From the ancient Greeks to calculus to modern set theory, Everything and More: A Compact History of Infinity by David Foster Wallace traces where concepts of infinity have impacted major developments in math theory. Negatively, in many cases, preventing progress until someone came along who was able and willing to include infinite concepts in their view of the math world. Wallace includes both the history of how things changed as new ideas and methods were developed, and an explanation of those concepts in enough detail to understand. Yet it’s not so detailed as to overwhelm the layman, which is quite the balancing act.
I have an bachelor’s degree in mathematics (and computer science), but it has been a good 20 years since I did any formal studying in the area, and even when I was spending time every day on this stuff it was mostly in the area of discrete math. Which made the format of Everything and More perfect for me, as Wallace takes pains to explain the concepts and jargon as he goes along, such that someone without the background (or like me, who has forgotten much of it) can keep up. He also keeps the tone of the book light, for the most part, which helps when the concepts are complicated and one might be tempted to give up…the author is usually right there with an encouraging word or additional example to keep you going. I’ll admit that I did not absorb everything in this first reading - I was able to understand as Wallace explained things, but it would take several more readings to really get all the ways that everything ties together, not to mention how much deeper you could go with many of the sources in the bibliography. I may very well pick this one up again, months or years down the line, and see what additional understanding I can glean.
Here are two quotes that I feel sum up the tone and direction nicely:
- from section 2d: “All of which is just resoundingly weird.” This could describe a large number of the concepts covered!
- from section 7c: “The proof is both ingenious and beautiful - a total confirmation of art’s compresence in pure math.” The author’s admiration for the accomplishments of the mathematicians really does come through, all the way through the book.
This was one of my gifts from this year’s Secret Santa exchange, which was some truly excellent stalking on the part of my santa. I think any of our resident math nerds would greatly enjoy this one, particularly if infinities and set theory aren’t your area but you’d like to know a bit more about it all.