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Journey through Genius: The Great Theorems of Mathematics
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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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Azeena Hassan
Briefly in the Newton and Bernoulli chapters (7 & 8).
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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
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.
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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I enjoyed this tour through the history of the development of mathematics, from Euclidean geometry to the more abstract challenges of modern theory. The author tells a good story, and there is plenty of mathematical detail for those who are interested. In particular, the explanation of Cantor’s work on infinity is the clearest I have seen.
Sometimes the story may be too good. My confidence in the history I did not know was reduced by two errors (both on page 129) in the history that I do know. Th ...more
Sometimes the story may be too good. My confidence in the history I did not know was reduced by two errors (both on page 129) in the history that I do know. Th ...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
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
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
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
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 decent trawl through a few millennia of mathematics, focusing on specific theorems that the author describes as "the great theorems of mathematics". The pen pictures of the mathematicians are good but what sets the book apart from the large number of similar books is the focus on specific theorems and their proofs. So there's quite a lot of actual mathematics in the book. For me this is both a strength and a weakness - the former because it makes the achievements more real but the latter becau ...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 a phrase, this is one of my favorite books on mathematics. I read it first when it was recommended by my Calculus I professor and thought it was great. I read it again when I took a course in the history of mathematics and thought it was brilliant. Now it remains one of my favorites and I return to it regularly for discussion of some remarkable theorems and the great minds who produced them.
One of the first questions anyone might have before reading a book about mathematics is what level of m ...more
One of the first questions anyone might have before reading a book about mathematics is what level of m ...more
As a Calculus teacher, I am always baffled at students knowledge of history especially in regard to the mathematics. This of course is the fault of stale 21st century curriculum that teaches math as mastery of procedure than as the art of problem solving. It pains when when I ask students which mathematical mastermind derived such a beautiful argument, and of a sample size of 100 only 2 to 3 have heard of Archimedes let alone Gauss or Euler. As such, I began intentionally adding historical and s
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I read this book for a history of mathematics course I took in college. It was an excellent introduction to the history of mathematics. Talking to William Dunham was also an interesting experience. He mentioned that the publishers didn't want anything to be included that required more knowledge than some basic calculus, and he also didn't like the title "Journey Through Genius" at first though it grew on him as the book gained popularity.
Dunham teaches (or taught, I don't know) a history of math ...more
Dunham teaches (or taught, I don't know) a history of math ...more
It took me a while to finally read this book but I believe it to be an all time classic. This sets the example for great math history books. Of course there is an inherent risk at choosing to tell certain stories (in this case, certain theorems) above others, Dunham really does make a great selection of great, unexpected, brilliant theorems that are easy to explain, easy to understand, that had a great impact and with solutions that were truly a work of genius.
Dunham does a great job at linking ...more
Dunham does a great job at linking ...more
Journey Through Genius contains mathematics histories and technical details on important subjects, written for layman. With this huge subject, Dunham probably put a lot of thoughts into selecting what to include, and how.
Readers will get some sense on the broad pattern of mathematics development and how it fits into human civilization progression. Readers will also find detailed stories such as how Issac Newton left his work on Calculus unpublished for years.
Dunham shares with readers several ...more
Readers will get some sense on the broad pattern of mathematics development and how it fits into human civilization progression. Readers will also find detailed stories such as how Issac Newton left his work on Calculus unpublished for years.
Dunham shares with readers several ...more
An enjoyable romp through the history of mathematics, some of its most remarkable theorems, and the brains behind them. Giants galore with shoulders to stand on. A pyramid of most intriguing discoveries and proofs. Newton, Euler, Cantor - to name just a few.
The author concludes with Proclus (5th Century): 'This, therefore, is mathematics: she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes the oblivion and ...more
The author concludes with Proclus (5th Century): 'This, therefore, is mathematics: she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes the oblivion and ...more
The author had an interesting idea for a book. Unfortunately, by only scratching a tiny portion of the surface, he executed that idea very poorly. I know ... I should have expected that from reading the Contents.
The real detraction for me is Dunham's overt prejudices: anti-Oriental; anti-Islamic; anti-German; and, anti-Catholic.
Leave this book on the shelf.
The real detraction for me is Dunham's overt prejudices: anti-Oriental; anti-Islamic; anti-German; and, anti-Catholic.
Leave this book on the shelf.
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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“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.”