“God created the integers…”

No, it’s not about theology. It’s about math!

The title of this book, edited by Stephen Hawking, is the first half of a famous quotation from Leopold Kronecker: “God created the integers, all else is the work of man.”

Actually, what he wrote was “Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.” The usual translation—the one that I gave in the previous paragraph—is slightly inaccurate. We’ll discuss that issue below. But first, what is this math book really about?

As usual, we’ll start by consulting the subtitle. It’s typical these days for publishers to give a non-fiction book a subtitle that tells you what the book is really about (in contrast to the main title, which is a ploy by marketers to attract the unsuspecting buyer). So we see that it is about “the mathematical breakthroughs that changed history.” Chapters are arranged chronologically. Each chapter focuses on an important mathematician from Euclid to Turing and includes a commentary by Hawking followed by a substantial excerpt from a primary source. “Substantial” is indeed the word, resulting in a 1326-page book (in the “new” edition). So no one is going to sit down and read the whole thing cover-to-cover, although a few amateur reviewers on Amazon and Quora imply that they have done just that.

Speaking of the amateur reviewers, I want to raise a few important points about them:

  • First of all, a few readers were snared by the title and expected a book about theology. Obviously they didn’t flip through the chapters or read any of the book before coming to an expectation! Hawking was well known to be an agnostic on the atheist side of agnosticism, so that ship won’t sail. The issue for both Kronecker and Hawking is whether mathematics is discovered or invented, and the quotation comes down firmly in the wishy-washy middle ground, claiming that whole numbers are discovered (found in nature) but those other numbers on the cover (note the prominence of π) are created. I’m not going to argue that point here, merely wishing to point out that Platonists believe that all of mathematics is discovered. Most—certainly not all—mathematicians are Platonists, as am I.
  • Second, several reviewers complained about typos in the book. Since I have the so-called “new” edition, those seem to have been fixed—not that I read any of it closely enough to spot any. The point is that this is not a textbook! It is meant for the general public, and typos aren’t debilitating the way they would be in a textbook.
  • Third, some reviewers were unhappy about the difficulty of the mathematics. Sorry, but it’s real math! If you want something simpler, there are plenty of other available books.
  • Fourth, some reviewers were unhappy about Hawking’s selection of mathematicians. Sorry, but nobody can make a selection that will please everyone. Inevitably—as with all those “ten best” lists about restaurants, music, movies, or whatever—you will say that this list is bad because it left out X, Y, or Z.
  • Fifth, some reviewers felt misled because Hawking didn’t write the bulk of the book—but the cover clearly states “edited, with commentary, by Stephen Hawking,” not “written by Stephen Hawking.”

If you want a shorter and more accessible book with a similar theme, try Journey through Genius by William Dunham. Coming in at only 320 pages, this one also focuses on theorems as well as mathematicians, still arranged chronologically. Again, look at the subtitle. That’s The Great Theorems of Mathematics in this case. Each chapter opens with the historical context, including both a bio of the mathematician and a discussion of what led to the Great Theorem; then comes a proof of the theorem, written for a general audience rather than fellow mathematicians; finally comes an explanation of the consequences, i.e. what makes it “great.” I’ve assigned chapters from it to various honors-level classes, as well as associated questions to answer and problems to solve, and it works well, with a nice interdisciplinary flavor.

Hawking’s book is a great resource for teachers, but probably not suitable as a bar mitzvah present for your nephew.

Categories: Books, Math