fundamental logic of numbers is as elusive as the theology of God. Apparently, just like any other believers, mathematicians make an act of faith every time they form an hypothesis, attempt a proof, or demonstrate a theorem. The reason that faith is necessary is that when the foundations of mathematics are probed far enough, they are shown to be, not built on sand, but entirely absent. All of mathematics, including number theory, floats above an intellectual void known as Godel’s Incompleteness Theorem. Kurt Godel showed in the 1930’s that no logical system, of which basic arithmetic is one, can contain the axioms necessary to ensure its own reliability. The consequences of Godel’s discovery are even more profound for mathematics than the discovery of Quantum Uncertainty is for physics.
So Incompleteness raises some important issues which Doxiadis uses as the substrate of his story. If mathematics is suspect, what hope is there for any other science? Or for human thought in general? The Incompleteness Theorem seems to suggest that everything is relative, that intellectual discipline is a fraud, that science is some kind of con game which we pretend to take seriously. And yet, mathematicians, scientists, engineers, and the check-out assistants in the supermarket continue to work away with numbers as if nothing were amiss. Is their apparent faith different from that of Christians, Jews, Muslims, and Mormons who also create doctrines, liturgies, and ethics over an abyss empty of ultimate reason and without sufficient reasons they can articulate?
Uncle Petros introduces these issues implicitly in his concern with the so-called Goldbach Conjecture, an hypothesis first formulated by an 18th century mathematician: “Every number greater than 2 can be written as a sum of two primes.” When he started his career, Uncle Petros was unaware of the Conjecture’s relation to the Incompleteness Theorem since the latter had yet to be formulated. But he had a certain faith, not just in his own mathematical ability but, more importantly, in the power of mathematics to ultimately prove or disprove what was Goldbach’s intuitive guess. One could accurately call this ‘blind’ faith but not as a reproach and not in the manner of religious faith, which when it is blind is often dangerous.
The first difference between religious and mathematical faith, of course, is that mathematical hypotheses such as that of Goldbach are based on empirical observation; mathematics is very much an empirical discipline. Every specific number greater than two which has been analysed can be shown to be the sum of two primes. But such empirical proof is inadequate for mathematics no matter how often it is observed. There could be some number among the infinity of numbers for which this general rule doesn’t apply. Hence the importance of the Conjecture if it can be proven abstractly as an invariable condition for any number at all and not just specific numbers.
This is where the mathematician’s second difference with religious believers comes into play. Mathematical logic works backwards from an hypothesis to discover the logic by which the hypothesis can be derived from communally accepted axioms. This logic can be both positive - if X, then Y etc. - or it can be negative - if not X, then Y or not Y etc. This latter form is that of a logical reductio ad absurdam, a contradiction which both affirms and denies a conclusion. Almost everything about religious faith is subject to a reductio ad absurdam. For example the proposition to reject the religious claim that ‘God created everything’ is compatible with both the axioms ‘the world is inherently good’ and ‘there is tremendous evil in the world.’ Creation is both good and not good with or without a divine origin. Mathematicians would view such a theological conclusion therefore as meaningless.*
The final difference in matters of faith concerns the fundamental axioms and their status in mathematics and religion. The difference here is somewhat surprising. Theology relies on fixed axioms from which it the derives its conclusions. These axioms are given the status of revealed truth and are the dogmatic focus of religious faith. Mathematicians since Godel on the other hand know that the fundamental axioms of their science are somewhat arbitrary. Euclid’s axioms of three dimensional space, for example, can be replaced by the n-dimensional space of Riemannian geometry with no loss of logical rigor. Euclid is not proven wrong but merely shown to be a special case of the more general conditions of Riemann.
This is an illustration as well of a crucial difference in method. Mathematics seeks to continuously extend the generality of its conclusions by discovering more and more inclusive axioms from which to work. Religious faith seeks to fix the axioms in order to preserve, limit and restrict doctrinal conclusions. Put another way: mathematics looks into the abyss of the Incompleteness Theorem and considers it an horizon to be striven toward painfully, incrementally, and with ho chance of complete success. This takes intellectual and, dare one say it, moral courage. The theologian looks into a similar abyss and considers that the horizon has arrived at his location. There is nothing to explore, nothing to find beyond the axioms which have been set by tradition. This sort of faith isn’t one of courage but stubbornness. It ramifies ‘conclusive’ conclusions because it takes its axioms for granted.
So the faith of the mathematician is not the faith of the religious believer. The faith required to attack the apparent intractability if the Goldbach Conjecture has nothing to do with the faith that proclaims One God or a religious ethic of forgiveness, or retribution, or community. The mathematician must have perseverance; the theologian merely persistence. The mathematician is concerned about expanding the world we know, the theologian with limiting what we know of the world. One requires genuine creative faith; the other futile insistence. Doxiadis quotes the 19th century mathematician, David Hilbert: “We must know, we shall know! In mathematics there is no ignorabimus!" Compare that with the commitment of religious faith by the first Christian theologian, Paul of Tarsus: “But if there be no resurrection of the dead, then is Christ not risen: and if Christ be not risen, then is our preaching vain, and your faith is also vain.”**
Both mathematicians and theologians tend to be obsessives. Both types are probably born not made. But mathematicians reach their intellectual peak in their relative youth. The best theologians are usually old men. I suspect the reason for this has to do with the paradoxical character of experiential wisdom. Young mathematicians have an intuitive grasp of reality unsullied by too much knowledge of what others call the world; while old theologians have been pickled in cultural history and traditions of thought that distort much of reality.
Uncle Petros himself tends to slide into quasi-theological reverie about mathematics in his dotage after suffering the slings and arrows of family as a failed mathematical prodigy, and especially after the publication of Godel’s Incompleteness Theorem. In a sense he has lost his faith in mathematics and replaced it with an entirely different kind of faithful resignation to cultural inevitability. This is why Petros loves chess: as in theology, its axioms are fixed, its rules invariably traditional.
It takes his nephew to help Uncle Petros understand that Godel freed mathematics from theological pretensions. There is no firm foundation for mathematics. Even David Hilbert thought there was but he was wrong; and so was Uncle Petros if he thought that firm intellectual foundations were necessary for his continuing commitment to mathematics. As Doxiadis has Alan Turing say, “Truth is not not always provable.” But this doesn’t invalidate mathematics or its method. Unlike theology, the commitment to mathematics is to an entirely unknown, and unnamed, future state of knowing. The content of that state is not, and cannot be, specified much less proven. Doxiadis compares it to being in love.
This is an important message from a young mathematician to an old one about a very different sort of tradition and a very different sort of faith, one that does away with “attainable goals.” And it is a message that makes Doxiadis’s little book a lot bigger than its size.
———————————————————————————————————-
*Neil Gaiman, in his American Gods captures the character of the reductio in theology rather well: “I believe in a personal god who cares about me and worries and oversees everything I do. I believe in an impersonal god who set the universe in motion and went off to hang with her girlfriends and doesn't even know that I'm alive. I believe in an empty and godless universe of causal chaos, background noise, and sheer blind luck.”
** For those who have forgotten their school Latin ‘ignorabimus’ is future tense: “we will be ignorant.” St. Paul, significantly, is concerned solely about the present but only in terms of the past in his exhortation.
March 9, 2021
Η εικασία του Γκόλντμπαχ:
«ΚΑΘΕ ΖΥΓΟΣ ΑΡΙΘΜΟΣ ΜΕΓΑΛΥΤΕΡΟΣ ΤΟΥ 2 ΜΠΟΡΕΙ ΝΑ ΕΚΦΡΑΣΤΕΙ ΩΣ ΑΘΡΟΙΣΜΑ ΔΥΟ ΠΡΩΤΩΝ»
Στο τέλος του καλοκαιριού του 1999, η εικασία συμπλήρωσε αισίως 250 χρόνια ύπαρξης. Και παραμένει ακόμη αναπόδεικτη.
«Ο θείος Πέτρος και η εικασία του Γκόλντμπαχ» είναι ένα ψυχογράφημα, μια βιογραφία του επιφανούς και αναγνωρισμένου απο τα μεγαλύτερα πανεπιστήμια του κόσμου μαθηματικού Πέτρου Παπαχρήστου.
Ο Α. Δοξιάδης σε αυτό το έργο του ταξιδεύει μέσα σε σελίδες γραπτών που αναγνωρίζονται ως είδος μαθηματικής λογοτεχνίας.
Εάν το σχολιάσω ως αμιγώς μαθηματικό δημιούργημα θα εκφράσω άποψη δυσαρέσκειας, αίσθηση μη αντιληπτικής ικανότητας και ανατριχιαστικές λέξεις που εκφράζουν τη φιλοσοφία των μαθηματικών που δεν κατάλαβα ποτέ και που μίσησα την ύπαρξη τους στα μαθητικά μου χρόνια παράλληλα με οργή και λύπη διότι πάντα καταφέρναν να με τρομοκρατούν και να με βουλιάζουν μέσα σε έναν βάλτο με βούρκους ατέλειωτους απο αξιώματα, θεωρήματα και επαγωγικές αποδείξεις.
Τα μαθηματικά και τα παρακλάδια τους υπήρξαν πάντα τα στοιχειά της πνευματικής μου ενάργειας, αυτά που με έκαναν πάντα να αισθάνομαι ηλίθια, άχρηστη, ανίκανη να κατανοήσω τουλάχιστον το προφανές αυτής της ψηφιακής και αναλογικής γλώσσας που είναι σπουδαία και απαραίτητη για την περαιτέρω εξέλιξη αναφορικά με τις θετικές επιστήμες και τα επιστημονικά επιτεύγματα.
Που την έχουν κατά κάποιο ειδικό και γενικό κανόνα κοινής αποδοχής ανάγει στο πάνθεον της επεξεργασμένης και ταλαντούχας ιδιοφυΐας των μελών της απανταχού μαθηματικής εταιρίας όπου τα θαύματα θεωρούνται αληθινά και αποδεδειγμένα ακόμα κι όταν αυτοαναιρούνται ως ψεύδη τα στοιχεία τους και το περιεχόμενο τους.
Ωστόσο αν «Ο Θείος Πέτρος και η εικασία του Γκόλντμπαχ», βοήθησε να ξεκινήσει η «μαθηματική φαντασία» σαν είδος λογοτεχνίας όπως αναφέρεται ρητά και έμεσα απο διάφορες πηγές σε σχέση με την καταξίωση του συγγραφέα σε πολύ νεαρή ηλικία,
Ο κοινότοπος και οικείος παράλληλα ανιστορηματικός τρόπος προσέγγισης της πραγματικότητας είναι αρχαίος και κατά το πλείστον αλαζονικός και παράφρων όσο και ο ασυνήθιστα προικισμένος με ευφυΐα και ακατανόητη διάνοια άνθρωπος.
Αντίθετα, η αποδεικτική λογική διαδικασία είναι αμιγώς Ελληνική ( τώρα αισθάνομαι πιο τούβλο, γιατί να
μην ήταν αλαμπουρνέζικη άρα ακαταλαβίστικη απο τους κοινούς λογικούς θνητούς, απο τις χρυσές μετριότ��τες, οπου κάπου εκεί, κι εγώ ανάμεσα τους θα αδιαφορούσα για μια επιστήμη της κατωτάτης αλαμπουρνέζικης υποστάθμης) έχει συγκεκριμένη ημερομηνία και τόπο γέννησης: πριν δυόμιση χιλιάδες χρόνια, στην πόλη που ζούμε, την Αθήνα.( Ποιος είπε πως η ζωή είναι δίκαιη)
Η παραδοσιακή άποψη βλέπει τους δύο τρόπους ως εντελώς διαφορετικούς, συχνά εκ διαμέτρου αντίθετους. Αλλά νεότερες απόψεις σχετικά με τη φιλοσοφική λίθο των μαθηματικών και συζητήσεις που τοποθετούν και τις αλχημιστικές τελετουργίες με προθρησκευτικά δρώμενα που αντιτίθενται στην ελληνική μαθηματική παιδεία
( οι πρώτοι αριθμοί είναι άπειροι, όπως απέδειξε ο Ευκλείδης τον
3 π. Χ αιώνα )και τους δύο μέσα σε ένα ενιαίο μοντέλο, όπου κυριαρχεί η αφήγηση.
Και, χρησιμοποιώντας την εις άτοπον απαγωγή, υποθέτει αρχικά το αντίθετο απο αυτό που θέλει να αποδείξει, δλδ πως οι πρώτοι αριθμοί είναι πεπερασμένοι, το οποίο αντιφάσκει με την αρχική μας υπόθεση. Η παραδοχή του πεπερασμένου τους μας οδηγεί σε αντίφαση. Άρα οι πρώτοι αριθμοί είναι άπειροι.
Όπερ έδει δείξαι. Με απλά επεξηγηματικά λόγια παρουσιάζονται οι αποδείξεις του σοφού μας προγόνου. ( Εδώ μου δίνει την χαριστική βολή).
Με δύο διαφορετικές προσεγγίσεις, από τη λογοτεχνία και τα μαθηματικά, παρουσιάζονται οι αιτίες και η μορφή αυτής της συγγένειας.
Αυτά και αλλά πολλά γράφτηκαν μέσα σε αυτό το μαθηματικό λογοτέχνημα μα εγώ θέλησα να επικεντρώσω αποκλειστικά και μόνο στην βιοθεωρία και την βιοψυχολογία ενός ανθρώπου που χαρακτηρίστηκε μαθηματική διάνοια και χαράμισε όλη του τη ζωή στην απόδειξη του αναπόδεικτου. Ή στην μη παραδοχή του πως μέχρι την τελευταία ανάσα που πήρε ως ζωντανός δεν ήταν η εικασία του μη επαληθεύσιμη ή κάποια διαδικαστικό πλαίσιο μέσα στο οποίο η φαινομενική απουσία οποιασδήποτε εξακριβωμένης αρχής που να ορίζει την ακολουθία των πρώτων αριθμών έχει στοιχειώσει τους μαθηματικούς επι αιώνες και ευθύνεται σε μεγάλο βαθμό για τη μαγεία της Θεωρίας των Αριθμών.
Λαβυρινθώδεις σκέψεις και πορίσματα που οδηγούν στην παράνοια όποιον αφιερωθεί ψυχή τε και σώματι σε αυτό το μυστήριο αντάξιο της υψηλότερης διάνοιας.
Προσωπικά θεωρώ πως τα μαθηματικά έχουν τα προβλήματα τους και τις λύσεις τους - στο πλαίσιο του εφικτού - απο κει και μετά παγώνει κάθε υπόνοια φαντασίας και ονείρου λογοτεχνικής δημιουργικότητας, εφόσον το ερώτημα που τίθεται και η λύση του - με όσες διαφορετικές προσεγγίσεις κι αν βρεθεί- δεν αλλάζουν ποτέ.
Καλέ μου θείε Πέτρο συγχαρητήρια, Αποτύχατε.
Δεν ζήσατε, μοναχά πεθάνατε. Λυπηρό και θλιβερό.
Ευχαρίστως ναι, αλλά απο εμένα είναι όχι.
1️⃣2️⃣3️⃣4️⃣5️⃣6️⃣7️⃣8️⃣9️⃣🔟➕➗➖✖️〰️➰➿
Καλή ανάγνωση.
Πολλούς και σεμνούς ασπασμούς.
«ΚΑΘΕ ΖΥΓΟΣ ΑΡΙΘΜΟΣ ΜΕΓΑΛΥΤΕΡΟΣ ΤΟΥ 2 ΜΠΟΡΕΙ ΝΑ ΕΚΦΡΑΣΤΕΙ ΩΣ ΑΘΡΟΙΣΜΑ ΔΥΟ ΠΡΩΤΩΝ»
Στο τέλος του καλοκαιριού του 1999, η εικασία συμπλήρωσε αισίως 250 χρόνια ύπαρξης. Και παραμένει ακόμη αναπόδεικτη.
«Ο θείος Πέτρος και η εικασία του Γκόλντμπαχ» είναι ένα ψυχογράφημα, μια βιογραφία του επιφανούς και αναγνωρισμένου απο τα μεγαλύτερα πανεπιστήμια του κόσμου μαθηματικού Πέτρου Παπαχρήστου.
Ο Α. Δοξιάδης σε αυτό το έργο του ταξιδεύει μέσα σε σελίδες γραπτών που αναγνωρίζονται ως είδος μαθηματικής λογοτεχνίας.
Εάν το σχολιάσω ως αμιγώς μαθηματικό δημιούργημα θα εκφράσω άποψη δυσαρέσκειας, αίσθηση μη αντιληπτικής ικανότητας και ανατριχιαστικές λέξεις που εκφράζουν τη φιλοσοφία των μαθηματικών που δεν κατάλαβα ποτέ και που μίσησα την ύπαρξη τους στα μαθητικά μου χρόνια παράλληλα με οργή και λύπη διότι πάντα καταφέρναν να με τρομοκρατούν και να με βουλιάζουν μέσα σε έναν βάλτο με βούρκους ατέλειωτους απο αξιώματα, θεωρήματα και επαγωγικές αποδείξεις.
Τα μαθηματικά και τα παρακλάδια τους υπήρξαν πάντα τα στοιχειά της πνευματικής μου ενάργειας, αυτά που με έκαναν πάντα να αισθάνομαι ηλίθια, άχρηστη, ανίκανη να κατανοήσω τουλάχιστον το προφανές αυτής της ψηφιακής και αναλογικής γλώσσας που είναι σπουδαία και απαραίτητη για την περαιτέρω εξέλιξη αναφορικά με τις θετικές επιστήμες και τα επιστημονικά επιτεύγματα.
Που την έχουν κατά κάποιο ειδικό και γενικό κανόνα κοινής αποδοχής ανάγει στο πάνθεον της επεξεργασμένης και ταλαντούχας ιδιοφυΐας των μελών της απανταχού μαθηματικής εταιρίας όπου τα θαύματα θεωρούνται αληθινά και αποδεδειγμένα ακόμα κι όταν αυτοαναιρούνται ως ψεύδη τα στοιχεία τους και το περιεχόμενο τους.
Ωστόσο αν «Ο Θείος Πέτρος και η εικασία του Γκόλντμπαχ», βοήθησε να ξεκινήσει η «μαθηματική φαντασία» σαν είδος λογοτεχνίας όπως αναφέρεται ρητά και έμεσα απο διάφορες πηγές σε σχέση με την καταξίωση του συγγραφέα σε πολύ νεαρή ηλικία,
Ο κοινότοπος και οικείος παράλληλα ανιστορηματικός τρόπος προσέγγισης της πραγματικότητας είναι αρχαίος και κατά το πλείστον αλαζονικός και παράφρων όσο και ο ασυνήθιστα προικισμένος με ευφυΐα και ακατανόητη διάνοια άνθρωπος.
Αντίθετα, η αποδεικτική λογική διαδικασία είναι αμιγώς Ελληνική ( τώρα αισθάνομαι πιο τούβλο, γιατί να
μην ήταν αλαμπουρνέζικη άρα ακαταλαβίστικη απο τους κοινούς λογικούς θνητούς, απο τις χρυσές μετριότ��τες, οπου κάπου εκεί, κι εγώ ανάμεσα τους θα αδιαφορούσα για μια επιστήμη της κατωτάτης αλαμπουρνέζικης υποστάθμης) έχει συγκεκριμένη ημερομηνία και τόπο γέννησης: πριν δυόμιση χιλιάδες χρόνια, στην πόλη που ζούμε, την Αθήνα.( Ποιος είπε πως η ζωή είναι δίκαιη)
Η παραδοσιακή άποψη βλέπει τους δύο τρόπους ως εντελώς διαφορετικούς, συχνά εκ διαμέτρου αντίθετους. Αλλά νεότερες απόψεις σχετικά με τη φιλοσοφική λίθο των μαθηματικών και συζητήσεις που τοποθετούν και τις αλχημιστικές τελετουργίες με προθρησκευτικά δρώμενα που αντιτίθενται στην ελληνική μαθηματική παιδεία
( οι πρώτοι αριθμοί είναι άπειροι, όπως απέδειξε ο Ευκλείδης τον
3 π. Χ αιώνα )και τους δύο μέσα σε ένα ενιαίο μοντέλο, όπου κυριαρχεί η αφήγηση.
Και, χρησιμοποιώντας την εις άτοπον απαγωγή, υποθέτει αρχικά το αντίθετο απο αυτό που θέλει να αποδείξει, δλδ πως οι πρώτοι αριθμοί είναι πεπερασμένοι, το οποίο αντιφάσκει με την αρχική μας υπόθεση. Η παραδοχή του πεπερασμένου τους μας οδηγεί σε αντίφαση. Άρα οι πρώτοι αριθμοί είναι άπειροι.
Όπερ έδει δείξαι. Με απλά επεξηγηματικά λόγια παρουσιάζονται οι αποδείξεις του σοφού μας προγόνου. ( Εδώ μου δίνει την χαριστική βολή).
Με δύο διαφορετικές προσεγγίσεις, από τη λογοτεχνία και τα μαθηματικά, παρουσιάζονται οι αιτίες και η μορφή αυτής της συγγένειας.
Αυτά και αλλά πολλά γράφτηκαν μέσα σε αυτό το μαθηματικό λογοτέχνημα μα εγώ θέλησα να επικεντρώσω αποκλειστικά και μόνο στην βιοθεωρία και την βιοψυχολογία ενός ανθρώπου που χαρακτηρίστηκε μαθηματική διάνοια και χαράμισε όλη του τη ζωή στην απόδειξη του αναπόδεικτου. Ή στην μη παραδοχή του πως μέχρι την τελευταία ανάσα που πήρε ως ζωντανός δεν ήταν η εικασία του μη επαληθεύσιμη ή κάποια διαδικαστικό πλαίσιο μέσα στο οποίο η φαινομενική απουσία οποιασδήποτε εξακριβωμένης αρχής που να ορίζει την ακολουθία των πρώτων αριθμών έχει στοιχειώσει τους μαθηματικούς επι αιώνες και ευθύνεται σε μεγάλο βαθμό για τη μαγεία της Θεωρίας των Αριθμών.
Λαβυρινθώδεις σκέψεις και πορίσματα που οδηγούν στην παράνοια όποιον αφιερωθεί ψυχή τε και σώματι σε αυτό το μυστήριο αντάξιο της υψηλότερης διάνοιας.
Προσωπικά θεωρώ πως τα μαθηματικά έχουν τα προβλήματα τους και τις λύσεις τους - στο πλαίσιο του εφικτού - απο κει και μετά παγώνει κάθε υπόνοια φαντασίας και ονείρου λογοτεχνικής δημιουργικότητας, εφόσον το ερώτημα που τίθεται και η λύση του - με όσες διαφορετικές προσεγγίσεις κι αν βρεθεί- δεν αλλάζουν ποτέ.
Καλέ μου θείε Πέτρο συγχαρητήρια, Αποτύχατε.
Δεν ζήσατε, μοναχά πεθάνατε. Λυπηρό και θλιβερό.
Ευχαρίστως ναι, αλλά απο εμένα είναι όχι.
1️⃣2️⃣3️⃣4️⃣5️⃣6️⃣7️⃣8️⃣9️⃣🔟➕➗➖✖️〰️➰➿
Καλή ανάγνωση.
Πολλούς και σεμνούς ασπασμούς.
September 15, 2025
It seems at least, that every integer greater than 2 can be written as the sum of three primes.
Goldbach, in a letter to Euler, 7/06/1742
That ... every even integer is a sum of two primes, I regard as a completely certain theorem, although I cannot prove it.
Euler, in a letter to Goldbach, 30/06/1742
I absolutely loved this short novel written by a Greek mathematician, turned director, turned writer. As the story developed, Goldbach's conjecture, one of the most famous unsolved mathematical problems, became an epitome of talent and hubris, obsession and insanity, life and death.
Especially recommended to those who ever experienced a mathematically-induced thrill (for example, while learning about fascinating number properties and elegant mathematical proves, or while solving an interesting mathematical problem). On the other hand, if you think an interesting mathematical problem is an oxymoron, beware: in your case, this novel comes with no warranty.
Goldbach partitions of the even integers from 4 to 28. (Image credit: Adam Cunningham and John Ringland, CC BY-SA 3.0 , via Wikimedia Commons)
P.S. This novel was first published in 1992. I've just read a bit on Goldbach's Conjecture all over again and saw that the so called Goldbach's weak conjecture (every odd number greater than 5 can be expressed as the sum of three primes) was proved in 2013 by Harald Helfgott. The proof combines previous computations for smaller numbers (computing all the way up to huge numbers, actually) and Helfgott's general analytical proof for sufficiently large numbers.
The strong Goldbach Conjecture, in the meantime, has been verified up to 10 to the 18th. There's still a name for this number, by the way -- quintillion. Also, a sugar cube contains about 10 to the 23rd power of molecules. On the other hand, according to ChatGpt's estimation, the amount of beans (uncle Petros's mathematical visualization device) on Earth is only about 10 to the 13th-14th power. Even with soybeans, lentils, chickpeas, peas, and other pulses, there are only a few quadrillion (10¹⁵) beans/pulses on Earth at any given time. Anyway, beans or no beans, it might take a while to prove Goldbach Conjecture yet, but somehow the enterprise looks less hopeless now.;)
Goldbach, in a letter to Euler, 7/06/1742
That ... every even integer is a sum of two primes, I regard as a completely certain theorem, although I cannot prove it.
Euler, in a letter to Goldbach, 30/06/1742
I absolutely loved this short novel written by a Greek mathematician, turned director, turned writer. As the story developed, Goldbach's conjecture, one of the most famous unsolved mathematical problems, became an epitome of talent and hubris, obsession and insanity, life and death.
Especially recommended to those who ever experienced a mathematically-induced thrill (for example, while learning about fascinating number properties and elegant mathematical proves, or while solving an interesting mathematical problem). On the other hand, if you think an interesting mathematical problem is an oxymoron, beware: in your case, this novel comes with no warranty.
Goldbach partitions of the even integers from 4 to 28. (Image credit: Adam Cunningham and John Ringland, CC BY-SA 3.0 , via Wikimedia Commons)
P.S. This novel was first published in 1992. I've just read a bit on Goldbach's Conjecture all over again and saw that the so called Goldbach's weak conjecture (every odd number greater than 5 can be expressed as the sum of three primes) was proved in 2013 by Harald Helfgott. The proof combines previous computations for smaller numbers (computing all the way up to huge numbers, actually) and Helfgott's general analytical proof for sufficiently large numbers.
The strong Goldbach Conjecture, in the meantime, has been verified up to 10 to the 18th. There's still a name for this number, by the way -- quintillion. Also, a sugar cube contains about 10 to the 23rd power of molecules. On the other hand, according to ChatGpt's estimation, the amount of beans (uncle Petros's mathematical visualization device) on Earth is only about 10 to the 13th-14th power. Even with soybeans, lentils, chickpeas, peas, and other pulses, there are only a few quadrillion (10¹⁵) beans/pulses on Earth at any given time. Anyway, beans or no beans, it might take a while to prove Goldbach Conjecture yet, but somehow the enterprise looks less hopeless now.;)
March 18, 2018
Εξαιρετικό βιβλίο!
Ένα υπέροχο παραμύθι που σε ταξιδεύει στον παράξενο κόσμο των μαθηματικών. Ο Δοξιάδης γράφει απλά, δεν χρησιμοποιεί βαρύγδουπες εκφράσεις και άλλα μέσα εντυπωσιασμού, καταφέρνει όμως να σε μυήσει στη μαγεία ενός άλλου κόσμου, ο οποίος φαντάζει τόσο ξένος (και πιο ενδιαφέρον) από τη μονοδιάστατη καθημερινότητα που βιώνουμε και αντιλαμβανόμαστε.
Και, μολονότι η ιστορία καταπιάνεται με ένα από τα πιο δημοφιλή άλυτα προβλήματα των μαθηματικών, σε κανένα σημείο δεν κουράζει με τις σχετικές μαθηματικές αναφορές σε όρους και πράξεις, ούτε μειώνει στο ελάχιστο το ενδιαφέρον του αναγνώστη.
Πραγματικά, ένα 'must read' βιβλίο για όλους!!! (9/10)
Ένα υπέροχο παραμύθι που σε ταξιδεύει στον παράξενο κόσμο των μαθηματικών. Ο Δοξιάδης γράφει απλά, δεν χρησιμοποιεί βαρύγδουπες εκφράσεις και άλλα μέσα εντυπωσιασμού, καταφέρνει όμως να σε μυήσει στη μαγεία ενός άλλου κόσμου, ο οποίος φαντάζει τόσο ξένος (και πιο ενδιαφέρον) από τη μονοδιάστατη καθημερινότητα που βιώνουμε και αντιλαμβανόμαστε.
Και, μολονότι η ιστορία καταπιάνεται με ένα από τα πιο δημοφιλή άλυτα προβλήματα των μαθηματικών, σε κανένα σημείο δεν κουράζει με τις σχετικές μαθηματικές αναφορές σε όρους και πράξεις, ούτε μειώνει στο ελάχιστο το ενδιαφέρον του αναγνώστη.
Πραγματικά, ένα 'must read' βιβλίο για όλους!!! (9/10)
February 8, 2017
Εξαιρετικό βιβλίο για τα μαθηματικά από τον Απόστολο Δοξιάδη, ο οποίος - μεταξύ άλλων - είναι ένας περήφανος μαθηματικός. Η γραφή του είναι απλή και ουσιώδης, με αποτέλεσμα το βιβλίο να είναι προσιτό σε όλους (θυμάμαι το είχα διαβάσει μαθήτρια ακόμα). Ο αφηγητής είναι ένας νεαρός μαθητής που προσπαθεί να μάθει περισσότερα στοιχεία για τον παράξενο θείο Πέτρο, το μαύρο πρόβατο της οικογένειας, που οι υπόλοιποι πάντα θεωρούσαν ότι βρισκόταν σε έναν δικό του κόσμο.
Πράγματι, ο θείος Πέτρος βρισκόταν βυθισμένος στον κόσμο των μαθηματικών, προσπαθώντας να αποδείξει την εικασία του Γκόλντμπαχ (ένας θρυλικός γρίφος, δεν έχει σημασία τι λέει), το οποίο είχε γίνει αυτοσκοπός της ζωής του. Με τη σχέση που αναπτύσσεται ανάμεσα σε θείο και ανηψιό, ο αναγνώστης ταξιδεύει με μέσο τα μαθηματικά σε πολλές ωραίες εποχές και ακούει ενδιαφέρουσες ιστορίες. Δεν χρειάζεται να ξέρετε μαθηματικά, το ύφος δεν είναι επιτηδευμένο, χαλαρώστε και απολαύστε το! Εξάλλου, όλοι είδατε το "Ένας υπέροχος άνθρωπος" και ας μην καταλάβατε τη Θεωρία Παιγνίων (εκτός κι αν την καταλάβατε από το Γιάνη, οπότε να την πείτε και σε μένα!!!!!)
Πράγματι, ο θείος Πέτρος βρισκόταν βυθισμένος στον κόσμο των μαθηματικών, προσπαθώντας να αποδείξει την εικασία του Γκόλντμπαχ (ένας θρυλικός γρίφος, δεν έχει σημασία τι λέει), το οποίο είχε γίνει αυτοσκοπός της ζωής του. Με τη σχέση που αναπτύσσεται ανάμεσα σε θείο και ανηψιό, ο αναγνώστης ταξιδεύει με μέσο τα μαθηματικά σε πολλές ωραίες εποχές και ακούει ενδιαφέρουσες ιστορίες. Δεν χρειάζεται να ξέρετε μαθηματικά, το ύφος δεν είναι επιτηδευμένο, χαλαρώστε και απολαύστε το! Εξάλλου, όλοι είδατε το "Ένας υπέροχος άνθρωπος" και ας μην καταλάβατε τη Θεωρία Παιγνίων (εκτός κι αν την καταλάβατε από το Γιάνη, οπότε να την πείτε και σε μένα!!!!!)
July 12, 2020
Ένα υπέροχο νεανικό βιβλιο που με έβγαλε από αναγνωστικό μπλοκάρισμα. Γραφή απλή και κατανοητή. Δεν είχα ξαναδιαβάσει Δοξιάδη. Εξαιρετικός.
September 10, 2019
This is more of a short story than a novel. On the surface it is about the fictional mathematical prodigy Petros Papachristos. His life goal has been to prove one of the oldest unsolved problems of number theory, Goldbach's Conjecture. This states that every even integer greater than two is the sum of two primes. Petros’ nephew tells the story.
First of all, mathematical axioms, theories and proofs do take up a significant portion of the text. For me, much of the mathematical reasoning went in one ear and immediately out the other. Nevertheless, you need not master the theoretical mathematical reasoning to grasp the intent of the tale. Real life, historically famed mathematicians, such as G.H. Hardy, J.E. Littlewood, Srinivasa Ramanujan, Kurt Gödel and Alan Turing, play pivotal roles in the plot.
In my view there is more to the story than just mathematics. The central focus is instead how individuals set their life goals. Should goals be obtainable? How does one cope with lack of success when goals are not attained? To what extent do we need goals to go on living? Is it pure craziness to stretch toward a dream that may be unobtainable? I personally do not think so.
Part of the tale is told rather than actively lived and experienced alongside the characters. This is when the nephew as a middle-aged man looks back on his own life and relates what he has learned about his paternal uncle. The story picks up again when the nephew confronts his uncle, demanding that they discuss their shared past and the reasons behind his uncle’s actions. It is here one gets to the message the tale is meant to convey.
Keith Szarabajka narrates the audiobook very, very well. The characters’ feelings are well portrayed. Different accents are employed. The narration is clear and easy to follow.
I have given both the audiobook narration and the written text four stars, despite the rather tiring mathematical details of the story. I like very much what the story says.
First of all, mathematical axioms, theories and proofs do take up a significant portion of the text. For me, much of the mathematical reasoning went in one ear and immediately out the other. Nevertheless, you need not master the theoretical mathematical reasoning to grasp the intent of the tale. Real life, historically famed mathematicians, such as G.H. Hardy, J.E. Littlewood, Srinivasa Ramanujan, Kurt Gödel and Alan Turing, play pivotal roles in the plot.
In my view there is more to the story than just mathematics. The central focus is instead how individuals set their life goals. Should goals be obtainable? How does one cope with lack of success when goals are not attained? To what extent do we need goals to go on living? Is it pure craziness to stretch toward a dream that may be unobtainable? I personally do not think so.
Part of the tale is told rather than actively lived and experienced alongside the characters. This is when the nephew as a middle-aged man looks back on his own life and relates what he has learned about his paternal uncle. The story picks up again when the nephew confronts his uncle, demanding that they discuss their shared past and the reasons behind his uncle’s actions. It is here one gets to the message the tale is meant to convey.
Keith Szarabajka narrates the audiobook very, very well. The characters’ feelings are well portrayed. Different accents are employed. The narration is clear and easy to follow.
I have given both the audiobook narration and the written text four stars, despite the rather tiring mathematical details of the story. I like very much what the story says.
June 27, 2018
Δεν ξέρω αν το βιβλίο θεωρείται νεανικό (;) ή τι ακριβώς υποτίθεται πως έπρεπε να είναι: Στην Ελλάδα πέρασε απαρατήρητο, δεν είχα (και μάλλον δεν έχω – ακόμα) ιδέα ποιος ακριβώς είναι ο Δοξιάδης, φαίνεται πως οι παλιοί και ψαγμένοι βιβλιοπώλες τον ξέρουν καλά, τόσο που μάλλον χαίρονται όταν κάποιος αναζητεί τα βιβλία του, (Δοξιάδη! Βέβαια! Μου είπαν στο Μοναστηράκι τις προάλλες με τρελή χαρά) κάποιοι βιάστηκαν να τον θάψουν, ειδικά όταν στο εξωτερικό το συγκεκριμένο βιβλίο αγκαλιάστηκε θερμά, μεταφράστηκε ξανά και ξανά, έγραψαν γι αυτό από τον Στάινερ (!!) μέχρι τον Όλιβερ Σακς (!) κι όμως εδώ βρήκε σε τοίχο.
Αν και πρόκειται για 290 τίγκα στα μαθηματικά σελίδες, διαβάζεται άνετα από ενήλικες έως και παιδιά δημοτικού. Μπορεί να διαβαστεί ευχάριστα από έναν αναγνώστη χωρίς ιδιαίτερη κλίση/λόξα/γνώσεις στα μαθηματικά σε λίγες ώρες (όπως εγώ), μπορεί να προσφέρει υλικό για να ασχοληθεί ο πιο πωρωμένος για μήνες ολόκληρους.
Παρά τις χαριτωμένες αδεξιότητες ενίοτε στην αφήγηση και παρά το ότι μάλλον δεν έχει κάποια λογική εξήγηση αυτό που θα πω ούτε και μπορώ να το αιτιολογήσω με κάτι περισσότερο από το τι εξέλαβα κατά τη διάρκεια της ανάγνωσης και ειδικότερα όσο το βιβλίο πλησίαζε προς το τέλος (πόσο ατυχές για ένα βιβλίο μαθηματικών να λες κάτι «θεωρητικά» και χωρίς απόδειξη :D ) ο συγγραφέας πρέπει να είναι ένας γλυκύτατος άνθρωπος.
Οπωσδήποτε θα διαβάσω περισσότερο Δοξιάδη.
Αν και πρόκειται για 290 τίγκα στα μαθηματικά σελίδες, διαβάζεται άνετα από ενήλικες έως και παιδιά δημοτικού. Μπορεί να διαβαστεί ευχάριστα από έναν αναγνώστη χωρίς ιδιαίτερη κλίση/λόξα/γνώσεις στα μαθηματικά σε λίγες ώρες (όπως εγώ), μπορεί να προσφέρει υλικό για να ασχοληθεί ο πιο πωρωμένος για μήνες ολόκληρους.
Παρά τις χαριτωμένες αδεξιότητες ενίοτε στην αφήγηση και παρά το ότι μάλλον δεν έχει κάποια λογική εξήγηση αυτό που θα πω ούτε και μπορώ να το αιτιολογήσω με κάτι περισσότερο από το τι εξέλαβα κατά τη διάρκεια της ανάγνωσης και ειδικότερα όσο το βιβλίο πλησίαζε προς το τέλος (πόσο ατυχές για ένα βιβλίο μαθηματικών να λες κάτι «θεωρητικά» και χωρίς απόδειξη :D ) ο συγγραφέας πρέπει να είναι ένας γλυκύτατος άνθρωπος.
Οπωσδήποτε θα διαβάσω περισσότερο Δοξιάδη.
August 16, 2017
Posseduto dalla passione
Ebbene sì. ... si può essere posseduti anche dalla passione... per la matematica.
Il breve romanzo parla della vita di Petros, brillante e giovane mente, che decide di dedicare la sua vita ad una causa incomprensibile ai più, la risoluzione di un difficilissimo problema matematico: la congettura di Goldbach.
Non importa quanto sia ardua l'impresa, confidente nelle proprie capacità e disposto ad una dedizione totale alla causa, si chiude nel suo studio sicuro del proprio successo.
“L’ampliamento di verità e di bellezza che si rivela con la comprensione di un teorema importante non è raggiungibile attraverso nessuna altra esperienza umana, se non forse con il misticismo religioso”
Petros, dedito alla ricerca, un po' come Alan Turing del recente Imitation Game, non vive più nella realtà, ma pensa solo ad arrivare all'agognato risultato...
“La solitudine del ricercatore che si dedica a una matematica originale non assomiglia a nessun altra. Egli “vive” in un universo del tutto inaccessibile sia al grande pubblico che all’universo che lo circonda”
Visto come un fallito dai fratelli, perché perso in un obbiettivo di difficile realizzazione, Petros spende in realtà la sua esistenza dedicandola alla propria passione.
Ma come è giusto procedere nella vita? Bisogna solo darsi obbiettivi raggiungibili e mediocri per essere felici? Non è forse più corretto non giudicare e pensare che ogni persona debba essere libera di porsi gli obbiettivi che crede, anche smisuratamente ambiziosi, libera di esporsi al fallimento o alla delusione nel caso alla fine non riesca a raggiungerli?
“Ogni persona ha il diritto di esporsi a tutte le delusioni che si è scelta”
Un romanzo che è un invito a non isolarsi, ad essere sempre umili, ad affrontare la vita senza certezze.
Il racconto ha inoltre il pregio di introdurre in maniera abbastanza semplice e divulgativa il mondo della ricerca matematica, sfatando il mito che fare matematica sia fare di conto.
3,5*
May 1, 2019
Δυσκολα μαθηματικα για μενα που εχω τοοοοσο καιρο να ερθω σε επαφη με αυτα. Παρολα αυτα ηταν πολυ ενδιαφερουσα ιστορια . Ο θειος Πετρος ηταν Φιλος με πολλους κοινους γνωστους και το απολαυσα
August 7, 2017
"Le forme create dal matematico, come quelle create dal pittore o dal poeta, devono essere belle; le idee, come i colori o le parole, devono legarsi armoniosamente. La bellezza è il requisito fondamentale: al mondo non c'è un posto perenne per la matematica brutta."
Ecco di cosa parla il libro: del fascino della matematica, intesa come disciplina che deve soddisfare criteri estetici, creativi ed artistici. La matematica come arte, in quanto richiede creatività, deve generare prodotti necessariamente belli e trasmettere messaggi, ovviamente a chi è in grado di coglierli (qualcuno sarà svenuto dopo questa affermazione.... I saliii portate i saliiii).
Il romanzo racconta la vita di Petros, un fallito secondo i suoi famigliari, che dedica la propria vita alla matematica, con un amore per essa che diventa ossessione e che lo porta alla distruzione fisica e psicologica, perché perso nella ricerca della dimostrazione della cosiddetta "Congettura di Goldbach". La congettura, secondo la quale ogni numero pari maggiore di due sarebbe la somma di due numeri primi, fu formulata per la prima volta dal matematico russo Goldbach, ma mai dimostrata da nessuno. La dimostrazione della congettura è uno dei tre maggiori problemi irrisolti della matematica e circola nientepopodimeno che dall'epoca di Eulero e Leibniz.
I numeri primi sono quei numeri che possono essere divisi solo per sé stessi e per uno, definiti da qualcuno "gli atomi della matematica". La loro successione sembra caotica e casuale, ma se osservata con maggiore attenzione diventa quasi "magica e misteriosa".
Ma perché Petros vuole risolvere la congettura, compromettendo la sua vita personale, rinunciando all'amore e ad una vita di relazione? Semplice. Per diventare immortale, per poter essere ricordato nel tempo. Per un matematico la mediocrità non serve a nulla, bisogna essere esageratamente bravi. Per esempio, risolvere per primi un problema importante, anzi no, importantissimo; come la dimostrazione della congettura.
"Archimede sarà ricordato quando Eschilo sarà dimenticato, perché le lingue muoiono ma le idee matematiche no. Immortalità è forse una parola ingenua ma, qualunque cosa significhi, un matematico ha le migliori probabilità di conseguirla."
Petros dedica vent’anni al tentativo di risoluzione della congettura. In questo periodo non fa altro che studiarla e sognarla, ossessionato dal tempo che passa, perché la mente di un matematico è fertile e produttiva solo quando è in giovane età.
"Nessun matematico può permettersi di dimenticare che la matematica, più di qualsiasi altra arte o di qualsiasi altra scienza, è un'attività per giovani" diceva Harold Hardy.
Lui crede fermamente nel fatto che se la congettura è vera, allora esiste una dimostrazione disponibile al primo che la trova. si ispira cioè a ciò che diceva il grande matematico David Hilbert nel 1900: "Noi dobbiamo sapere, noi sapremo".
Ma ad un certo punto.... arriva un ometto strano, ipocondriaco, magrissimo, con gli occhiali, un austriaco chiamato Godel. Che gli fa crollare il mondo addosso, perché dimostra..... che non è detto che debba esistere una dimostrazione, ossia che la congettura potrebbe essere anche indimostrabile. La vita di Petros improvvisamente perde di senso. E... si arrende.
Molto interessante il romanzo, che mescola personaggi inventati (Petros) con persone famose realmente esistite, quali Hardy, Littlewood, Ramanujan, Godel e Turing e che riesce ad appassionare anche chi non sa nulla di matematica. Il libro porta a chiedersi cosa sia la matematica e perché l'uomo ne sia così affascinato. E ci fa capire che l'uomo non deve limitarsi a cercare di raggiungere solo obiettivi raggiungibili, ma deve osare. Solo così è possibile il progresso; senza lo sforzo immane di persone che spendono la propria vita dietro obiettivi sulla carta impossibili, la maggior parte delle scoperte scientifiche non ci sarebbero state.
Ecco di cosa parla il libro: del fascino della matematica, intesa come disciplina che deve soddisfare criteri estetici, creativi ed artistici. La matematica come arte, in quanto richiede creatività, deve generare prodotti necessariamente belli e trasmettere messaggi, ovviamente a chi è in grado di coglierli (qualcuno sarà svenuto dopo questa affermazione.... I saliii portate i saliiii).
Il romanzo racconta la vita di Petros, un fallito secondo i suoi famigliari, che dedica la propria vita alla matematica, con un amore per essa che diventa ossessione e che lo porta alla distruzione fisica e psicologica, perché perso nella ricerca della dimostrazione della cosiddetta "Congettura di Goldbach". La congettura, secondo la quale ogni numero pari maggiore di due sarebbe la somma di due numeri primi, fu formulata per la prima volta dal matematico russo Goldbach, ma mai dimostrata da nessuno. La dimostrazione della congettura è uno dei tre maggiori problemi irrisolti della matematica e circola nientepopodimeno che dall'epoca di Eulero e Leibniz.
I numeri primi sono quei numeri che possono essere divisi solo per sé stessi e per uno, definiti da qualcuno "gli atomi della matematica". La loro successione sembra caotica e casuale, ma se osservata con maggiore attenzione diventa quasi "magica e misteriosa".
Ma perché Petros vuole risolvere la congettura, compromettendo la sua vita personale, rinunciando all'amore e ad una vita di relazione? Semplice. Per diventare immortale, per poter essere ricordato nel tempo. Per un matematico la mediocrità non serve a nulla, bisogna essere esageratamente bravi. Per esempio, risolvere per primi un problema importante, anzi no, importantissimo; come la dimostrazione della congettura.
"Archimede sarà ricordato quando Eschilo sarà dimenticato, perché le lingue muoiono ma le idee matematiche no. Immortalità è forse una parola ingenua ma, qualunque cosa significhi, un matematico ha le migliori probabilità di conseguirla."
Petros dedica vent’anni al tentativo di risoluzione della congettura. In questo periodo non fa altro che studiarla e sognarla, ossessionato dal tempo che passa, perché la mente di un matematico è fertile e produttiva solo quando è in giovane età.
"Nessun matematico può permettersi di dimenticare che la matematica, più di qualsiasi altra arte o di qualsiasi altra scienza, è un'attività per giovani" diceva Harold Hardy.
Lui crede fermamente nel fatto che se la congettura è vera, allora esiste una dimostrazione disponibile al primo che la trova. si ispira cioè a ciò che diceva il grande matematico David Hilbert nel 1900: "Noi dobbiamo sapere, noi sapremo".
Ma ad un certo punto.... arriva un ometto strano, ipocondriaco, magrissimo, con gli occhiali, un austriaco chiamato Godel. Che gli fa crollare il mondo addosso, perché dimostra..... che non è detto che debba esistere una dimostrazione, ossia che la congettura potrebbe essere anche indimostrabile. La vita di Petros improvvisamente perde di senso. E... si arrende.
Molto interessante il romanzo, che mescola personaggi inventati (Petros) con persone famose realmente esistite, quali Hardy, Littlewood, Ramanujan, Godel e Turing e che riesce ad appassionare anche chi non sa nulla di matematica. Il libro porta a chiedersi cosa sia la matematica e perché l'uomo ne sia così affascinato. E ci fa capire che l'uomo non deve limitarsi a cercare di raggiungere solo obiettivi raggiungibili, ma deve osare. Solo così è possibile il progresso; senza lo sforzo immane di persone che spendono la propria vita dietro obiettivi sulla carta impossibili, la maggior parte delle scoperte scientifiche non ci sarebbero state.
June 17, 2011
Apparently maths can be fun. Not something I ever really appreciated as a child. Mostly maths was a lesson in which eye contact was to be avoided, a) to limit the chances of being called upon to make any kind of answer regarding anything even vaguely numeric and b) because the maths teacher was kind of creepily weird. This book is what I'd regard as one of the more unconventional additions to the 1001 books list and I really enjoyed learning about the maths as well as Uncle Petros' life story. Big bonus points for combining super-scary mathematical theorum with nice jaunty readable prose. However, possibly more impressive than the story itself is the authors own scholarly achievements which are listed in glorious technicolour in the his mini biog at the back of the book. Child maths prodigy, university alumnus at 15, writer, film producer, scientist, playwrite and all round full on genius. Basically he's the type of guy who'd have had the school boy Professor Brian Cox running to hide behind the back of the bike sheds to weep big ovo-spherical lacrimosal excretions over the fact that he's just not that smart. In fact if the Greek Government sought out Apostolos Doxiadis, he'd probably be able to generate an economy saving algorithm on the back of a packet of Karelia while simulataneously writing a screen play about it.
March 6, 2017
Alla fine, torno all'epigrafe
“Archimede sarà ricordato anche quando ci si dimenticherà di Eschilo, poiché le lingue muoiono, ma le idee matematiche no. ‘Immortalità’ può essere una parola ingenua, ma un matematico ha più probabilità di chiunque altro di raggiungere ciò che essa designa.” G.H. Hardy, Apologia di un matematico.
Questa l’epigrafe al libro, che ha colpito la mia attenzione non all’inizio ma a lettura finita, quando sono tornata sui miei passi a controllare se ci fosse una prefazione. Sfogliando le pagine, rileggendo ciò che avevo segnato a margine, mi sono resa conto che più di una dichiarazione è di questo tenore: “D’altro canto, il non-matematico non può neanche immaginare le gioie che gli sono negate. L’amalgama di verità e bellezza che si rivela con la comprensione di un teorema importante non è raggiungibile attraverso nessun’altra esperienza umana…”. Ma questo assunto è vero? Questa congettura – ancor prima di quella di Goldbach - è dimostrabile? E se così fosse, cosa mi son persa, e insieme a me, molti altri? E’ proprio vero che il motore del mondo, dell’evoluzione, è collegato strettamente alla matematica? Oppure il pensiero - quello filosofico - ha perlomeno lo stesso merito? E tutta questa presunzione, questo obiettivo posto così in alto, non sono fastidiosi all’orecchio del lettore? NO. Lo zio Petros è persona dolcissima, determinata, riservata, autonoma, non invadente, defilata, che tende per così dire a “stare nel suo brodo”, a non affliggere gli altri con i suoi insuccessi o con i suoi tentativi, al punto che nonostante dica “al mondo c’era forse qualcuno che, per riuscirvi, fosse più attrezzato di me, Petros Papachristos?”, non risulta essere spocchioso, ma si è conquistati dalla sua fiducia, dal suo accanimento, dalla sua grande volontà, e gli atti di “piccineria” - come il non voler pubblicare risultati intermedi per non facilitare l’eventuale ricerca di altri matematici – vengono perdonati come le azioni stravaganti di un eccentrico vanitoso - viene perdonato solo perché talentuoso, intendiamoci. Ho addirittura trovato più supponente e a suo modo arrogante – anche se in buona fede - il giovane nipote con la sua intenzione di voler far riconoscere allo zio i veri motivi del suo fallimento, non definibile come sfortuna, ma come resa a un quesito la cui soluzione superava i propri limiti. Sì, lo zio è dolcissimo, con la sua personificazione dei numeri, con i suoi sogni, con i suoi fagioli che fanno pensare agli approcci più elementari alla matematica – e per elementare non si intende facile, ma collegato agli elementi, come si legge nel libro.
Lineare la scrittura, chiara nonostante due o tre ripetizioni sparse qua e là che fanno pensare di aver perso il segno, senza però passaggi di particolare bellezza; almeno un refuso (pagina 104). Penso che ricorderò lo zio Petros – magari non con il nome proprio, magari con una approssimazione - anche fra qualche tempo…
“Archimede sarà ricordato anche quando ci si dimenticherà di Eschilo, poiché le lingue muoiono, ma le idee matematiche no. ‘Immortalità’ può essere una parola ingenua, ma un matematico ha più probabilità di chiunque altro di raggiungere ciò che essa designa.” G.H. Hardy, Apologia di un matematico.
Questa l’epigrafe al libro, che ha colpito la mia attenzione non all’inizio ma a lettura finita, quando sono tornata sui miei passi a controllare se ci fosse una prefazione. Sfogliando le pagine, rileggendo ciò che avevo segnato a margine, mi sono resa conto che più di una dichiarazione è di questo tenore: “D’altro canto, il non-matematico non può neanche immaginare le gioie che gli sono negate. L’amalgama di verità e bellezza che si rivela con la comprensione di un teorema importante non è raggiungibile attraverso nessun’altra esperienza umana…”. Ma questo assunto è vero? Questa congettura – ancor prima di quella di Goldbach - è dimostrabile? E se così fosse, cosa mi son persa, e insieme a me, molti altri? E’ proprio vero che il motore del mondo, dell’evoluzione, è collegato strettamente alla matematica? Oppure il pensiero - quello filosofico - ha perlomeno lo stesso merito? E tutta questa presunzione, questo obiettivo posto così in alto, non sono fastidiosi all’orecchio del lettore? NO. Lo zio Petros è persona dolcissima, determinata, riservata, autonoma, non invadente, defilata, che tende per così dire a “stare nel suo brodo”, a non affliggere gli altri con i suoi insuccessi o con i suoi tentativi, al punto che nonostante dica “al mondo c’era forse qualcuno che, per riuscirvi, fosse più attrezzato di me, Petros Papachristos?”, non risulta essere spocchioso, ma si è conquistati dalla sua fiducia, dal suo accanimento, dalla sua grande volontà, e gli atti di “piccineria” - come il non voler pubblicare risultati intermedi per non facilitare l’eventuale ricerca di altri matematici – vengono perdonati come le azioni stravaganti di un eccentrico vanitoso - viene perdonato solo perché talentuoso, intendiamoci. Ho addirittura trovato più supponente e a suo modo arrogante – anche se in buona fede - il giovane nipote con la sua intenzione di voler far riconoscere allo zio i veri motivi del suo fallimento, non definibile come sfortuna, ma come resa a un quesito la cui soluzione superava i propri limiti. Sì, lo zio è dolcissimo, con la sua personificazione dei numeri, con i suoi sogni, con i suoi fagioli che fanno pensare agli approcci più elementari alla matematica – e per elementare non si intende facile, ma collegato agli elementi, come si legge nel libro.
Lineare la scrittura, chiara nonostante due o tre ripetizioni sparse qua e là che fanno pensare di aver perso il segno, senza però passaggi di particolare bellezza; almeno un refuso (pagina 104). Penso che ricorderò lo zio Petros – magari non con il nome proprio, magari con una approssimazione - anche fra qualche tempo…
April 23, 2009
A beautiful, compelling, and tragic story of mathematical obsession. As the story starts, Uncle Petros, once a promising young mathematician, has wasted his intellectual gifts, amounted to very little professionally, and his family holds him in contempt but takes care of him. As his nephew tries to discover what happened from him, Uncle Petros reveals his story of how his brilliant start was eclipsed by his all-consuming obsession to crack Goldbach's conjecture. Along the way he crosses paths with many of the famous mathematical personalities of the early 20th centiry.
I thought the novel was remarkably accurate in conveying the passion, frustrations, and angst of pursuing mathematical research. Basically, only the first one to get a correct proof published gets the glory, even if someone else was really close, or even cracked it first but didn't manage to tell anyone. The paranoia of having your work "scooped" is omnipresent. The other omnipresent fear is that of wasting the best years of your life, or perhaps one should say the most potent CPU cycles of your brain, on a dead end; a commonly held aphorism is that a mathematician's best work is done before the age of thirty. This fear of losing one's edge can be so overwhelming that some mathematicians have committed suicide when they felt that their powers had peaked (the tragic case of Taniyama, whose conjecture with Shimura was one of the key ideas in the proof of Fermat's Last Theorem, being the first to come to mind).
While I thought Uncle Petros' fall from grace was a rather exaggerated reaction, given that the entire mathematical community had to deal with the exact same problem, it is entirely believable that someone of his brilliance and passion could have experienced the kind of visceral, distraught flameout that he displayed at the thought that his work might be inevitably doomed to failure.
I wholeheartedly recommend this book for anyone who wants to read a passionate depiction of the emotions of mathematical inquiry.
I thought the novel was remarkably accurate in conveying the passion, frustrations, and angst of pursuing mathematical research. Basically, only the first one to get a correct proof published gets the glory, even if someone else was really close, or even cracked it first but didn't manage to tell anyone. The paranoia of having your work "scooped" is omnipresent. The other omnipresent fear is that of wasting the best years of your life, or perhaps one should say the most potent CPU cycles of your brain, on a dead end; a commonly held aphorism is that a mathematician's best work is done before the age of thirty. This fear of losing one's edge can be so overwhelming that some mathematicians have committed suicide when they felt that their powers had peaked (the tragic case of Taniyama, whose conjecture with Shimura was one of the key ideas in the proof of Fermat's Last Theorem, being the first to come to mind).
While I thought Uncle Petros' fall from grace was a rather exaggerated reaction, given that the entire mathematical community had to deal with the exact same problem, it is entirely believable that someone of his brilliance and passion could have experienced the kind of visceral, distraught flameout that he displayed at the thought that his work might be inevitably doomed to failure.
I wholeheartedly recommend this book for anyone who wants to read a passionate depiction of the emotions of mathematical inquiry.
November 30, 2017
IL DIAVOLO
libellino divertente e ben scritto, una storia anche con un certo valore pedagogico pur se a mio avviso senza ambizioni letterarie “alte”
quanto alla pazzia dei matematici, non ho dati puntuali ma tenderei a pensare che non si discosta molto da quella in altri campi dell’arte (vedi mozart, van gogh o altro)
la verità è che i veri geni sono matti e visionari, in qualsiasi campo si adoperino, e giacché la matematica è la somma arte i matematici sono un po’ più pazzi degli altri, tutto qua (ma questo accade solo nelle eccellenze, gran parte dei sedicenti matematici sono semplici mestieranti come il sottoscritto)
invece tutto il terrore per la matematica che rilevo in ogni dove (e che trapela anche qui in ahinoii) proprio non lo capisco, c’è qualcosa di profondamente sbagliato nella scuola italiana (questione annosa). A volte però ho l’impressione che sia un po’ una posa, un crogiolarsi nel proprio ristretto mondo senza volersi mettere alla prova: cosa c’è di meglio che questo breve romanzetto, divertente e leggero, per cominciare? Si tratta di narrativa, ma che pensate che ci sia la dimostrazione di Wiles? Poi magari uno si ritrova a dirsi ”Beh però…”
libellino divertente e ben scritto, una storia anche con un certo valore pedagogico pur se a mio avviso senza ambizioni letterarie “alte”
quanto alla pazzia dei matematici, non ho dati puntuali ma tenderei a pensare che non si discosta molto da quella in altri campi dell’arte (vedi mozart, van gogh o altro)
la verità è che i veri geni sono matti e visionari, in qualsiasi campo si adoperino, e giacché la matematica è la somma arte i matematici sono un po’ più pazzi degli altri, tutto qua (ma questo accade solo nelle eccellenze, gran parte dei sedicenti matematici sono semplici mestieranti come il sottoscritto)
invece tutto il terrore per la matematica che rilevo in ogni dove (e che trapela anche qui in ahinoii) proprio non lo capisco, c’è qualcosa di profondamente sbagliato nella scuola italiana (questione annosa). A volte però ho l’impressione che sia un po’ una posa, un crogiolarsi nel proprio ristretto mondo senza volersi mettere alla prova: cosa c’è di meglio che questo breve romanzetto, divertente e leggero, per cominciare? Si tratta di narrativa, ma che pensate che ci sia la dimostrazione di Wiles? Poi magari uno si ritrova a dirsi ”Beh però…”
June 9, 2022
Καθαρό πεντάρι!
Το ξεκίνησα χθες το μεσημέρι και σήμερα το πρωί το τελείωσα. Δεν μπορείς να σταματήσεις. Είναι λίγα τα βιβλία που ως τώρα μου έχουν δημιουργήσει αυτή την αδυναμία διακοπής της ανάγνωσης τους.
Δεν είναι απλώς ένα βιβλίο το οποίο είναι φιλικό και σε όσους δηλώνουν άσχετοι περί μαθηματικών (όπως εγώ που φτάνω βαριά - για πολύ βαριά μιλάμε όμως - μέχρι την διαίρεση), αλλά είναι ένα βιβλίο «φιλικό» προς κάθε αναγνώστη. Άμεσο, λιτό και ταυτόχρονα πλούσιο.
Η ιστορία του θείου Πέτρου μού έδωσε σε προσωπικό επίπεδο ένα βαθύ και υψίστης σημασίας μάθημα, το οποίο θα φροντίσω να μην ξεχάσω ποτέ προς όφελος μου.
Το ξεκίνησα χθες το μεσημέρι και σήμερα το πρωί το τελείωσα. Δεν μπορείς να σταματήσεις. Είναι λίγα τα βιβλία που ως τώρα μου έχουν δημιουργήσει αυτή την αδυναμία διακοπής της ανάγνωσης τους.
Δεν είναι απλώς ένα βιβλίο το οποίο είναι φιλικό και σε όσους δηλώνουν άσχετοι περί μαθηματικών (όπως εγώ που φτάνω βαριά - για πολύ βαριά μιλάμε όμως - μέχρι την διαίρεση), αλλά είναι ένα βιβλίο «φιλικό» προς κάθε αναγνώστη. Άμεσο, λιτό και ταυτόχρονα πλούσιο.
Η ιστορία του θείου Πέτρου μού έδωσε σε προσωπικό επίπεδο ένα βαθύ και υψίστης σημασίας μάθημα, το οποίο θα φροντίσω να μην ξεχάσω ποτέ προς όφελος μου.
July 21, 2019
The title of the book enticed me. I am a sucker for themes that involve math stories. In some way I feel i am redeeming myself for not studying math well enough in my school days.
This is a very interesting story of a "could have been great" mathematician Petros Papachristos. He took on an very tough old math problem of the Goldbach Conjecture and attempted to solve it to achieve fame - and thereby win back his first and only girlfriend Isolde.
The story is set in the time of G H HArdy and Ramanujam who were Number Theorists and also were in pursuit of similar tough problems such as the Riemann Hypothesis and Fermat Theorem.
I felt the story was well narrated and kept the pace right through - maybe because of my own interest. I think the narrative is good even for those who are not interested in the math portion of the story as it does not get technical at all. Highly recommended.
This is a very interesting story of a "could have been great" mathematician Petros Papachristos. He took on an very tough old math problem of the Goldbach Conjecture and attempted to solve it to achieve fame - and thereby win back his first and only girlfriend Isolde.
The story is set in the time of G H HArdy and Ramanujam who were Number Theorists and also were in pursuit of similar tough problems such as the Riemann Hypothesis and Fermat Theorem.
I felt the story was well narrated and kept the pace right through - maybe because of my own interest. I think the narrative is good even for those who are not interested in the math portion of the story as it does not get technical at all. Highly recommended.
August 19, 2013
Se podría decir que yo soy un entusiasta de la matemática, y me ha tocado estudiarla como parte de mi carrera de Ingeniería, pero disto mucho de tener esa madera de matemático natural de la que están hechos los genios que se nombran en esta excelente obra de Apostolos Doxiadis. Definitivamente hay que contar con una configuración cerebral y mental bien particular para poder lograr los niveles de abstracción que requiere el pensamiento matemático puro. Creo que esta obra es un homenaje a esa genialidad, a través de la historia ficticia de Petros Papachristos y su lucha de una vida para probar la famosa Conjetura de Goldbach. Incluir más detalles, sin incurrir en "spoilers", es bastante difícil, por lo que simplemente me limito a recomendarla para los entusiastas de la ciencia en general y todo aquel que requiera de una inspiración para estudiar la matemática.
September 10, 2017
La conformazione psicologica del vero matematico è vicina a quella del poeta o del compositore o, in altre parole, di una persona interessata alla creazione della bellezza e alla ricerca dell’armonia e della perfezione.
La vera protagonista di questo romanzo è la matematica. Non quella arida e noiosa che si insegna a scuola, fatta di astruse procedure di calcolo, ma quella grandiosa costruzione della mente umana che è comparabile da un lato all’arte e dall’altro alla filosofia. La matematica può regalare gioie grandissime ma è un’amante molto esigente e possessiva. Chi si dedica alla matematica deve farlo in maniera completa, lasciarsi trasportare nel suo mondo, che può essere anche molto lontana dalla realtà. La matematica, però, può essere anche un abbraccio mortale che macina menti brillanti e le esaurisce nel volgere di pochi anni. La storia della matematica è piena di grandi menti che hanno avuto vite molto difficili (e molti sono citati anche nel romanzo) e sono o morti giovanissimi o caduti nella pazzia.
La congettura di cui si parla nel titolo è una delle più famose questioni irrisolte di cui è ricca la matematica. La congettura afferma che ogni numero pari maggiore di 2 è scrivibile come somma di due numeri primi. Un’affermazione di una semplicità e (apparente) ovvietà disarmante ma che in più di 200 anni nessuno è riuscito a dimostrare. Si può vivere senza una prova della congettura di Goldbach o della ipotesi di Riemann? Certamente sì! Ma ci sono matematici che possono accettare la sfida del provare qualcosa che a nessuno è mai riuscito e decidere di dedicargli tutta la vita.
L’autore del romanzo ha studiato matematica, ne ha sperimentato il fascino e, allo stesso tempo, percepito la propria limitatezza. Nel mio piccolo anche io ho respirato quell’aria, conosco il piacere che si prova quando si riesce a cogliere la bellezza di un teorema complesso, la tensione spasmodica quando si cerca di risolvere un problema e l’orgoglio quando si riesce a risolverlo, la delusione nello scoprire di essere arrivati secondi (nella ricerca scientifica conta solo chi arriva primo). Forse, proprio per questo ho apprezzato così tanto questo romanzo. Non so, però, possa essere apprezzato da chi non ha mai avuto rapporti con la matematica.
La vera protagonista di questo romanzo è la matematica. Non quella arida e noiosa che si insegna a scuola, fatta di astruse procedure di calcolo, ma quella grandiosa costruzione della mente umana che è comparabile da un lato all’arte e dall’altro alla filosofia. La matematica può regalare gioie grandissime ma è un’amante molto esigente e possessiva. Chi si dedica alla matematica deve farlo in maniera completa, lasciarsi trasportare nel suo mondo, che può essere anche molto lontana dalla realtà. La matematica, però, può essere anche un abbraccio mortale che macina menti brillanti e le esaurisce nel volgere di pochi anni. La storia della matematica è piena di grandi menti che hanno avuto vite molto difficili (e molti sono citati anche nel romanzo) e sono o morti giovanissimi o caduti nella pazzia.
La congettura di cui si parla nel titolo è una delle più famose questioni irrisolte di cui è ricca la matematica. La congettura afferma che ogni numero pari maggiore di 2 è scrivibile come somma di due numeri primi. Un’affermazione di una semplicità e (apparente) ovvietà disarmante ma che in più di 200 anni nessuno è riuscito a dimostrare. Si può vivere senza una prova della congettura di Goldbach o della ipotesi di Riemann? Certamente sì! Ma ci sono matematici che possono accettare la sfida del provare qualcosa che a nessuno è mai riuscito e decidere di dedicargli tutta la vita.
L’autore del romanzo ha studiato matematica, ne ha sperimentato il fascino e, allo stesso tempo, percepito la propria limitatezza. Nel mio piccolo anche io ho respirato quell’aria, conosco il piacere che si prova quando si riesce a cogliere la bellezza di un teorema complesso, la tensione spasmodica quando si cerca di risolvere un problema e l’orgoglio quando si riesce a risolverlo, la delusione nello scoprire di essere arrivati secondi (nella ricerca scientifica conta solo chi arriva primo). Forse, proprio per questo ho apprezzato così tanto questo romanzo. Non so, però, possa essere apprezzato da chi non ha mai avuto rapporti con la matematica.
May 15, 2018
Ενδιαφέρον και ευκολοδιάβαστο.
October 25, 2016
Uncle Petros is considered the black sheep of the family, one of “life’s failures”, by his two younger brothers. His nephew, the first person narrator of the story, sees his uncle only once a year when the family gathers for a ritual visit. The nephew is intrigued by the man and especially by his library of books containing some mysterious symbols like ∀ and ∃ and ∫. One day he finds out that uncle Petros was a mathematician when he was young. The boy starts to get an interest in mathematics himself but before he really starts, he promises to prove to his uncle his natural talent for dealing with numbers. “Mathematicus nascitur, non fit,” is what Petros says. “A Mathematician is born, not made.” The task Petros poses to his nephew isn’t easy, and by the end of the summer their relationship has become quite different than it was before…
This may sound like a novel for (math-) nerds, but it isn’t at all. Although the titular Goldbach’s conjecture is indeed a well-known math problem you don’t need any math to enjoy the book. If you know what a prime number is, and if you can add integers, you’re pretty much set. In fact it’s even better to not lookup the conjecture on Wikipedia, because knowing what it says would somewhat spoil the beginning of the novel. And if you always wanted to know how mathematicians tick you should give this book a try. The author succeeds in bringing us a little closer to this strange kind of species, with all of its quirks, successes, and failures. Oliver Sacks calls this novel “very funny” and “charming” in his praise on the cover of the Kindle edition that I read. I don’t know where Mr Sacks got this from. For me there were only very few comic events here, and the charm is quite limited. The first adjective that comes to my mind is “tragic” actually.
One personal highlight was the mentioning of Kurt Gödel and Alan Turing and the connection of their respective results with Goldbach’s conjecture. Both of these two great scientists, who also suffered a tragic fate, appear briefly as characters in the book. There are a couple more mathematical problems mentioned, two of which had been proved since the book was first published and the publishers announced a $1 million prize for anybody who proved Goldbach’s conjecture within two years (until 2002). Needless to say the prize was never awarded.
Don’t be put off by the little math there is! We have here a really good and inspiring book about the tragic life of a scientist. Only the prose occasionally feels a little stilted to me.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
August 27, 2016
Δεν είμαι σίγουρη με ποιά κριτήρια να αξιολογήσω το βιβλίο αυτό, και θα εξηγήσω αμέσως το ...θεώρημα μου.
Το πρώτο μέρος του βιβλίου, πριν μάθουμε δηλαδή την ιστορία του θείου Πέτρου, δεν έχει ουδεμία σχέση με το δεύτερο μέρος, δηλαδή την ιστορία της μαθηματικής του καριέρας.
Στο πρώτο μέρος, η υπεραπλουστευμένη πλοκή, η "αφελής" γλώσσα, οι μονοδιάστατοι χαρακτήρες και ο άχρωμος-άοσμος-άγευστος αφηγητής, μου έδωσαν την εντύπωση ότι διάβαζα εφηβικό μυθιστόρημα, γεγονός που με απογοήτευσε γιατί είχα προετοιμάσει τον εαυτό μου για ένα σοβαρό ιστορικό μυθιστόρημα.
Το δεύτερο μέρος ήταν σαφώς καλύτερο. Εδώ μαθαίνουμε την (φανταστική δυστυχώς) ιστορία του θείου Πέτρου, του μαθηματικού με το σπουδαίο ταλέντο που δούλεψε δίπλα σε κάποιους από τους μεγαλύτερους μαθηματικούς της εποχής και αφιέρωσε την ζωή του στην λύση ενός πανδύσκολου μαθηματικού προβλήματος, της Εικασίας του Γκολντμπαχ.
Όμως και εδώ υπάρχει πρόβλημα. Ο συγγραφέας μας περιγράφει ξερά τα γεγονότα, χωρίς να εκμεταλλευτεί την ευκαιρία να μας μπάσει στο (κοινωνικο-πολιτικό) κλίμα της εποχής ή να μας κάνει να γνωρίσουμε σε κάποιο βάθος τα ιερά τέρατα των Μαθηματικών που συναντά ο θείος Πέτρος στην πορεία του (Καραθοδωρή, Τιούριγκ κλπ). Ούτε μια περιγραφή της εμφάνισης τους τουλάχιστον! Τί τρώγαν, τί πίναν, τι φόραγαν, πως ήταν αυτοί οι άνθρωποι τέλος πάντων! Οι μεταξύ τους διαλόγοι ήταν βαρετοί και στεγνοί, και δεν πρόδιδαν τίποτε για τον χαρακτήρα τους. Μου ήρθε να παρατήσω το βιβλίο στην μέση και να πιάσω μια βιογραφία του Τιούριγκ ή, αν μη τι άλλο, ένα πιό καλογραμμένο μυθιστόρημα. Με λίγα λόγια, δεν ικανοποιήθηκαν πλήρως ούτε οι λογοτεχνικές μου ανάγκες (λόγω της υπερβολικά λιτής γραφής) ούτε η περιέργεια μου να μάθω για τις προσωπικότητες που με ενδιέφεραν.
Παρ' όλα αυτά, έχω μάθει αρκετά ενδιαφέροντα πραγματάκια σχετικά με την ιστορία των μαθηματικών απ' αυτό το βιβλίο, και μου έχει κινήσει την περιέργεια να μάθω ακόμα περισσότερα.
Το τρίτο μέρος του μυθιστορήματος "δένει" τα δύο πρώτα μεταξύ τους και οδηγεί την πλοκή σε ένα καλογραμμένο και σασπενσιάρικο τέλος, ενώ η στρωτή και σωστή γραφή του μυθιστορήματος μου επέτρεψε να το διαβάσω άνετα μέσα σε μία μέρα.
Με λίγα λόγια το βιβλίο δεν ήταν καθόλου άσχημο, απλώς ο συγγραφέας καταπιάστηκε με ένα εξαιρετικά ενδιαφέρον θέμα που θα μπορούσε να το είχε εκμεταλλευτεί πολύ καλύτερα.
Το πρώτο μέρος του βιβλίου, πριν μάθουμε δηλαδή την ιστορία του θείου Πέτρου, δεν έχει ουδεμία σχέση με το δεύτερο μέρος, δηλαδή την ιστορία της μαθηματικής του καριέρας.
Στο πρώτο μέρος, η υπεραπλουστευμένη πλοκή, η "αφελής" γλώσσα, οι μονοδιάστατοι χαρακτήρες και ο άχρωμος-άοσμος-άγευστος αφηγητής, μου έδωσαν την εντύπωση ότι διάβαζα εφηβικό μυθιστόρημα, γεγονός που με απογοήτευσε γιατί είχα προετοιμάσει τον εαυτό μου για ένα σοβαρό ιστορικό μυθιστόρημα.
Το δεύτερο μέρος ήταν σαφώς καλύτερο. Εδώ μαθαίνουμε την (φανταστική δυστυχώς) ιστορία του θείου Πέτρου, του μαθηματικού με το σπουδαίο ταλέντο που δούλεψε δίπλα σε κάποιους από τους μεγαλύτερους μαθηματικούς της εποχής και αφιέρωσε την ζωή του στην λύση ενός πανδύσκολου μαθηματικού προβλήματος, της Εικασίας του Γκολντμπαχ.
Όμως και εδώ υπάρχει πρόβλημα. Ο συγγραφέας μας περιγράφει ξερά τα γεγονότα, χωρίς να εκμεταλλευτεί την ευκαιρία να μας μπάσει στο (κοινωνικο-πολιτικό) κλίμα της εποχής ή να μας κάνει να γνωρίσουμε σε κάποιο βάθος τα ιερά τέρατα των Μαθηματικών που συναντά ο θείος Πέτρος στην πορεία του (Καραθοδωρή, Τιούριγκ κλπ). Ούτε μια περιγραφή της εμφάνισης τους τουλάχιστον! Τί τρώγαν, τί πίναν, τι φόραγαν, πως ήταν αυτοί οι άνθρωποι τέλος πάντων! Οι μεταξύ τους διαλόγοι ήταν βαρετοί και στεγνοί, και δεν πρόδιδαν τίποτε για τον χαρακτήρα τους. Μου ήρθε να παρατήσω το βιβλίο στην μέση και να πιάσω μια βιογραφία του Τιούριγκ ή, αν μη τι άλλο, ένα πιό καλογραμμένο μυθιστόρημα. Με λίγα λόγια, δεν ικανοποιήθηκαν πλήρως ούτε οι λογοτεχνικές μου ανάγκες (λόγω της υπερβολικά λιτής γραφής) ούτε η περιέργεια μου να μάθω για τις προσωπικότητες που με ενδιέφεραν.
Παρ' όλα αυτά, έχω μάθει αρκετά ενδιαφέροντα πραγματάκια σχετικά με την ιστορία των μαθηματικών απ' αυτό το βιβλίο, και μου έχει κινήσει την περιέργεια να μάθω ακόμα περισσότερα.
Το τρίτο μέρος του μυθιστορήματος "δένει" τα δύο πρώτα μεταξύ τους και οδηγεί την πλοκή σε ένα καλογραμμένο και σασπενσιάρικο τέλος, ενώ η στρωτή και σωστή γραφή του μυθιστορήματος μου επέτρεψε να το διαβάσω άνετα μέσα σε μία μέρα.
Με λίγα λόγια το βιβλίο δεν ήταν καθόλου άσχημο, απλώς ο συγγραφέας καταπιάστηκε με ένα εξαιρετικά ενδιαφέρον θέμα που θα μπορούσε να το είχε εκμεταλλευτεί πολύ καλύτερα.
May 23, 2016
What stayed with me, long after I had read A Sense of the Mysterious: Science and the Human Spirit by Alan Lightman, was the tone of regret, that powerful, haunting emotion. He writes of his own regrets in discovering in his thirties that his chosen life was over. He was a physicist, he no longer had any expectation of doing anything that mattered.
and of maths:
https://alittleteaalittlechat.wordpre...
When I directed an astrophysics conference one summer and realised that most of the exciting research was being reported by ambitious young people in their midtwenties, waving their calculations and ideas in the air and scarcely slowing down to acknowledge their predecessors, I would have instantly traded my position for theirs....None of my fragile childhood dreams, my parents' ambitious encouragement, my education at all the best schools, prepared me for this early seniority, this stiffening at age thirty-five.
and of maths:
https://alittleteaalittlechat.wordpre...
December 2, 2010
Uncle Petros and Goldbach's Conjecture tells the story of a brilliant mathematician obsessed with proving Goldbach's Conjecture (as reformulated by Euler: every even number greater than two is the sum of two primes). Despite the seemingly difficult mathematical subject, the book is a quick and easy read. This is a testament to the clear and simple prose of the author, himself a mathematician by training.
While math is the main focus of the book, an underlying theme is the question of how and why we should select attainable goals. As the nephew puts it in a romantic outburst:
While math is the main focus of the book, an underlying theme is the question of how and why we should select attainable goals. As the nephew puts it in a romantic outburst:
"While his brothers were studying and getting married, raising children and running the family business, wearing out their lives along with the rest of nameless humanity in the daily routines of subsistence, procreation and killing time, he, Prometheus-like, had striven to cast light into the darkest and most inaccessible corner of knowledge."
December 28, 2023
3.5 stars. An interesting, short novel about Uncle Petros. The narrator is his young nephew who discovers that his uncle was once a celebrated mathematician. In his family, the narrator has been told by his father, that Uncle Petros is an oddball who never amounted to much.
The narrator over the years learns that Uncle Petros, who is now an ageing recluse living alone in an Athens suburb, was once a professor of mathematics in Germany in the 1930s and a very good chess player who could have been a ‘master’ chess player.
I found the novel to be a very engaging, thought provoking, quick read. There is some discussion of mathematic problems and the mathematical world of the elite. I particularly enjoyed the first two thirds of the book.
The author was admitted to New York’s Columbia University at the age of fifteen after submitting an original paper to the Department of Mathematics.
This book was first published in 1992.
The narrator over the years learns that Uncle Petros, who is now an ageing recluse living alone in an Athens suburb, was once a professor of mathematics in Germany in the 1930s and a very good chess player who could have been a ‘master’ chess player.
I found the novel to be a very engaging, thought provoking, quick read. There is some discussion of mathematic problems and the mathematical world of the elite. I particularly enjoyed the first two thirds of the book.
The author was admitted to New York’s Columbia University at the age of fifteen after submitting an original paper to the Department of Mathematics.
This book was first published in 1992.
March 14, 2019
Gerçek MATEMATİK okulda öğrenilen toplama çıkarma işlemlerine benzemez; onun derdi SOYUT ZİHİNSEL KURGULARDIR, maddi duyularla algılanabilir dünya ile bir alıp veremediği yoktur. Matematikçinin ruhsal yapısı, bir ŞAİRİN, bir BESTECİNİN ya da başka bir deyişle GÜZELLİK yaratmaya çalışan ve UYUM ve MÜKEMMELLİK peşinde koşan bir insanınkiyle hemen hemen aynıdır.
MATEMATİKÇİLER, gerçek bir KAVRAM CENNETİNİ, kapılarını matematikle ilgisi olmayan AYAKTAKIMINA asla açmayan, muhteşem bir ŞİİRSEL ÂLEMİ mekân tutmuşlardı.
Petros Amca, Prometheus gibi, BİLGİNİN en karanlık ve ULAŞILMAZ köşesini AYDINLATMAK için uğraşıp durmuştu (Matematikteki GOLDBACH HİPOTEZİ'ni çözmek için ömrünü harcamıştı: "2 den büyük her ÇİFT sayı, iki ASAL sayının toplamıdır"; hipotez inanılmaz büyüklükteki çift sayılar için bile ispatlanmış ama hâlâ kimse GENEL İSPAT YOLUNU bulamamıştır).
BİLİM İNSANLARININ (en saf, en uçukları dahil) sadece ve sadece İNSANLIĞIN İYİLİĞİ uğruna, GERÇEĞİN PEŞİNE düştüğünü iddia eden kişi ya ne SÖYLEDİĞİNİ bilmiyordur ya da düpedüz YALAN söylüyordur; maddi kazancı pek umursamazlarsa da, ARALARINDA İHTİRASLA ve GÜÇLÜ BİR REKABETÇİ DÜRTÜYLE hareket etmeyen tek bir kişi bile yoktur ve hepsinin rüyalarını süsleyen tek şey ŞAN'dır.
BİLMEK ZORUNDAYIZ, matematikte BİLİNMEZLİĞE yer yoktur; matematik MUTLAK GERÇEKLİĞİN cennetidir ve ÖKLİD'in hayali, TUTARLILIK ve TÜMLÜK hayalidir (David Hilbert).
İSPATLANAMAZ İSTİSNAİ DOĞRULAR da vardır (mutlak formundaki gerçekliğe en çok yaklaşmış olan Kurt Gödel).
BİLİMLERİN KRALİÇESİ MATEMATİK üzerine çalışan, yani GERÇEKLİK'e çok YAKLAŞANLAR, parlak fakat ZALİM ve YAKICI bir IŞIĞA doğru sürüklenen gece KELEBEKLERİNE benzerler ve DELİ MATEMATİKÇİ sözü masal değil gerçektir.
Öte yandan, matematikle ilgisi olmayan bir kişi MAHRUM kaldığı HAZLARI aklına bile getiremez; önemli bir TEORİYİ ANLAYARAK ulaşılan GERÇEKLİK VE GÜZELLİK karışımına, başka insani etkinliklerin hiçbiriyle ULAŞAMAZSINIZ.
Matematik, "İDEAL"in VARLIĞINI gerçekten inandırıcı ve gözle görülür hale getirir.
MATEMATİKÇİLER, gerçek bir KAVRAM CENNETİNİ, kapılarını matematikle ilgisi olmayan AYAKTAKIMINA asla açmayan, muhteşem bir ŞİİRSEL ÂLEMİ mekân tutmuşlardı.
Petros Amca, Prometheus gibi, BİLGİNİN en karanlık ve ULAŞILMAZ köşesini AYDINLATMAK için uğraşıp durmuştu (Matematikteki GOLDBACH HİPOTEZİ'ni çözmek için ömrünü harcamıştı: "2 den büyük her ÇİFT sayı, iki ASAL sayının toplamıdır"; hipotez inanılmaz büyüklükteki çift sayılar için bile ispatlanmış ama hâlâ kimse GENEL İSPAT YOLUNU bulamamıştır).
BİLİM İNSANLARININ (en saf, en uçukları dahil) sadece ve sadece İNSANLIĞIN İYİLİĞİ uğruna, GERÇEĞİN PEŞİNE düştüğünü iddia eden kişi ya ne SÖYLEDİĞİNİ bilmiyordur ya da düpedüz YALAN söylüyordur; maddi kazancı pek umursamazlarsa da, ARALARINDA İHTİRASLA ve GÜÇLÜ BİR REKABETÇİ DÜRTÜYLE hareket etmeyen tek bir kişi bile yoktur ve hepsinin rüyalarını süsleyen tek şey ŞAN'dır.
BİLMEK ZORUNDAYIZ, matematikte BİLİNMEZLİĞE yer yoktur; matematik MUTLAK GERÇEKLİĞİN cennetidir ve ÖKLİD'in hayali, TUTARLILIK ve TÜMLÜK hayalidir (David Hilbert).
İSPATLANAMAZ İSTİSNAİ DOĞRULAR da vardır (mutlak formundaki gerçekliğe en çok yaklaşmış olan Kurt Gödel).
BİLİMLERİN KRALİÇESİ MATEMATİK üzerine çalışan, yani GERÇEKLİK'e çok YAKLAŞANLAR, parlak fakat ZALİM ve YAKICI bir IŞIĞA doğru sürüklenen gece KELEBEKLERİNE benzerler ve DELİ MATEMATİKÇİ sözü masal değil gerçektir.
Öte yandan, matematikle ilgisi olmayan bir kişi MAHRUM kaldığı HAZLARI aklına bile getiremez; önemli bir TEORİYİ ANLAYARAK ulaşılan GERÇEKLİK VE GÜZELLİK karışımına, başka insani etkinliklerin hiçbiriyle ULAŞAMAZSINIZ.
Matematik, "İDEAL"in VARLIĞINI gerçekten inandırıcı ve gözle görülür hale getirir.
January 8, 2017
Ο άχρηστος, ο αποτυχημένος. Γιατί πάντοτε οτιδήποτε διαφορετικό είναι κάτι άχρηστο, προβληματικό, κάτι τελείως περιττό κι ανάξιο λόγου. Έτσι αντιμετωπίζεται ο θείος Πέτρος από την οικογένειά του, από την κοινωνία αλλά κυρίως από τον ίδιο του τον εαυτό.
Από τον ίδιο άνθρωπο που κάποτε πίστεψε, πίστεψε βαθιά σ’ ένα όραμα. Ότι μπορούσε να βρει τη λύση στην περιβόητη «Εικασία του Γκόλντμπαχ», ένα πρόβλημα που προσπαθούσαν εις μάτην να επιλύσουν γενεές μαθηματικών. Ένα σπουδαίο ταλέντο, που καταλήφθηκε από την αγωνία να ξεχωρίσει, να αποδείξει ότι είναι κάτι πραγματικά σπουδαίο, γιατί πίστευε ότι είναι κάτι σπουδαιότερο από τους υπόλοιπους. Ακόμα κι αν ήταν έτσι, αν ήταν όντως σπουδαιότερος από άλλους ο θείος Πέτρος πέρασε όλη του τη ζωή, σε σκιερά δωμάτια, απαλλαγμένος από τις ανάγκες ενός φυσιολογικού ανθρώπους, σκυμμένος σε υπολογισμούς, σε θεωρίες, σε αποδείξεις ενός ανέφικτου στόχου.
Κι έτσι ο θείος Πέτρος δεν έζησε τη ζωή ενός σπουδαίου, αλλά ενός δειλού, ενός αποτυχημένου, ενός λιποτάκτη.
Κι η αποτυχία του ήταν ότι δεν κατάφερε ποτέ να δει το πρόβλημά του με καθαρό μυαλό, απαλλαγμένο τον υπέρμετρο εγωισμό. Δεν κατάφερε ποτέ να αποδεχτεί την αποτυχία του κι έτσι συμβιβάστηκε με την απομόνωση, την αργία, τη μοναξιά και την τρέλα.
Ο Απόστολος Δοξιάδης έγραψε ένα σπουδαίο βιβλίο για τη λεπτή γραμμή που διαχωρίζει την ιδιοφυία από τη σχιζοφρένια. Για τα χαμένα ταλέντα, τις ζωές των ξεχωριστών ανθρώπων που χάνονται στον ωκεανό του χαρισμάτός τους, της ματαιοδοξίας και της μοναξιάς.
*πάντα φοβάμαι μήπως γίνω ο θείος Πέτρος
Από τον ίδιο άνθρωπο που κάποτε πίστεψε, πίστεψε βαθιά σ’ ένα όραμα. Ότι μπορούσε να βρει τη λύση στην περιβόητη «Εικασία του Γκόλντμπαχ», ένα πρόβλημα που προσπαθούσαν εις μάτην να επιλύσουν γενεές μαθηματικών. Ένα σπουδαίο ταλέντο, που καταλήφθηκε από την αγωνία να ξεχωρίσει, να αποδείξει ότι είναι κάτι πραγματικά σπουδαίο, γιατί πίστευε ότι είναι κάτι σπουδαιότερο από τους υπόλοιπους. Ακόμα κι αν ήταν έτσι, αν ήταν όντως σπουδαιότερος από άλλους ο θείος Πέτρος πέρασε όλη του τη ζωή, σε σκιερά δωμάτια, απαλλαγμένος από τις ανάγκες ενός φυσιολογικού ανθρώπους, σκυμμένος σε υπολογισμούς, σε θεωρίες, σε αποδείξεις ενός ανέφικτου στόχου.
Κι έτσι ο θείος Πέτρος δεν έζησε τη ζωή ενός σπουδαίου, αλλά ενός δειλού, ενός αποτυχημένου, ενός λιποτάκτη.
Κι η αποτυχία του ήταν ότι δεν κατάφερε ποτέ να δει το πρόβλημά του με καθαρό μυαλό, απαλλαγμένο τον υπέρμετρο εγωισμό. Δεν κατάφερε ποτέ να αποδεχτεί την αποτυχία του κι έτσι συμβιβάστηκε με την απομόνωση, την αργία, τη μοναξιά και την τρέλα.
Ο Απόστολος Δοξιάδης έγραψε ένα σπουδαίο βιβλίο για τη λεπτή γραμμή που διαχωρίζει την ιδιοφυία από τη σχιζοφρένια. Για τα χαμένα ταλέντα, τις ζωές των ξεχωριστών ανθρώπων που χάνονται στον ωκεανό του χαρισμάτός τους, της ματαιοδοξίας και της μοναξιάς.
*πάντα φοβάμαι μήπως γίνω ο θείος Πέτρος
December 13, 2009
Repetitive and dull. The meddle of an author is easily tested by how often he or she uses the same phrase to describe something. While Goldbach's Conjecture is central to the plot of the novella the author says the conjecture dozens of time when this reference is un-needed. The author in no way indicates the actual progress of the problem and the introduction of Kurt Godel and Alan Turing was a dis-service to their memory when presented with such dull dialog.
The end was both a twist and totally expected, a phenomenon that happens two other times in the book.
The end was both a twist and totally expected, a phenomenon that happens two other times in the book.
July 24, 2010
This is a short book--a fast and easy read. The story describes how a good mathematician sank into an obsession that swallowed up his life. The storyteller's mathematician friend, Sammy, mentions that the trail of a mathematical quest will be littered with intermediate, published results on a variety of topics. So, why didn't Uncle Petros publish his intermediate--but important--results?
Interestingly, I do not remember another novel with as many footnotes as this one! (Actually, I don't remember any novels with an author's footnotes.)
Interestingly, I do not remember another novel with as many footnotes as this one! (Actually, I don't remember any novels with an author's footnotes.)
January 7, 2018
Incidentally, I read it while I was trying to built a non-fiction narrative in Urdu on limits of rationality and mysteries surrounding interplay of reason and intuition in the process of mathematical discovery. I absolutely loved how Doxiadis transformed this well-known thread of history of mathematics into an unputdownable novel. It is amazing how simple his characters look and yet how intricately complex their inner struggles are. The bits about Hardy, Littlewood, Godel and Turing are well blended and adds to the overall value of the reader's experience.
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