Journey through genius: the great theorems of mathematics I William Dunham. p. cm. Includes bibliographical references (p. ). 1. Mathematics-History. 2. Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William. Journey through Genius book. Read reviews from the world's largest community for readers. Like masterpieces of art, music, and literature, great math. .
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Journey Through Genius: The Great Theorems of Mathematics. By William Dunham. Joe Albree Department of Mathematics Auburn University. Book Journey Through Genius THE GREAT THEOREMS OF MATHEMATICS pdf the history of mathematics, with emphasis on why the theorems were significant and how Global Solutions of Schrodinger Equations pdf. William Dunham, “Problems for Journey Through Genius: The Great Theorems of Mathematics,” MAA. Convergence (July ), featuring “PROBLEMS for Great.
Not too bad - but way too easy: I was expecting something at a higher level. I was misled by comments by other reviewers into believing that the level of sophistication of the items treated in this book was reasonably good.
View all 4 comments. Jul 04, Bryan Higgs rated it really liked it Shelves: The preface to this book contains the following explanation, which I think suffices to explain its reason for being: 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 The preface to this book contains the following explanation, which I think suffices to explain its reason for being: 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 with the men and women who produced them.
The present book offers an analogous approach to mathematics, where the creative unit is not the novel or symphony, but the theorem. There are, however, some shortcomings: Of course, the book was published in , so what it stated was true at the time of writing. A second shortcoming, in my estimation, is the total absence of any mention of Group Theory, its origins during the French Revolution Evariste Galois and subsequent enhancements by Sophus Lie, both of whom have fascinating histories, albeit tragic ones.
Perhaps the importance of Group Theory was not apparent in , but I doubt that. Bottom line: The book needs a new edition. Just as I would have a hard time going through one of the standard "great masterpieces of fiction" tomes because of my lack of appreciation of many so-called classics, so a typically non-mathematical reader would probably have a difficult time reading this book, at least in the sections that deal with the proofs of the theorems.
Even I, with a strong mathematical background, found my eyes glazing over during some of the proofs -- especially those based on Euclidean style geometry all the ancient Greek and other ancient cultures were based on this kind of geometry. You know, the kind of geometry where, in school, you were asked to prove that this angle is equal to that other angle.
I was never very good at that -- perhaps I lacked the spatial aptitude, and there never seemed to be any real rules to follow; it was basically trial and error. I found the last two chapters, "The Non-Denumerability of the Continuum" and "Cantor and the Transfinite Realm", to be particularly interesting, because I had not previously learned about those areas.
One final comment, which applies not only to this book but to most if not all mathematics books I've read or studied: I feel that one of the reasons why so many people stop paying detailed attention glazed eye onset to a mathematical proof is not only that it's often difficult to understand, but that it's often presented in a very dense manner.
Essential steps are subsumed into a single paragraph with no attempt to identify each step. I believe that, if there was an express attempt to present the proof using bulleted or numbered lists, with relatively short explanations in each item, more people could stay awake longer and be more likely to understand the proof. Perhaps this is because it would provide more of a visual aid than densely written paragraphs.
View 2 comments. 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.
Dec 15, Shelly rated it it was amazing Shelves: 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 I finally finished this book! Each chapter is about one of the more important theorems in mathematics. I loved almost every chapter. I was a little bored by the two Cantor chapters, but I think that was primarily because I don't love set theory and didn't study it a whole lot in college. I'd give the book five stars if not for those two chapters.
The chapter dealing with Sir Isaac Newton nearly had me in tears. His accomplishments and understanding are just mind boggling. I took a course on the history of mathematics in college. It was horribly boring. I had to fight sleep off. This book would have been a brilliant text for that class. Sure it doesn't cover every blasted mathematical discovery since the beginning of time, but the approach this book takes seems so much more practical and well rounded.
It has just the right mix of history and proofs, and was almost always very engaging and interesting. It covers so many of the really really important things. My class would have been much better if it had used this sort of approach verses the linear, this happened then this happened then this happened History can be so boring, but this book was very fun.
People who don't like math, and wouldn't care to follow a proof while reading won't like this one bit.
Journey through Genius: The Great Theorems of Mathematics
One final thought: Newton once explained that the reason he was so successful at solving problems was "by thinking on them continuously. Sure, I've got to be able to multitask a little, but wouldn't it be nice to use a bit more focus in our lives? I think I could get more done, and do it better, if I'd procrastinate less, and not do things in pieces, but just set about doing a task, and get it done. If that makes sense. Isn't Newton inspiring in so many ways?
Don't we all wish we could be like him? Except maybe a little more well adjusted and happy? Mar 27, Martin Cohen rated it really liked it Shelves: 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, The math history presented is very good.
I don't know why this was done, since it is easy to prove the divisibility directly, using the Binomial Equation discussed at length in the book.
Later in the same chapter, mentioning the formula for geometric series would have made much clearer Euler's work on factoring Fermat numbers.
Overall I would recommend the book. If you are not that much into proofs, there is much of interest in the biographical and historical material.
If you are willing to do a little work in following the proofs, there is much to appreciate. May 13, James Swenson rated it really liked it. 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 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 The title is a fair description: 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 influenced the future of mathematics.
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In addition to the "great theorems," he finds time to describe many other masterpieces. Of Dunham's twelve "Great Theorems," Heron's formula and Newton's general binomial theorem have by far the weakest credentials.
Looking for candidates to replace them, though, gives a good idea of why they were chosen. I recommend this book to a general reader interested in the history of mathematics, and particularly to undergraduate students of mathematics: Oct 27, Melanie rated it really liked it Shelves: 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!
Even if math isn't your thing, you can skip the proofs and just read the blurbs about the life, times and genius-inspiring circumstances of great historical figures. Sep 11, Alyssa rated it really liked it Shelves: 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 Bad habits die hard, so let's start with a quotation, shall we?
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. If you ask me, this quite sums up the idea of the book in the sense that, by going through the history behind some of mathematics' greatest theorems, it shows the beauty of mathematics In other words, I don't think it suits people who would only be interested in the historical side of mathematics, you need to know a bit of the mathematics themselves.
Or maybe you can just skip over the proof and technical details, but I'm not sure if it's enjoyable to read this book that way. That aside, from a kinda mathematics student POV, it's a very enjoyable reading. When you go through years of studies, you usually only get the technical side of stuffs unless you have special profs who like to add anecdotes to their classes --those are the best, it makes it more interesting imo and all history is swept under the rug.
With this book, I got to catch up a bit on history. I think there's only Cardano's solution of the cubic chapter 6 and Cantor's infinites chapters for which I knew most of the story already. In any case, all through the book, I was reminded of my many many classes, a small trip down memory lane so to say.
It covers a variety of domains: And although the table contents seems to indicate that only a couple of great mathematicians are included in the book, there are actually so many more that come into the picture as you go through the chapters a couple of them I've never even heard of. Another interesting point was to be confronted to those long-ass sentences they used to use.
Maybe it's because my classes were all taught in French and the phrasing is slightly different from the modern English one, but sometimes I had to read it over a couple times to grasp the idea. The only bad point I have in mind is that it was too short although I do admit that a longer book might have been harder to digest. Feb 06, Billy rated it really liked it. 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 At times the proofs can be a little hard to follow, but the book was definitely written for the layman with some calculus background.
The most striking point of the entire book to me was how miserable the vast majority of the featured mathematicians lives were. They lived lonely lives and suffered from bouts of mental illness. I wonder if people like Cardano, Cantor, Newton, and Turing succeeded because of their faults or in spite of them.
Their work was a great service to humanity, but was it worth it in the end for them.
Would they have traded their greatness for a normal, happy life? Reading about their lives is enough to make one hope that they never accomplish anything great. Of course, there are plenty of people who lead miserable lives without accomplishing anything too. The example that really sits with me was the final one illustrated by Cantor. He was a brilliant man who tackled the problem of the infinite. He spent much of his life struggling to prove or disprove his continuum hypothesis.
It is believed that his obsession over this problem contributed to his bouts of mental illness and the complete breakdowns that he suffered. It may have even expedited his death. Twenty years after his death it was proven that this hypothesis could not be disproved.
Another twenty years later it was also proven that the hypothesis could not be proven. This meant that he spent his life obsessing over a problem that could not be solved. View 1 comment. Jun 17, Dan Cohen rated it liked it Shelves: 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 A decent trawl through a few millennia of mathematics, focusing on specific theorems that the author describes as "the great theorems of mathematics".
For me this is both a strength and a weakness - the former because it makes the achievements more real but the latter because it's been many years since I had the patience to go through a mathematical proof properly.
I wasn't entirely enamoured of the choice of theorems but I understand the author's dilemma in wanting to choose theorems whose proofs could be understood by non-mathematicians and also wanting to include contributions from the most important mathematicians in his list.
Ultimately, I felt that the book was only partially successful in convincing me of the beauty of the proofs and I suspect that this was partly down to the choice of theorems covered. Cantor's diagonal arguments being some of the more successful examples in this regard. Apr 10, Wes Townsend rated it really liked it. 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.
Book Journey Through Genius THE GREAT THEOREMS OF MATHEMATICS pdf
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.
I would definitely recommend it to anyone A book about mathematics, written for the layman, but with some pretty deep math in there. I would definitely recommend it to anyone who thinks math is fun.
Not as good as I expected it to be. Feb 12, Matthew Paul rated it it was amazing. 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 only 2 to 3 have heard of Archimedes let alone Gauss or Euler. As such, I began intentionally adding historical and s As a Calculus teacher, I am always baffled at students knowledge of history especially in regard to the mathematics.
As such, I began intentionally adding historical and small bios of history's finest in to as many lessons as I could. I feel that this shift has brought mathematics to more life in the classroom, as the focus is now viewing math as a body of knowledge that humanity has building upon and exploring together for thousands of years.
It also helps build connections among their other classroom studies building stronger academic awareness. After reading Journey through Genius, I have learned so much more history and beautiful arguments to bring into the classroom. The author's ability to tell a story was gripping, his ability to present mathematical proofs coherently and seamlessly was incredible, and the wide array of tangential tidbits of historical figures and factoids was masterfully chosen.
I am truly inspired by this book, and believe that my students will love to hear these stories in the classroom. Aug 16, Uge Saurio rated it it was amazing. 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.
This study guide contains the following sections: The Great Theorems of Mathematics is a survey of twelve great theorems selected by author William Dunham for the importance to the field of mathematics as well as for how they represent the prevailing ideas and ideals of the times in which they appear.
Dunham takes a chronological path through the subject, beginning with the ancient Greeks and the thinkers centered in Alexandria, the site of the greatest collection of learning in the ancient world.
These three mathematicians have an impact so great nobody approaches their advances for many centuries. Dunham picks up the thread in the 16th century with the eccentric and superstitious Gerolamo Cardano who is jailed for heresy at one point but manages to solve equations once thought unsolvable. He describes the contentious Bernoulli brothers, Johann and Jakob, who despite their bickering manage to transform the mathematics of their day. Dunham is especially reverent toward Leonhard Euler and Georg Cantor, two incredibly prolific mathematicians who push the boundaries of theoretical math despite physical and mental challenges.
In each chapter, Dunham presents the proof of a "great theorem" by the subject of the chapter surrounded by introductory biographical and historical background to place the theorem in context, as well as an epilogue describing how the great theorem is received and the importance it holds for subsequent thinkers.
Dunham's demonstrations are thorough and require careful attention, but do not rely on any advanced knowledge of mathematics to comprehend. Rather than drill the math, Dunham wishes to present the theorems in a setting that enhances their historical importance and it is not necessary to completely comprehend each theorem to grasp their influence.
Dunham also charts the metaphysical aspects of mathematics through the centuries, from the Pythagorean idea that the natural world can be measured in whole units of fixed proportions to Georg Cantor's religious notions about God's role in his exploration of the infinite. He describes the reluctance of mathematicians to divulge their discoveries, sometimes out of fear of having their precious assets taken from them, but also sometimes because of a fear that some more theoretical ideas might not be accepted among their colleagues.
Dunham ably describes how theoretical math is often at the forefront, and how ideas that seem too bizarre to publish in one era come to have practical significance in another once science and technology have caught up.
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Copyrights Journey Through Genius: All rights reserved. Toggle navigation. Sign Up. Sign In. Get Journey Through Genius: The Great Theorems of Mathematics from site. View the Study Pack. View the Lesson Plans.I was never very good at that -- perhaps I lacked the spatial aptitude, and there never seemed to be any real rules to follow; it was basically trial and error. He describes the reluctance of mathematicians to divulge their discoveries, sometimes out of fear of having their precious assets taken from them, but also sometimes because of a fear that some more theoretical ideas might not be accepted among their colleagues.
May 13, James Swenson rated it really liked it. I know In each chapter, Dunham presents the proof of a "great theorem" by the subject of the chapter surrounded by introductory biographical and historical background to place the theorem in context, as well as an epilogue describing how the great theorem is received and the importance it holds for subsequent thinkers. Login Join Give Shops. Open Preview See a Problem? I believe that, if there was an express attempt to present the proof using bulleted or numbered lists, with relatively short explanations in each item, more people could stay awake longer and be more likely to understand the proof.
One final thought: Shelves: history-mathematics , mathematics 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.