What do you think?
Rate this book
The Mathematics of the Gods and the Algorithms of Men: A Cultural History
Is mathematics a discovery or an invention? Have we invented numbers or do they truly exist? What sort of reality should we attribute to them? Mathematics has always been a way of understanding and ordering the world: from sacred ancient texts and pre-Socratic philosophers to twentieth-century logicians such as Russell and Frege and beyond.
In this masterful, elegant book, mathematician and philosopher Paolo Zellini offers a brief cultural and intellectual history of mathematics, from ancient Greece to India to our contemporary obsession with algorithms, showing how mathematical thinking is inextricably linked with philosophical, existential and religious questions—and indeed with our cosmic understanding of the world.
In this masterful, elegant book, mathematician and philosopher Paolo Zellini offers a brief cultural and intellectual history of mathematics, from ancient Greece to India to our contemporary obsession with algorithms, showing how mathematical thinking is inextricably linked with philosophical, existential and religious questions—and indeed with our cosmic understanding of the world.
240 pages, Hardcover
First published October 1, 2016
74 people are currently reading
750 people want to read
About the author
Paolo Zellini
12 books19 followersPaolo Zellini (Trieste, 1946) è un matematico, saggista e accademico italiano.
Nei suoi saggi si è dedicato ad una disamina dell'evoluzione del pensiero matematico attraverso il concetto di infinito e ad un approfondimento della nozione di numero in una prospettiva che abbraccia e mette in gioco tutta la storia del pensiero non solo occidentale. In queste ricerche ha dichiarato esser stato ispirato dall'opera di Elémire Zolla.
Nei suoi saggi si è dedicato ad una disamina dell'evoluzione del pensiero matematico attraverso il concetto di infinito e ad un approfondimento della nozione di numero in una prospettiva che abbraccia e mette in gioco tutta la storia del pensiero non solo occidentale. In queste ricerche ha dichiarato esser stato ispirato dall'opera di Elémire Zolla.
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 30 of 33 reviews
October 4, 2021
An Abuse of Mysticism
In their arguments, conspiracy theorists and religious fundamentalists reveal more about themselves than about their point of view. Sometimes so do really enthusiastic academic mathematicians like Zellini.They all typically want to make the point that the rest of us are persecuting them. What makes some mathematicians so defensive about their subject? Are they victims of derision on the street? Do their academic budgets suffer because of underestimation of their intellectual worth? Or did they just feel unloved as children?
Whatever the reason for the apparent existential crisis in mathematics, the solution proposed by books like this one is ridiculous. Zellini wants us to know not just how important mathematics is but also how real it is. For him mathematics is so real that it permeates the universe. It is a force that exists quite independently our thinking about it. And he wants us to appreciate this reality as much as any evangelical preacher wants us to believe on the Lord.
Zellini’s specific grievance that there is “distorted image of mathematics as a merely linguistic game” (He doesn’t name names, but you know who you are!). He wants us to accept the fact that the language of mathematics is spoken everywhere throughout the cosmos if we only listen carefully enough: “... ancient arithmetic and geometry were beginning to assume the role not so much of describing or simulating real things as offering a foundation for the very reality of which they were a part.”
So for Zellini, mathematics is the most real thing there is: “... we are faced with a great mass of knowledge [in mathematics] designed to capture the most internal and invisible – as well as the most real – aspect of the things that exist in nature.” This should give mathematicians comfort. The things they do are essentially revelatory and spiritual in nature. They see what others can’t, the essence of reality. We must listen.
This is, of course, all nonsense. It takes a very profound inferiority complex to make such outrageous claims. Zellini‘s issue seems to stem from the body-blow to mathematical certainty in the early 20th century. Essentially, mathematicians themselves showed that even elementary arithmetic could not be proven to be consistent in its own terms. Mathematics was constructed on foundations of sand; its coherence, much less its reality, was questionable.
But, thinks Zellini, there is a way to restore confidence in mathematics. The saving concept is the algorithm. “The concept of algorithm would inherit the sense of mathematical reality”, he thinks. In other words, what is real is not numbers per se, as Pythagoras and Plato thought, but a process by which numbers reveal what is actually there. Algorithm is the carrier, as it were, of reality: “... in order to be real , the very same mathematical entities [numbers] that have been constructed through a process of calculation must be capable of being thought of in the same way as efficient algorithms.”
The book has some interesting things to say about the ancient connections between mathematics and religion. And no doubt there are intriguing mystical aspects to mathematics. But it seems that for Zellini mathematics is indeed a religion in itself, and a highly dogmatic one at that. The algorithm is its creed. His references to ancient Vedic and Greek theological texts are not merely intellectually inspirational; these texts are sacred scripture. How Zellini can construe the reality of an algorithmic relationship as more real than the numbers which are part of that relationship is beyond what I am able to follow in his discursive arguments except as quasi-religious principles emanating from these texts.
What I am able to understand is a sort of neurotic compulsion to prove that mathematics is the ur-language of the universe. This is scientism, the thinker’s attempt at world domination. I can only recommend therapy, or escape to a sympathetic totalitarian country.
In their arguments, conspiracy theorists and religious fundamentalists reveal more about themselves than about their point of view. Sometimes so do really enthusiastic academic mathematicians like Zellini.They all typically want to make the point that the rest of us are persecuting them. What makes some mathematicians so defensive about their subject? Are they victims of derision on the street? Do their academic budgets suffer because of underestimation of their intellectual worth? Or did they just feel unloved as children?
Whatever the reason for the apparent existential crisis in mathematics, the solution proposed by books like this one is ridiculous. Zellini wants us to know not just how important mathematics is but also how real it is. For him mathematics is so real that it permeates the universe. It is a force that exists quite independently our thinking about it. And he wants us to appreciate this reality as much as any evangelical preacher wants us to believe on the Lord.
Zellini’s specific grievance that there is “distorted image of mathematics as a merely linguistic game” (He doesn’t name names, but you know who you are!). He wants us to accept the fact that the language of mathematics is spoken everywhere throughout the cosmos if we only listen carefully enough: “... ancient arithmetic and geometry were beginning to assume the role not so much of describing or simulating real things as offering a foundation for the very reality of which they were a part.”
So for Zellini, mathematics is the most real thing there is: “... we are faced with a great mass of knowledge [in mathematics] designed to capture the most internal and invisible – as well as the most real – aspect of the things that exist in nature.” This should give mathematicians comfort. The things they do are essentially revelatory and spiritual in nature. They see what others can’t, the essence of reality. We must listen.
This is, of course, all nonsense. It takes a very profound inferiority complex to make such outrageous claims. Zellini‘s issue seems to stem from the body-blow to mathematical certainty in the early 20th century. Essentially, mathematicians themselves showed that even elementary arithmetic could not be proven to be consistent in its own terms. Mathematics was constructed on foundations of sand; its coherence, much less its reality, was questionable.
But, thinks Zellini, there is a way to restore confidence in mathematics. The saving concept is the algorithm. “The concept of algorithm would inherit the sense of mathematical reality”, he thinks. In other words, what is real is not numbers per se, as Pythagoras and Plato thought, but a process by which numbers reveal what is actually there. Algorithm is the carrier, as it were, of reality: “... in order to be real , the very same mathematical entities [numbers] that have been constructed through a process of calculation must be capable of being thought of in the same way as efficient algorithms.”
The book has some interesting things to say about the ancient connections between mathematics and religion. And no doubt there are intriguing mystical aspects to mathematics. But it seems that for Zellini mathematics is indeed a religion in itself, and a highly dogmatic one at that. The algorithm is its creed. His references to ancient Vedic and Greek theological texts are not merely intellectually inspirational; these texts are sacred scripture. How Zellini can construe the reality of an algorithmic relationship as more real than the numbers which are part of that relationship is beyond what I am able to follow in his discursive arguments except as quasi-religious principles emanating from these texts.
What I am able to understand is a sort of neurotic compulsion to prove that mathematics is the ur-language of the universe. This is scientism, the thinker’s attempt at world domination. I can only recommend therapy, or escape to a sympathetic totalitarian country.
March 18, 2020
This is a fantastic book. It was hard to follow at the start, but I settled in quite nicely as I continued. The book dives into the philosophy of mathematics and sheds light on why things are the way they are, what it means to be real and what exists and what does not. Obviously the entire scope of the book centres on numbers in mathematics. I will definitely recommend this book to everyone, especially those that are interested in Numbers.
March 19, 2017
Paolo Zellini, almeno per un poveretto come me che non ha fatto le alte scuole, pone un problema di lettura. Io mi perdo sempre con tutte le sue citazioni di autori greci più o meno noti, e in questo caso mi sono anche trovato frammenti vedici che mi hanno completamente spiazzato e che confesso di non essere riuscito a comprendere. Tutto questo è un peccato, perché la tesi filosofica di base che Zellini presenta in questo testo meriterebbe di essere conosciuta. Secondo l'autore, gli antichi greci e indiani avevano infatti intuito il vero problema del passaggio dai numeri naturali a quelli irrazionali, vale a dire la crescita verso l'infinito come nel problema della duplicazione del cubo, non per nulla associata agli dèi. La cosa si può anche vedere pensando alle approssimazioni dei numeri irrazionali per mezzo di frazioni il cui numeratore e denominatore cresce sempre più. Il guaio è che a parte i frammenti vedici ho avuto spesso l'impressione che l'autore tendesse a ripetere lo stesso argomento solo con qualche minuscola variante, e quindi non capivo l'utilità delle ulteriori pagine.
Dal capitolo 16 in poi mi sono trovato molto più a mio agio, il che non è poi così strano perché siamo tornati in un terreno che mi è abbastanza noto, la complessità ed efficienza degli algoritmi (Nota personale: all'università ho seguito per mia curiosità alcune lezioni sulla complessità algoritmica, tenuta da un giovane professore di matematica, per l'appunto Zellini) Vedendo la cosa da un punto di vista filosofico, qui Zellini mostra gli stretti rapporti tra questi algoritmi - che dobbiamo tenere sott'occhio quando li implementiamo, perché rischiamo che le approssimazioni di rappresentazione del calcolatore ci impediscano di arrivare a una risposta anche solo approssimata - e i guai notati già dagli antichi. Non aspettatevi una lettura leggera, insomma.
Dal capitolo 16 in poi mi sono trovato molto più a mio agio, il che non è poi così strano perché siamo tornati in un terreno che mi è abbastanza noto, la complessità ed efficienza degli algoritmi (Nota personale: all'università ho seguito per mia curiosità alcune lezioni sulla complessità algoritmica, tenuta da un giovane professore di matematica, per l'appunto Zellini) Vedendo la cosa da un punto di vista filosofico, qui Zellini mostra gli stretti rapporti tra questi algoritmi - che dobbiamo tenere sott'occhio quando li implementiamo, perché rischiamo che le approssimazioni di rappresentazione del calcolatore ci impediscano di arrivare a una risposta anche solo approssimata - e i guai notati già dagli antichi. Non aspettatevi una lettura leggera, insomma.
October 4, 2021
"... Hence algorithmic constructability and efficiency are both requisite when establishing an ontology of numbers." is probably the sentence I'd choose as representative of the book, I mean its slightly interesting second half (and for the easily distracted, I would add that the very same sentence would probably be a good candidate for the SIP ("Statistically improbable phrases") section of the book's Amazon.com page, that is, if only Amazon.com didn't remove that wonderful feature and making newcomers scratch their head when they come across music albums such as "Statistically Improbable Phrases" by Kim Cascone (who, by the way, happens to be a composer that gave a workshop in Istanbul Bilgi University back in 2008, followed by a concert, focused on the topic of creating digital music by employing genetic algorithms). OK, enough with distractions! But you get the idea, don't you!?)
What I'm trying to say can be summarized along the lines of "why are you doing this to me professore?" I mean, if you feel equally at home with calculus, as well as with Vedic texts, ancient Greek philosophy, Kant, Nietzsche, Knuth, and error analysis of numerical methods, you should be considered smart enough to hire a good editor. And you need one, trust me, you need a very good editor if you're planning on writing this kind of book!
Maybe it's about the translation, I don't know. I'm not a native Italian speaker. Native Italian speakers who also had basic university level mathematics training and still has the passion to delve into the history of math, logic and philosophy should help us readers of the English translation: is the book, at least its first half equally problematic in its original?
I really wanted to like this book. I still do. But come on, who is your audience dear professor? And what exactly is it that you're trying to say? Why do you leave so many things hanging up in the air, while jumping from one name to another, one topic to another. Did I mention the need for an editor? Yes...
Not everything is negative though: the author's perspective on Wiener-Hopf integral equations, and his drawing attention to the differences in the concept of time in physics and concept of time in cybernetics, and then jumping to the topic of Toeplitz matrices, connecting (or forcing us to build some connections) to self-similarity, recurrence, etc. was a nice touch. This chapter, as well as the following few ones towards the end of the book managed to be more readable.
I have a strong feeling that this book needs to be reorganized and rewritten because then it would be probably considered a good addition to the popular literature on philosophy of mathematics.
Oh, by the way, the last chapter: he did it again! For god's sake, how does the work of Oskar Perron relate to PageRank algorithm? I mean, ok, Perron–Frobenius theorem, and so forth, but you don't say this in passing, leave it at that, then jump to a totally different topic by referring to some personal communication with Perron and abruptly finish the book in a few sentences, because... because we were talking about the ontological status of numbers and now it's PageRank without mentioning its name and then it's about some personal convictions of a German mathematician. Have some pity on the poor reader dear author, will you!
Now, dear reader, if you go and read this book after this review, at least I'm not the one to blame! But if you don't, then I hope you found a much better use of your limited time in this world.
What I'm trying to say can be summarized along the lines of "why are you doing this to me professore?" I mean, if you feel equally at home with calculus, as well as with Vedic texts, ancient Greek philosophy, Kant, Nietzsche, Knuth, and error analysis of numerical methods, you should be considered smart enough to hire a good editor. And you need one, trust me, you need a very good editor if you're planning on writing this kind of book!
Maybe it's about the translation, I don't know. I'm not a native Italian speaker. Native Italian speakers who also had basic university level mathematics training and still has the passion to delve into the history of math, logic and philosophy should help us readers of the English translation: is the book, at least its first half equally problematic in its original?
I really wanted to like this book. I still do. But come on, who is your audience dear professor? And what exactly is it that you're trying to say? Why do you leave so many things hanging up in the air, while jumping from one name to another, one topic to another. Did I mention the need for an editor? Yes...
Not everything is negative though: the author's perspective on Wiener-Hopf integral equations, and his drawing attention to the differences in the concept of time in physics and concept of time in cybernetics, and then jumping to the topic of Toeplitz matrices, connecting (or forcing us to build some connections) to self-similarity, recurrence, etc. was a nice touch. This chapter, as well as the following few ones towards the end of the book managed to be more readable.
I have a strong feeling that this book needs to be reorganized and rewritten because then it would be probably considered a good addition to the popular literature on philosophy of mathematics.
Oh, by the way, the last chapter: he did it again! For god's sake, how does the work of Oskar Perron relate to PageRank algorithm? I mean, ok, Perron–Frobenius theorem, and so forth, but you don't say this in passing, leave it at that, then jump to a totally different topic by referring to some personal communication with Perron and abruptly finish the book in a few sentences, because... because we were talking about the ontological status of numbers and now it's PageRank without mentioning its name and then it's about some personal convictions of a German mathematician. Have some pity on the poor reader dear author, will you!
Now, dear reader, if you go and read this book after this review, at least I'm not the one to blame! But if you don't, then I hope you found a much better use of your limited time in this world.
July 2, 2023
I had high hopes of gaining insights into the intersection of mathematics and human culture. Unfortunately, my experience left much to be desired, and I was underwhelmed by the author's approach.
One of the book's major shortcomings lies in its inability to strike a harmonious balance between accessibility and depth. While it claims to be a cultural history, it often delves into complex mathematical concepts without providing adequate explanations or context for readers who may not possess an extensive background in mathematics. This lack of clarity turns the book into an arduous read for those seeking a more general understanding and then hoping to follow some of the topics the book explores later on.
That being said, the book does have its moments of intrigue. I found the exploration of our early connection to mathematics through religion particularly interesting. There was the mystical aspects of mathematics in ancient civilisations and it was refreshing to see how mathematics was intertwined with the spiritual beliefs of our ancestors.
I believe that mathematics serves as a powerful tool for understanding and finding the deepest secrets of our universe, as the book suggests in its discussion of algorithms. However, I view the numbers and inputs we use in mathematics merely as a syntax we have developed to help us create and express those relationships. They are not an inherent, immutable truth but a human construct. So in my opinion I felt some of the arguments made in the book were a bit much. Perhaps if I understood more of what I was reading I could offer a better insight. Any reviewers who liked this book are welcome to comment and say I didn’t get it, they would be right
One of the book's major shortcomings lies in its inability to strike a harmonious balance between accessibility and depth. While it claims to be a cultural history, it often delves into complex mathematical concepts without providing adequate explanations or context for readers who may not possess an extensive background in mathematics. This lack of clarity turns the book into an arduous read for those seeking a more general understanding and then hoping to follow some of the topics the book explores later on.
That being said, the book does have its moments of intrigue. I found the exploration of our early connection to mathematics through religion particularly interesting. There was the mystical aspects of mathematics in ancient civilisations and it was refreshing to see how mathematics was intertwined with the spiritual beliefs of our ancestors.
I believe that mathematics serves as a powerful tool for understanding and finding the deepest secrets of our universe, as the book suggests in its discussion of algorithms. However, I view the numbers and inputs we use in mathematics merely as a syntax we have developed to help us create and express those relationships. They are not an inherent, immutable truth but a human construct. So in my opinion I felt some of the arguments made in the book were a bit much. Perhaps if I understood more of what I was reading I could offer a better insight. Any reviewers who liked this book are welcome to comment and say I didn’t get it, they would be right
June 6, 2021
Interessante, ma troppo complicato per me.
December 1, 2020
I only got 25% of the way into this book before I found that whole pages were failing to make sense to me. The thesis is fascinating - that the roots of mathematical thought lie in the contemplation and worship of the gods - & I was content for a time to be carried along by Zellini's potent mixture of maths and philosophy, even though I wasn't understanding all of it. But finally it got too much for me - and I do read a great deal of popular science. This is not that kind of book. So beware ... but it exercises the mind.
Read
September 29, 2021DROPPED!!
This was a quite anticipated book for me, but turned out to be unbelievably disappointing. Listened to 30% of it three times to figure out the points of the author, but every time it sounded even more gibberish! I won't criticize the author though, since I'm no expert on the topic and I defiantly won't be! Paolo Zellini knows how to make a great idea into one of the least interesting books ever.
This was a quite anticipated book for me, but turned out to be unbelievably disappointing. Listened to 30% of it three times to figure out the points of the author, but every time it sounded even more gibberish! I won't criticize the author though, since I'm no expert on the topic and I defiantly won't be! Paolo Zellini knows how to make a great idea into one of the least interesting books ever.
March 9, 2024
2.5. I prefer "Brief history of the infinite" (worth reading), which offers more insights and nuances (and a linear discourse). In fact this book seems as a reduction of Zellini's best insights... Furthermore I don't engage with his style of writing, sometimes opaque for those not acquainted with the praxis of maths.
Anyway, this book has to be read with caution: it is not easy to grasp the intention of Zellini...Speculation? Scientism? Religion?. I won't take it as a defence of the misticism and absolute truth of maths, although some readers interpret that. Zellini quotes Veda's texts, Poincare, Bergson and Heidegger with respect, which clearly indicates openness and diversity of trends. He doesn't also deny Quine contributions against Cantor and Rusell's logicism.
In my opinion it is just an essay to reflect about the trascendence of maths during western history and how it has been put into relation with physics and reality...written by a math lover. The problem of this book is that, although some interesting insights can be found, he stays halfway...It lacks clarifications and anthropological grounds.
I recommend better to read, in addition to "Brief history of the infinite" (Zellini), authors such as John Barrow, Ian Hawkings and Enmanuel Lizcano. Different authors with different perspectives about maths (misticism, philosophy, constructivism...).
Anyway, this book has to be read with caution: it is not easy to grasp the intention of Zellini...Speculation? Scientism? Religion?. I won't take it as a defence of the misticism and absolute truth of maths, although some readers interpret that. Zellini quotes Veda's texts, Poincare, Bergson and Heidegger with respect, which clearly indicates openness and diversity of trends. He doesn't also deny Quine contributions against Cantor and Rusell's logicism.
In my opinion it is just an essay to reflect about the trascendence of maths during western history and how it has been put into relation with physics and reality...written by a math lover. The problem of this book is that, although some interesting insights can be found, he stays halfway...It lacks clarifications and anthropological grounds.
I recommend better to read, in addition to "Brief history of the infinite" (Zellini), authors such as John Barrow, Ian Hawkings and Enmanuel Lizcano. Different authors with different perspectives about maths (misticism, philosophy, constructivism...).
July 18, 2020
Este libro requiere de una base matemática muy sólida para disfrutarlo al 100%. Algunos capítulos se me han hecho muy amenos, otros sin embargo se me atragantaron. He subrayado mucho y he tenido que tirar de internet en ocasiones, a pesar de que el libro en general está muy bien explicado, con numerosas notas al margen, bibliografía, etc. El autor demuestra ser un gran erudito de la historia de la ciencia matemática desde los sabios griegos hasta nuestros días, y lo sabe transmitir. Un libro muy entretenido, para leer despacito.
July 11, 2024
Loved it. A lot of questions asked that I never even thought to consider at the heart of mathematics. Will return to it in the future for sure!
April 16, 2019
Cartea urmareste relatia dintre conceptul de numar si cresterea numerelor si conceptul contemporan de algoritm, respectiv utilizarea algoritmilor in informatica teoretica si in ingineria calculatoarelor.
Intrebandu-se cum se naste matematica, autorul face legatura intre primele religii ale civilizatiilor stravechi si necesitatea lor de a construi temple din ce in ce mai mari, dar identice cu teorii matematice antice (geometria lui Euclid) si cu teorii moderne (e.g. binomul lui Newton) pe care le priveste de fapt ca reformulari ale unor probleme stravechi.
Apoi, autorul abordeaza intrebari cum ar fi: este matematica o inventie sau o descoperire, este o realitate sau un formalism, poate fi rmatematica dedusa din logica?, ceea ce ii da prilejul sa vorbeasca despre criza fundamentelor matematicii de la inceputul secolului 20, paradoxurile lui Zenon, modul de aparitie a conceptelor de numere rationale, irationale sau reale si legatura lor cu filosofia si conceptele de timp, aruncand o lumina noua asupra lucrarilor lui Euclid, Dedekind, Weierstrass, Newton, Gauss, Cramer sau Cantor.
Unele dintre problemele abordate sunt accesibile unui cititor familiarizat cu matematica de liceu, cele mai multe insa necesita cunostinte de matematici speciale specifice facultatilor in care se studiaza matematica la un nivel avansat. Aceasta face cartea greu accesibila unui public general, ceea ce mi se pare principalul neajuns al cartii.
Totusi, cartea ar putea fi folosita pentru introducerea unor lectii de matematica, de la binomul lui Newton, introducerea numerelor irationale (radacina patrata a lui 2), la conceptul de limita, matrice, determinant sau numar real, in clase cu elevi care se intreaba care este rostul tuturor acestor concepte matematice.
Intrebandu-se cum se naste matematica, autorul face legatura intre primele religii ale civilizatiilor stravechi si necesitatea lor de a construi temple din ce in ce mai mari, dar identice cu teorii matematice antice (geometria lui Euclid) si cu teorii moderne (e.g. binomul lui Newton) pe care le priveste de fapt ca reformulari ale unor probleme stravechi.
Apoi, autorul abordeaza intrebari cum ar fi: este matematica o inventie sau o descoperire, este o realitate sau un formalism, poate fi rmatematica dedusa din logica?, ceea ce ii da prilejul sa vorbeasca despre criza fundamentelor matematicii de la inceputul secolului 20, paradoxurile lui Zenon, modul de aparitie a conceptelor de numere rationale, irationale sau reale si legatura lor cu filosofia si conceptele de timp, aruncand o lumina noua asupra lucrarilor lui Euclid, Dedekind, Weierstrass, Newton, Gauss, Cramer sau Cantor.
Unele dintre problemele abordate sunt accesibile unui cititor familiarizat cu matematica de liceu, cele mai multe insa necesita cunostinte de matematici speciale specifice facultatilor in care se studiaza matematica la un nivel avansat. Aceasta face cartea greu accesibila unui public general, ceea ce mi se pare principalul neajuns al cartii.
Totusi, cartea ar putea fi folosita pentru introducerea unor lectii de matematica, de la binomul lui Newton, introducerea numerelor irationale (radacina patrata a lui 2), la conceptul de limita, matrice, determinant sau numar real, in clase cu elevi care se intreaba care este rostul tuturor acestor concepte matematice.
December 14, 2016
Spesso, quando mi trovo a leggere dei saggi, ho l'abitudine di annotarmi e/o condividere i passaggi che ritengo più interessanti.
Con La matematica degli dèi e gli algoritmi degli uomini di Paolo Zellini la cosa mi rimane difficile perché, un po' come la storia della mappa di Borges, il risultato delle mie annotazioni tendono essere una mappa uno a uno e a coincidere con il libro stesso.
Con La matematica degli dèi e gli algoritmi degli uomini di Paolo Zellini la cosa mi rimane difficile perché, un po' come la storia della mappa di Borges, il risultato delle mie annotazioni tendono essere una mappa uno a uno e a coincidere con il libro stesso.
Read
September 16, 2023An interesting, albeit dense book that requires a solid foundation in theoretical mathematics (which I absolutely do not have).
My understanding/ thoughts are as follows:
1. what is applied mathematics?
The thesis is that applied mathematics, i.e. the mathematics that combines the theoretical concepts in mathematics to understanding physical events, is a combination of reasoning and calculation. The combination of theoretical assumptions underpinning the use of mathematical equations is combined with the actual algorithms and operations used to solve the problems to end up in an approximation of the physical natural environment.
2. what is the nature of mathematics
To that end, because it is an approximation but also because it represents aspects of the natural world, it is a reality unto its own and not just a consolidated thought or concept. It exists in the tangible way that we understand nature, in part because the relativity between distances and physical objects are quantified in standard manners through mathematics
3. what is computational mathematics
the issue behind computational mathematics is that as algorithms expand and grow, so does 1) the computational power to arrive at the actual solution (i.e. the computational complexity) and; 2) the approximations needed to get at that solution, resulting in an exponential increase in the error of the system and loss of reliability of the algorithm.
Computational mathematics used principles originating from as early as the Vedas, whereby the growth of proportional vedic altars (specifically that worshipping Agni) were calculated. This principle of arithmetical continuum continues to underpin computational mathematics today
My understanding/ thoughts are as follows:
1. what is applied mathematics?
The thesis is that applied mathematics, i.e. the mathematics that combines the theoretical concepts in mathematics to understanding physical events, is a combination of reasoning and calculation. The combination of theoretical assumptions underpinning the use of mathematical equations is combined with the actual algorithms and operations used to solve the problems to end up in an approximation of the physical natural environment.
2. what is the nature of mathematics
To that end, because it is an approximation but also because it represents aspects of the natural world, it is a reality unto its own and not just a consolidated thought or concept. It exists in the tangible way that we understand nature, in part because the relativity between distances and physical objects are quantified in standard manners through mathematics
3. what is computational mathematics
the issue behind computational mathematics is that as algorithms expand and grow, so does 1) the computational power to arrive at the actual solution (i.e. the computational complexity) and; 2) the approximations needed to get at that solution, resulting in an exponential increase in the error of the system and loss of reliability of the algorithm.
Computational mathematics used principles originating from as early as the Vedas, whereby the growth of proportional vedic altars (specifically that worshipping Agni) were calculated. This principle of arithmetical continuum continues to underpin computational mathematics today
This entire review has been hidden because of spoilers.
November 17, 2024
I must respectfully disagree with the negative assessments of this book, because they have neglected to discuss the final chapters in which Zellini distances himself from the traditional Pythagorean-Platonic perspective. In fact, regarding reality, Zellini argues that only those mathematical conceptions whose measure is in correspondence with an effective algorithm for calculation, and thus for representation of the thing itself, have reality. For example, Zellini provides examples of transcendental decimal sequences whose sequences of zeros grow factorially fast and thus cannot be represented in any effective way. I found this presentation to be nuanced and I came away with a new perspective on mathematics and its correspondence with reality, which is a prime point of meditation for any scientist. I read the book in the original Italian, so it is possible that something was lost in translation. Otherwise, I feel that the negative reviews did not read the entire book, because if one stopped halfway through they might come away with that perspective. But in fact, the nuance presented by Zellini will surprise you. I recommend this book wholeheartedly!
December 3, 2023
Good maths book, but some motivation is required, it is not light reading.
There are numerous references to philosophical and mathematical greats, wihich sometimes require a 2nd read or some thought to understand what the author is talking about, especially as an initiate.
It seems to work it's way from some of the ratio\ pattern based systems from indian and ancient greek all the way up to modern day alogorithms and matrices : Which is preciely what it says on the book cover!
Structure seems compemporarily logical to me: i.e. Religious then rational. Simplicity to the complex. Then Chonologically viz, the modern stuff later.
I wont claim to understand all of it, but it certainly gives one more interest and motivation to understand mathematics more; pure or logic.
The author did well at describing various things and had a vast quantity of classical and modern resources at his disposal ; I like this sort of non-fiction.
He also made a point of writing less than more in many areas, where some chapters were relatively short; given to the abstractness of the subject.
There are numerous references to philosophical and mathematical greats, wihich sometimes require a 2nd read or some thought to understand what the author is talking about, especially as an initiate.
It seems to work it's way from some of the ratio\ pattern based systems from indian and ancient greek all the way up to modern day alogorithms and matrices : Which is preciely what it says on the book cover!
Structure seems compemporarily logical to me: i.e. Religious then rational. Simplicity to the complex. Then Chonologically viz, the modern stuff later.
I wont claim to understand all of it, but it certainly gives one more interest and motivation to understand mathematics more; pure or logic.
The author did well at describing various things and had a vast quantity of classical and modern resources at his disposal ; I like this sort of non-fiction.
He also made a point of writing less than more in many areas, where some chapters were relatively short; given to the abstractness of the subject.
September 29, 2019
Very hard to understand something without a lot of background knowledge. Also, it's written in a very "personal heavy" style (meaning: lot's of personal opinions) which sometimes makes it difficult to follow the argumentation or to know what's a fact and what's an opinion. I think this book has the potential to be a treasure trove for experts because it can give them new insights into old problems.
July 9, 2025
Ja pirmās divas nodaļas patiesi ir kultūras vēsture, bet pārējās 3/4 grāmatas ir savstarpēji nesaistītas nodaļas, kurās autors brīvi apraksta matemātiskus konceptus tīri matemātiskā kontekstā, tad grāmatu saukt (un to virzīt kā) kultūras vēsturi ir maldinoši. Grāmatas kopīgajai domai ar lielu potenciālu trūkst gan kopīga virziena, gan mērķa, papildus autoram izvairoties no, iespējams, svarīgākā pienesuma diskusijās par matemātikas saistību ar pasauli – Gēdela otrās un trešās propozīcijas.
July 25, 2025
Id love to pretend i loved this and understood it . Far from the truth. Opened some very thought provoking philosophical ideas, my brain just isnt smart enough (and if i was kinder to myself / more arrogant, perhaps id say more patient) to fully comprehend
Still nice to listen along and tune in when my brain could absorb
Still nice to listen along and tune in when my brain could absorb
April 14, 2019
Interessante ma inutile per chi conosce il campo anche solo attraverso strumenti leggermente più profondi e precisi. La lettura è intriso di un gran significato filosofico, ma la lettura non è così piacevole come pensavo.
January 22, 2021
O dezamagire. Singurele fraze pe care le-am inteles sunt cele de pe spatele cartii. Exagerez, desigur, dar nu cu mult.
Nu va apucati de carte daca nu aveti cunostinte solide de filosofie si matematica.
Nu va apucati de carte daca nu aveti cunostinte solide de filosofie si matematica.
June 7, 2023
Le tengo que poner 3 estrellas porque me ha costado mucho entender bien muchas cosas. Muy filosófico y específico aunque interesante y seguramente da para reflexionar sobre el origen y el valor abstracto y concreto de los números.
June 1, 2021
Audio book: Audio quality: Excellent, Narration: Excellent
An interesting book about philosophy and mathematics. I really enjoyed it,even though I usually steer clear of mathematics.
An interesting book about philosophy and mathematics. I really enjoyed it,even though I usually steer clear of mathematics.
June 23, 2021
2.7 🌟 / 5
I don't know when it started, but at some point I kept asking myself why I was reading this, and what the point of the book was.
I don't know when it started, but at some point I kept asking myself why I was reading this, and what the point of the book was.
August 14, 2021
The subject was such a great idea. Unfortunately the execution was painfully boring. Such a missed opportunity...
July 2, 2022
I don't think I'm smart enough to understand it yet, but also written in a confusing way and lacking a clean structure.
September 27, 2022
comprehensive and conceptual history of maths and its very intimate relationship with logic. needed a stronger structure but interesting nonetheless.
May 13, 2023
This is not written for the layperson. It was a difficult read. You need to be a maths geek and maybe, just maybe, you'll enjoy this.
August 21, 2023
Lettura pesante e noiosa, non sono riuscito a finirlo
This entire review has been hidden because of spoilers.
April 11, 2025
Interesting, but - no real conclusion, tiptoed around many ideas. However, it made me think about things and engage in mathematic so that was nice. Paradoxes are playful.
Displaying 1 - 30 of 33 reviews