SHOULD BE REQUIRED READING FOR EVERY HIGH SCHOOL SENIOR. While it has the history and boigraphy of mathematics and mathematicians, the vast majority of the focus is on the mathematics. It shows the development of algebraic concepts and proofs the Pythagorean Theorem through development and derivation of infinite series such as Newton's and others' formulas for pi, and into more recent and esoteric areas such as Godel's proofs of many infinities. Calculus is not needed and is mainly described in the controversies over its invention/discovery by Newton and/or Leibniz.
Okay, there was about four pages on the life of some guy who developed the generic cubic formula (the next step up from the quadratic formula taught in high school) - these pages have nothing about math, but are all about the hard, terrible, sucky, bad-luck life he lived. I'm not sure of the point of that, perhaps that one can suffer and still make a significant contribution to mathematics. But nowhere else in the book is there a run of four pages without substantial mathematics content.
But that's only one percent of the book, and I've learned a lot more about mathmathematics (and not just who did what, but in many cases exactly how they did what they did) than many other books on and about math. The only thing remotely comparable is a collection of James R. Newman books such as his "Mathematics and The Imagination" and his four volume "The World of Mathematics," but this book still has much that others don't.
I wish I had read something like this before my first year of college (which was a few years before this book was first published), as I might have looked for a school with a mathematics major program.
It's not just "great theorems," it's about all the great discoveries. It's an excellent book on history/biography of mathematics and mathematicians. I give it really high marks. It covers Aristotle, Pythagoras and Erasthenes to Newton and Leibniz to Godel, and everyone you've heard of in between and their exact contributions to mathematics (or their most important contributions for the more prolific contributors), at detail I've not seen elsewhere, such as showing exactly how various infinite series for Pi were derived. Okay, there was about four pages on the life of some guy who developed the cubic equation formula, and these pages had nothing about math, but are about the hard, terrible, bad-luck life he lived. But that's only one percent of the book, and I've learned a lot more about math (especially who did what and how) than a lot of other books on math put together. Wish I had read something like this in college or high school.
From Amazon: In Journey through Genius, author William Dunham strikes an extraordinary balance between the historical and technical. He devotes each chapter to a principal result of mathematics, such as the solution of the cubic series and the divergence of the harmonic series. Not only does this book tell the stories of the people behind the math, but it also includes discussions and rigorous proofs of the relevant mathematical results.