Reddit reviews God Created The Integers: The Mathematical Breakthroughs that Changed History

A good book that would help you answer this question is God Created the Integers which is a book on the history of mathematics by Stephen Hawking (yes, him). Each chapter has a short introduction and history of a mathematician written by Hawking, and then the rest of the chapter is the paper or excerpt from their works that Hawking felt was most important to mathematical progress.

The first chapter is on Euclid, and includes his basic postulates on geometry, theory of proportion, and his proof of infinite prime numbers.

The second chapter is on Archimedes, and includes his proofs on the surface area of a sphere and cylinder, his estimation for pi, his "sand reckoner" where he defines a method of denoting very large numbers and uses that to estimate the number of sand grains that would fill up the entire known universe and show that it is still finite, and then his fulcrum/lever method that he derived that was an early analogue to integral calculus.

So the rest of the book goes on through Diophantus, Descartes, Newton, Euler, Laplace, Fourier, Gauss, Cauchy, Lobachevsky, Bolyai, Galois, Boole, Reimann, Weierstrass, Dedekind, Cantor, Lebesque, Godel, and Turing.

It's a pretty heady book and I'm only going through it very slowly, but one thing that was clear to me from the first few chapters is that even without the tools we have like symbolic notation, cartesian algebra, imaginary (or even negative!) numbers, etc., the early Greek mathematicians (more accurate to call them 'geometers') were able to do some really advanced things.

If you were to go back into their time and were able to communicate with them, the hardest part would be teaching them to understand and use the symbolic notation for mathematics that we now take for granted. For them everything was geometry, and if it couldn't be expressed as such it wasn't seriously regarded.

I really like the book "God Created The Integers: The Mathematical Breakthroughs That Changed History" from Stephen Hawking because he makes a historical introduction and then he puts the original texts.

Certainly, a worthful reading.

God Created the Integers, edited by Stephen Hawking. Includes selected works of various big names in mathematics with a brief biography of each preceding the math. The wiki article on the book has a list of all mathematicians included.

Prime Obsession, about Riemann and his famous hypothesis.

The Man Who Knew Infinity, about Ramanujan.

Some Amazon reviews say it contains a lot of errors: http://www.amazon.com/God-Created-Integers-Mathematical-Breakthroughs/dp/0762430044/ref=sr_1_1?ie=UTF8&qid=1464268435&sr=8-1&keywords=god+created+the+integers#customerReviews

God Created the Integers is the best there is that I know of. It gives you a synopsis of each (of 13) major innovators in mathematics, as well as a copy of one of their more famous or important proofs. It was edited by Stephen Hawking

It's awesome because it gives you a good history for people who like history, and then it gets down and dirty into the proofs for those who want the math.

The book by Stephen Hawking God Created the Integers has some (translated) excerpts from Cantor's paper. It's only $23, but I'd suggest trying to find a copy at a nearby library.

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> Pulled together for the first time, and paired with commentary from the world's most respected scholars, God Created the Integers presents history's extraordinary moments in math, culled from 2,500 years of history and 21 distinguished mathematicians, four more than the hardcover edition. Each chapter begins with a profile of one of these mathematical masters, followed by original printings of their relevant works. This new paperback edition includes the work of Euler, Galois, Bolyai, and Lobachevsky.