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title: "Journey through Genius: The Great Theorems of Mathematics"
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# Journey through Genius: The Great Theorems of Mathematics

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## Description

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 whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. “It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov

Review: A personal favorite - 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 mathematical sophistication is required on the part of the reader. In this case, the reader can feel pretty safe. While these are real and deep mathematical theorems, their proofs only require high-school level mathematics. In the vast majority of cases, the reader familiar with basic algebra and a little bit of geometry will have no trouble following the discussions. One theorem (Newton's approximation of pi) requires a little bit of integral calculus and another (the discussion of some of Euler's sums) requires a smidge of elementary trigonometry. In both cases, the author holds the reader's hand through the discussion so even if you haven't taken a course in trigonometry or calculus, you'll still be able to follow most of the conversation. In fact, even if you don't really have a lot of algebra and geometry, the bulk of the book will still be accessible to you. The majority of the text is a history of mathematics wherein the author discusses the context and importance of the theorems and some biographical details of their discoverers. While I find the recreations of the proofs themselves to be perhaps the most interesting part, the reader with a general interest (even if that interest is not supported by mathematical skill) will find the book fascinating. For those of us who do have some knowledge of mathematics, though, the recreations of the theorems presented in their historical context provides a rich and inspiring series of vignettes from the history of mathematics. This brings us to another important point. While this is a book about the history of mathematics. it is not *a* history of mathematics, and the theorems selected are not the only "great" theorems of mathematics, but a cross-section thereof. Many readers of sufficient mathematical background may quibble over the inclusion of some theorems at the expense of others--personally I would like to have seen more from combinatorics--but no one can deny that these theorems are remarkable in their elegance and in their importance in the development of mathematics from the Ancient Greeks to the very end of the nineteenth century. It might be helpful to know what theorems are actually included in the book. Aside from a handful of lemmas and minor results presented before or after each of the "Great Theorems," the book consists of a single major result per chapter. They are: *Hippocrates' quadrature of the lune *Euclid's proof of the Pythagorean Theorem *Euclid's proof of the infinitude of primes *Archimedes' determination of a formula for circular area *Heron's formula for triangular area *Cardano's solution of the cubic *Netwon's approximation of pi *Bernoulli's proof of the divergence of the harmonic series *Euler's evaluation of the infinite series 1+1/4+1/9+1/16+... *Euler's refutation of Fermat's conjecture *Cantor's proof that the interval (0,1) is not countable *Cantor's theorem that the power set of A has strictly greater cardinality than A Each of these theorems is surrounded by the historical discussion that makes this book a triumph not merely of teaching a dozen results to students but of actually educating students on the human enterprise of mathematics. It is not only interesting but, I think, important to be reminded of the human side of a field as abstract as mathematics, and Dunham bridges the mathematical and the biographical with remarkable dexterity. It is useful for the student of mathematics to understand that Cantor's work on the transfinite was resisted by the mathematicians of his day just as much as students struggle with it when they're exposed to it in today's lecture halls. It might further be useful to know that, perhaps partly due to his demeanor and perhaps partly due to the attacks on his work, Cantor spent much of his life in mental hospitals--and yet, despite his unhappy life his work has achieved immortality as one of the great developments in mathematical history. I can't recommend this book highly enough for the mathematician, the math student, or the merely curious. In fact, I recommend reading it twice. First, just read it straight through and enjoy the story of mathematics told through these vignettes. Then read it again with pencil and paper in hand and work through the theorems and proofs with the author as your guide. You'll come away with a much deeper understanding of and appreciation for these great theorems in particular and mathematics in general.
Review: One of the best math books i ever read. Buy this. - One of the best math books i ever read. Buy this.

## Technical Specifications

| Specification | Value |
|---------------|-------|
| Best Sellers Rank | #92,010 in Books ( See Top 100 in Books ) #55 in Mathematics History #203 in Scientist Biographies |
| Customer Reviews | 4.7 out of 5 stars 476 Reviews |

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## Customer Reviews

### ⭐⭐⭐⭐⭐ A personal favorite
*by B***S on June 13, 2019*

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 mathematical sophistication is required on the part of the reader. In this case, the reader can feel pretty safe. While these are real and deep mathematical theorems, their proofs only require high-school level mathematics. In the vast majority of cases, the reader familiar with basic algebra and a little bit of geometry will have no trouble following the discussions. One theorem (Newton's approximation of pi) requires a little bit of integral calculus and another (the discussion of some of Euler's sums) requires a smidge of elementary trigonometry. In both cases, the author holds the reader's hand through the discussion so even if you haven't taken a course in trigonometry or calculus, you'll still be able to follow most of the conversation. In fact, even if you don't really have a lot of algebra and geometry, the bulk of the book will still be accessible to you. The majority of the text is a history of mathematics wherein the author discusses the context and importance of the theorems and some biographical details of their discoverers. While I find the recreations of the proofs themselves to be perhaps the most interesting part, the reader with a general interest (even if that interest is not supported by mathematical skill) will find the book fascinating. For those of us who do have some knowledge of mathematics, though, the recreations of the theorems presented in their historical context provides a rich and inspiring series of vignettes from the history of mathematics. This brings us to another important point. While this is a book about the history of mathematics. it is not *a* history of mathematics, and the theorems selected are not the only "great" theorems of mathematics, but a cross-section thereof. Many readers of sufficient mathematical background may quibble over the inclusion of some theorems at the expense of others--personally I would like to have seen more from combinatorics--but no one can deny that these theorems are remarkable in their elegance and in their importance in the development of mathematics from the Ancient Greeks to the very end of the nineteenth century. It might be helpful to know what theorems are actually included in the book. Aside from a handful of lemmas and minor results presented before or after each of the "Great Theorems," the book consists of a single major result per chapter. They are: *Hippocrates' quadrature of the lune *Euclid's proof of the Pythagorean Theorem *Euclid's proof of the infinitude of primes *Archimedes' determination of a formula for circular area *Heron's formula for triangular area *Cardano's solution of the cubic *Netwon's approximation of pi *Bernoulli's proof of the divergence of the harmonic series *Euler's evaluation of the infinite series 1+1/4+1/9+1/16+... *Euler's refutation of Fermat's conjecture *Cantor's proof that the interval (0,1) is not countable *Cantor's theorem that the power set of A has strictly greater cardinality than A Each of these theorems is surrounded by the historical discussion that makes this book a triumph not merely of teaching a dozen results to students but of actually educating students on the human enterprise of mathematics. It is not only interesting but, I think, important to be reminded of the human side of a field as abstract as mathematics, and Dunham bridges the mathematical and the biographical with remarkable dexterity. It is useful for the student of mathematics to understand that Cantor's work on the transfinite was resisted by the mathematicians of his day just as much as students struggle with it when they're exposed to it in today's lecture halls. It might further be useful to know that, perhaps partly due to his demeanor and perhaps partly due to the attacks on his work, Cantor spent much of his life in mental hospitals--and yet, despite his unhappy life his work has achieved immortality as one of the great developments in mathematical history. I can't recommend this book highly enough for the mathematician, the math student, or the merely curious. In fact, I recommend reading it twice. First, just read it straight through and enjoy the story of mathematics told through these vignettes. Then read it again with pencil and paper in hand and work through the theorems and proofs with the author as your guide. You'll come away with a much deeper understanding of and appreciation for these great theorems in particular and mathematics in general.

### ⭐⭐⭐⭐⭐ One of the best math books i ever read. Buy this.
*by R***R on August 29, 2026*

One of the best math books i ever read. Buy this.

### ⭐⭐⭐⭐⭐ testimonial
*by C***S on May 18, 2006*

I am a recent college graduate with a BS in Math. I went through college simply as I could. I chose math because it was typically easy to me, but I never really tried to get any true grasp on it. I only began to understand the most basic concepts in math when I taught Algebra I for a semester to high school freshmen. That experience motivated me to develop a better understanding of the most basic concepts in math. Jump forward a year, and I am now about to enter grad school for applied math. After reading this book and soaking it in, I feel like I have the tools to be very successful now. I will take classes with a very different mind set. I am very excited to get started next week. I tell you that I am motivated so much that I am going to retake a few undergraduate math courses for my own sanity. Maybe I'm crazy. I have never been so excited about math or viewed it as a beautiful art. It is pure. Euclid's proof of the Pythagorean Theorem truly humbled me. I had viewed it before, but had never been motivated to try to understand it. That is where Dunham steps in. He creates such an excitement about it that it forces the reader to read and reread the proof. I have actually worked it out 3 times for myself to ensure that I truly get it. It feels powerful. Furthermore, I'm only about half way through the book. It is going to take me a while though. I have to convince myself that I can reproduce everything before I move on to the next chapter. Maybe I'm being hard on myself. For those of you who seem to suggest that if you took high school algebra and geometry everything is peaches and cream.... I don't get it. To read this book and really soak it in, one has to have the foundations of a true understanding of high school algebra and geometry. That is a different animal. It is easily attainable with the proper focus though. I ask that you read this book and make the world a bettter place!

## Frequently Bought Together

- Journey through Genius: The Great Theorems of Mathematics
- A History of Mathematics
- Infinite Powers: How Calculus Reveals the Secrets of the Universe

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*Last updated: 2026-11-05*