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Journey through Genius: The Great Theorems of Mathematics
Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician
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Paperback, 320 pages
Published
August 1st 1991
by Penguin Books
(first published 1990)
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(showing 1-30)
The preface to this book contains the following explanation, which I think suffices to explain its reason for being:
"For disciplines as diverse as literature, music, and art, there is a tradition of examining masterpieces -- the "great novels", the "great symphonies", the "great paintings" -- as the fittest and most illuminating objects of study. Books are written and courses are taught on precisely these topics in order to acquaint us with some of the creative milestones of the discipline and w ...more
"For disciplines as diverse as literature, music, and art, there is a tradition of examining masterpieces -- the "great novels", the "great symphonies", the "great paintings" -- as the fittest and most illuminating objects of study. Books are written and courses are taught on precisely these topics in order to acquaint us with some of the creative milestones of the discipline and w ...more
The title is a fair description: Dunham presents highlights from math history as great works of art. He carries this analogy through the book consistently, for example identifying Georg Cantor (-1918) as the mathematical parallel of his contemporary Vincent van Gogh.
Dunham has done an excellent job of selecting exemplary theorems that can be explained to an interested reader having no special mathematical training, that are associated with the most greatest mathematicians of all time, and that i ...more
Dunham has done an excellent job of selecting exemplary theorems that can be explained to an interested reader having no special mathematical training, that are associated with the most greatest mathematicians of all time, and that i ...more
The math history presented is very good. The mathematical exposition is uneven. Some of it is good and some not so good.
The chapter I had the most difficulty with was the one on Heron's formula. Theorems are presented without any indicator of where they are headed. Dunham keeps promising that the formula will eventually be derived, but I gave up beforehand.
The other chapter I would criticize is the one on Euler's number theory, but for different reasons. In developing Fermat's Little Theorem, ...more
The chapter I had the most difficulty with was the one on Heron's formula. Theorems are presented without any indicator of where they are headed. Dunham keeps promising that the formula will eventually be derived, but I gave up beforehand.
The other chapter I would criticize is the one on Euler's number theory, but for different reasons. In developing Fermat's Little Theorem, ...more
I finally finished this book! It's been a long time coming. I've owned it for almost ten years. I finally picked it up to read a few months ago. I don't know why I waited so long. It's a real gem. The main reason it took me so long to get through is the format. You can read it a chapter at a time, as you have time, and read other books in between, etc, and it really doesn't matter. I'd read a chapter, then read other books, then read another chapter, etc. Each chapter is about one of the more im
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This was a class book for a 'History of Math' course I took during my undergrad and it remains one of the few books from that era in my life that I actually return to now and then... Geeky, sure. Dorky, definitely, but this book provides a fascinating account of how advances in mathematics follows progress in civilization and vice versa.
From everybody's favorite theorem (the Pythagorean theorem that is) to the dreaded nightmare-inducing calculus (thank you, Sir Isaac Newton!) and beyond this li ...more
From everybody's favorite theorem (the Pythagorean theorem that is) to the dreaded nightmare-inducing calculus (thank you, Sir Isaac Newton!) and beyond this li ...more
What a merry walkthrough over the work of History’s mathematical geniuses!, faith in Humanity: Restored!
And in Bertrand Russels's words: Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
And in Bertrand Russels's words: Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
At times the proofs can be a little hard to follow, but the book was definitely written for the layman with some calculus background. However, since the book covers such diverse mathematical topics, it is difficult to fully appreciate every theorem. The author does try to present every theorem in its historical context and give background on the great minds of the discoverers.
The most striking point of the entire book to me was how miserable the vast majority of the featured mathematicians lives ...more
The most striking point of the entire book to me was how miserable the vast majority of the featured mathematicians lives ...more
A book about mathematics, written for the layman, but with some pretty deep math in there. As someone who likes math, this book was fascinating. A lot of it was about famous proofs I was already familiar with (Euclid's infinite primes, Cantor's diagonalization) but it was still really cool to read about them again. Dunham's tone is casual and fun, and even if the historical/biographical bits didn't seem very rigorous, the book was still very fun to read. I would definitely recommend it to anyone
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In Journey through Genius, William Dunham introduced some of the most influential mathematicians in history alongside explanations for one or two of their most profound discoveries in math. Journey through Genius gives a historical context for the mathematicians and their discoveries, and tries to convince the reader of the greatness of the discovery—the worthiness, as it may be, for why that piece of mathematical history has made it into this book. While the content provided in Journey through
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Bad habits die hard, so let's start with a quotation, shall we? Make it a double one, since in the book, it originally is a quotation already. (And, like I said, bad habits die hard, so this is actually the conclusion of the book.)
Mathematics, rightly viewed, possesses not only truth, but supreme beauty -a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a ster...more
"Already uneasy over the foundations of their subject, mathematicians got a solid dose of ridicule from a clergyman, Bishop George Berkeley (1685-1753). Bishop Berkeley, in his caustic essay 'The Analyst, or a Discourse addressed to an Infidel Mathematician,' derided those mathematicians who were ever ready to criticize theology as being based upon unsubstantiated faith, yet who embraced the calculus in spite of its foundational weaknesses. Berkeley could not resist letting them have it:
'All the ...more
'All the ...more
When you stop to think about it, this is actually a really impressive book. Without assuming any math background beyond high-school-level algebra and geometry, Dunham presents a condensed history of mathematics from Ancient Greece up through 1900s Europe. What's more, that isn't even his main focus! The point of the book is to detail to some of the greatest mathematical masterpieces from that history-- from Euclid's geometric constructions and infinite primes up through Cantor's diagonal argumen
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Viaje a través de los genios es un viaje apasionante por la historia de las matemáticas y de los matemáticos. William Dunham expone en 12 capítulos, 12 grandes teoremas matemáticos. Lo hace explicando las vidas de los matemáticos que los pensaron y el momento de la historia en el que lo hicieron. Con gran entusiasmo y admiración hacia estos genios. Dunham tiene el acierto de incluir las demostraciones de estos teoremas, a la vez que lo hace de manera clara y comprensible. No sólo explica la hist
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Loved it. Great exposition of some of the best ideas in the history of mathematics. I've seen some other books like this, but this is the first one that really explains the way the Greeks did their mathematics. I've seen Euclid's proof of the Pythagorean Theorem before, but this is the first time it really made sense, and the first time I understood why Euclid had to prove it that way: he had no concept of what we would call algebra. For him a square was just that, and the theorem isn't a^2 + b^
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Overall, I liked the book but there were a few things that detracted from the experience. It gives a lot of historical context from a broad perspective, and does a great job of foreshadowing (this mathematician shows up later in chapter 6, etc.) and referencing back to prior material. The author even draws comparisons and points out parallels between the evolution of art and mathematics. I found the math easy to follow and engaging.
Now for the downsides:
First, this book claims to be geared at so ...more
Now for the downsides:
First, this book claims to be geared at so ...more
Di storie della matematica ce ne sono davvero tante. Ma questa è un po' particolare. Dunham ha pensato infatti di strutturarla a partire dai grandi matematici della storia e soprattutto a partire da alcuni dei loro risultati più famosi. Iniziamo così dalla quadratura della lunula da parte di Ippocrate di Chio per arrivare a Cantor e ai suoi numeri transfiniti. I teoremi sono però solo la parte centrale dei capitoli, che parlano anche della vita del loro dimostratore e del contesto sia storico ch
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If you are reading this for general interest, it is a nice survey of the history of mathematics with each of the 12 chapters highlighting a theorem of particular importance. The history of mathematics between these "Great Theorems" is covered in the conclusion of the chapter or the introduction to the next. Each chapter also has an epilogue exploring some topic or historical figure related to the subject of the chapter.
I use this book when I teach History of Mathematics. It is written for a gen ...more
I use this book when I teach History of Mathematics. It is written for a gen ...more
This. This is why I believe in God.
From chapter 1:
In this sense, quadrature represented not only the triumph of human reason, but also the inherent simplicity and beauty of the universe itself.
Some great stories about geniuses who shaped the world of mathematics. Of course, some of these folks were a bit demented. Cardano (chapter 6) who geometrically, rather than algebraically, solved x^3 + mx = n in the 16th century was borderline insane. Isaac Newton shoved sticks behind his eyes to study ...more
From chapter 1:
In this sense, quadrature represented not only the triumph of human reason, but also the inherent simplicity and beauty of the universe itself.
Some great stories about geniuses who shaped the world of mathematics. Of course, some of these folks were a bit demented. Cardano (chapter 6) who geometrically, rather than algebraically, solved x^3 + mx = n in the 16th century was borderline insane. Isaac Newton shoved sticks behind his eyes to study ...more
Dunham does the field of mathematics a great service in this concise and entertaining history of the subject. Journey through Genius was one of the quickest reads I've ever had thanks to Dunham's intelligent-but-fun writing style. He does here what every math course I've ever taken failed to do: He provides the interested student with some context for the great theorems which we encounter over the years, from the times and cultures in which they were discovered to the characters who discovered t
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A fantastic overview of math history. I would have liked to set the math in context with the history of the times, but there was just enough of that to keep me happy. I found several short easy projects that I could do with my students, a wealth of math quotes to make a nerd swoon, and a couple of interesting discussions. For people afraid of math, I assure you, you can read the opening part of each chapter, get a sense for the historical context and significance and than skip on. The math has b
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This is one of my favourite books of all time. Although I have a degree in Mathematics I learned a lot from it, although you need no more than a rudimentary knowledge of mathematics to understand it (plus a fair amount of concentration).
The book is worth the price even if you only read the amazing geometric proof of Heron's formula. Heron seems to wander all over the place making apparently pointless constructions, but then brings everything together and suddenly pulls the rabbit out of the hat, ...more
The book is worth the price even if you only read the amazing geometric proof of Heron's formula. Heron seems to wander all over the place making apparently pointless constructions, but then brings everything together and suddenly pulls the rabbit out of the hat, ...more
I love the concept of this book, and I very much enjoyed the theorems included in it. It's given me an appreciation for what Math is really about--which is no insignificant feat.
On the other hand, I have to admit that it wasn't quite watered-down enough for me. There were plenty of places where I lost the thread of what was going on. Mostly, this happened when the author explained a concept in words (usually in a completely comprehensible way), and then said something like "which, of course, gi ...more
On the other hand, I have to admit that it wasn't quite watered-down enough for me. There were plenty of places where I lost the thread of what was going on. Mostly, this happened when the author explained a concept in words (usually in a completely comprehensible way), and then said something like "which, of course, gi ...more
This book is a history of math, via the great theorems of math.
So much fun. Readable anecdotes about the lives of the great mathematicians interspersed with lucid explanation of their greatest proofs. So often in school, the historical context is lost, which is a shame! How can one appreciate Euler's solution to the Basel Problem without knowing the earlier attempts by the Bernoullis and others to solve it?
The author is a master at explaining complex proofs. The Basel Problem, the Cantor Sets - ...more
So much fun. Readable anecdotes about the lives of the great mathematicians interspersed with lucid explanation of their greatest proofs. So often in school, the historical context is lost, which is a shame! How can one appreciate Euler's solution to the Basel Problem without knowing the earlier attempts by the Bernoullis and others to solve it?
The author is a master at explaining complex proofs. The Basel Problem, the Cantor Sets - ...more
I think this book is a masterpiece! W. Dunham describes the history of mathematics by going over some of the most remarkable theorems and ideas along with their inventors and proofs. The book begins on Hippocrates' quadrature of the lune and ends on Cantor's infinite sets and one may just stand and wonder at the genius and creativity of people described in the book. The book is fun to read as it includes aspects satisfiable to all kind of readers and knowledge seekers. It talks about theorems, e
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This was a good book, but I wasn't the target audience---it was aimed at a more lay audience. He wanted to present the history of mathematics with major theorems as touchstones. He (sort of, mostly) proved the theorems, put them in context, and discussed what followed. But he was hamstrung by needing to keep to theorems that he could prove with HS algebra.
Still, some cool stuff. Some very clever ways of proving the convergence of the harmonic series. And I hadn't seen Archimedes' proof that the ...more
Still, some cool stuff. Some very clever ways of proving the convergence of the harmonic series. And I hadn't seen Archimedes' proof that the ...more
This is a great book. The idea of presenting important mathematical results in a historical context is certainly not new, but Dunham's execution is notable. The history he includes is engaging and fits together into an overall narrative. His presentation of the math was equally well selected, as his choice of theorems allowed him to explore everything in an elementary manner. Those results he does offer without proof, which for the most part occur in the historical sections, are stated simply an
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I loved this book! I have re-read it several times. I have a fascination with geniuses (or genii, for you Latin snobs) and the wonderful legacies they leave to the rest of us mere mortals. Whether their field of interest was music, science, math, or literature, I find great inspiration in hearing their life stories and studying their works.
This book satisfied me on both counts. The biographical information about each mathematician enlightened me about their historical context and their humanity ...more
This book satisfied me on both counts. The biographical information about each mathematician enlightened me about their historical context and their humanity ...more
Journey through Genius: The Great Theorems of Mathematics
This book really has a niche audience. Anyone who is a math or math-history enthusiast will love this book. There are mathematical concepts here that are not "toned down" but nothing extreme. The average reader would probably struggle through this book but the average math enthusiast wouldn't have any trouble.
Did I enjoy this book? Yes.
Would I recommend it? Only to someone familiar with calculus level math or higher.
This book really has a niche audience. Anyone who is a math or math-history enthusiast will love this book. There are mathematical concepts here that are not "toned down" but nothing extreme. The average reader would probably struggle through this book but the average math enthusiast wouldn't have any trouble.
Did I enjoy this book? Yes.
Would I recommend it? Only to someone familiar with calculus level math or higher.
topics | posts | views | last activity | |
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Madison Mega-Mara...: #29 Journey Through Genius: The Great Theorems of Mathematics by William Dunham | 3 | 3 | Mar 26, 2015 06:03PM | |
calculus | 1 | 17 | Jun 07, 2007 01:38PM |
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“Already uneasy over the foundations of their subject, mathematicians got a solid dose of ridicule from a clergyman, Bishop George Berkeley (1685-1753). Bishop Berkeley, in his caustic essay 'The Analyst, or a Discourse addressed to an Infidel Mathematician,' derided those mathematicians who were ever ready to criticize theology as being based upon unsubstantiated faith, yet who embraced the calculus in spite of its foundational weaknesses. Berkeley could not resist letting them have it:
'All these points [of mathematics], I say, are supposed and believed by certain rigorous exactors of evidence in religion, men who pretend to believe no further than they can see... But he who can digest a second or third fluxion, a second or third differential, need not, methinks, be squeamish about any point in divinity.'
As if that were not devastating enough, Berkeley added the wonderfully barbed comment:
'And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, not yet nothing. May we not call them the ghosts of departed quantities...?'
Sadly, the foundations of the calculus had come to this - to 'ghosts of departed quantities.' One imagines hundreds of mathematicians squirming restlessly under this sarcastic phrase.
Gradually the mathematical community had to address this vexing problem. Throughout much of the eighteenth century, they had simply been having too much success - and too much fun - in exploiting the calculus to stop and examine its underlying principles. But growing internal concerns, along with Berkeley's external sniping, left them little choice. The matter had to be resolved.
Thus we find a string of gifted mathematicians working on the foundational questions. The process of refining the idea of 'limit' was an excruciating one, for the concept is inherently quite deep, requiring a precision of thought and an appreciation of the nature of the real number system that is by no means easy to come by. Gradually, though, mathematicians chipped away at this idea. By 1821, the Frenchman Augustin-Louis Cauchy (1789-1857) had proposed this definition:
'When the values successively attributed to a particular variable approach indefinitely a fixed value, so as to end by differing from it by as little as one wishes, this latter is called the limit of all the others.”
—
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'All these points [of mathematics], I say, are supposed and believed by certain rigorous exactors of evidence in religion, men who pretend to believe no further than they can see... But he who can digest a second or third fluxion, a second or third differential, need not, methinks, be squeamish about any point in divinity.'
As if that were not devastating enough, Berkeley added the wonderfully barbed comment:
'And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, not yet nothing. May we not call them the ghosts of departed quantities...?'
Sadly, the foundations of the calculus had come to this - to 'ghosts of departed quantities.' One imagines hundreds of mathematicians squirming restlessly under this sarcastic phrase.
Gradually the mathematical community had to address this vexing problem. Throughout much of the eighteenth century, they had simply been having too much success - and too much fun - in exploiting the calculus to stop and examine its underlying principles. But growing internal concerns, along with Berkeley's external sniping, left them little choice. The matter had to be resolved.
Thus we find a string of gifted mathematicians working on the foundational questions. The process of refining the idea of 'limit' was an excruciating one, for the concept is inherently quite deep, requiring a precision of thought and an appreciation of the nature of the real number system that is by no means easy to come by. Gradually, though, mathematicians chipped away at this idea. By 1821, the Frenchman Augustin-Louis Cauchy (1789-1857) had proposed this definition:
'When the values successively attributed to a particular variable approach indefinitely a fixed value, so as to end by differing from it by as little as one wishes, this latter is called the limit of all the others.”