The Nature and Growth of Modern Mathematics

"In modern societies, especially in America, there’s a tendency in popular culture to relegate the role of mathematics to the specialized few who are functional components of the scientific and technological sectors. Mathematicians are seen the same way as plumbers — instrumental members of society who are tossed certain things. It’s a fair way of looking for someone who’s not familiar with how math works. But there’s another way to look at mathematics, which is as an unreasonably effective lens for appreciating and understanding what the world is like. This is not because human mathematicians are geniuses—though many are, of course—but that’s not where it comes from. Reality itself has a fundamentally mathematical structure at some deep level. We can take these little symbols made up in ancient Mesopotamia to track grains—this practical set of tools, like a subset of language—and we’ve been able to grow it and build an intellectual edifice that somehow has this magical capacity to describe just about anything we look at it in a very satisfying way. “Reality itself has a fundamentally mathematical structure at some deep level” That’s one of the greatest mysteries of the universe. Why did this practical thing open up a vast universe of complexity and subtlety” Why are there prime numbers? Why do large numbers have weird properties? Why does the Pythagorean theorem exist? All these are questions about mathematics as somehow essential to the fabric of the universe. It really saddens me that math is taught in a way that turns off more than half the population as something scary and to be avoided. It’s especially tragic that this happens to young girls. Only a small subset explore the higher reaches of mathematics, and of that subset the vast majority end up having exactly the same instrumental view of mathematics that’s expected of them by society. Even if they’re extraordinarily talented, they never develop an appreciative understanding of math as a philosophical view of the world. It is the only book of its kind that has a big history of all of mathematics. Everything from pure number theory to prime numbers to calculus: all of it is covered. And it’s covered in a way that both highlights the practical applications of mathematics—which even non-mathematicians are able to see—and it brings out the philosophical beauty and wonder math can evoke. Even if you’re not mathematically trained and the best you can do is pre-calculus, this is a book worth reading as best as you can. Yes, you’ll get lost — there are equations in this book. I’ve had some grad-level training in mathematics and I got lost in parts. But that’s ok. The wonder is still conveyed. The book also has significant coverage of the stories of mathematicians and strikes a great balance between them as humans and what they did."