This is a list of mathematics books I find particularly accessible, interesting, or beautiful. Because I am not a mathematician, it is aimed at non-mathematicians. I don't pretend to understand any of them.
See also my (nascent) Physics for Liberal Arts Majors list.
Please suggest, if you know works that would fit here.
> General Topology 😢🔫
I went on my own math self-study journey a year or two ago and would also recommend these: - Infinite Powers by Steven Strogatz. It doubles as a book on calculus and partial history of math. It was by far the most accessible writing/prose of all the math books I read. - What is Mathematics, Really? by Reuben Hersh. It's pretty dry reading but still the best philosophy of math book I read. It has a lot to say on the "Was Math Invented or Discovered?" debate, and probably would have settled the debate if it was more widely-read. - How to Lie with Statistics by Darrel Huff. It teaches the basics of statistics while also teaching how to spot bad statistics, which is a hourly occurrence on social media and TV news. - Arithmetic by Paul Lockhart. It gets into how and why basic math came about in the first place
Would Field's Science without Numbers be too mathematical, too broadly scientific or too philosophical for this type of list? I know you probably want to cover more territory than specialise but I would tout Moschovakis' Notes on Set Theory over Halmos. Overall a more beautifully written book that makes for a better understanding of the natural intuitions for why we have a foundations of mathematics.
good list overall though, thanks for making.
Both added, thanks for the suggestions! Both are very much at home on this list.
knot theory in context of mathematics is so fucking insane. I literally don't fucking understand how anyone can put in the effort to figure them out. The most autistic yet honorable lust for knowledge. FYI Frenkel's Love and Math is also a great book that explores "What if math was taught like art, where we start with appreciating the masterpieces?"
That's an awesome premise! Added.
The OG knot theorists studied knots not purely for their own sake, but because they thought it was key to creating a model for the universe and the fundamental forces of physics. Even with some era-defining geniuses at the helm, this didn't really pan out and was ultimately overshadowed by the dawning of relativity and quantum mechanics, but they were true believers in the sense that you had to be in order to pursue such a grand and hopeless task with such primitive tools. It wasn't until mathematicians realized that topology was the right language to think about knots that it took off as a field in and of itself, well into the 20th century. The appeal is easy to see, I think. It's very pretty, great for visual thinkers, and does kind of distill the satisfaction of making or detangling ties and braids and knots in life. Funnily enough, it was the re-interactions with physics in the '80s that really cemented its place as a respectable discipline. This time, not because you could apply math to the physics, but because you could apply the physics to the math! In other words, the relevant mathematics objects, invented and studied by pure thought, far removed from real-world consideration on the scale of decades, are nonetheless "physical" in some deep sense. Absolutely wild.
I enjoyed Mathematics and Its History by John Stillwell, e: the Story of a Number by Eli Maor, Incompleteness: The Proof and Paradox of Kurt Godel by Rebecca Goldstein , and Everything and More: A Compact History of Infinity by David Foster Wallace. All of which should be approachable if you have taken high school Calculus. Great list btw.
Added, thanks!
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Have you ever looked at G. H. Hardy's *A Mathematician's Apology* (1940)? It's probably one of the most-read essays among mathematicians. It's written by a great mathematician as he truly realizes that his powers are fading. (Some mathematicians take this especially hard, Lang on your list is another famous example.) This colors its tone and it has some controversial statements (e.g. "mathematics is a young man's game") that have been endlessly debated in tea rooms and grad student offices, but it expresses the raw emotions and special motivations of a pure mathematics researcher better than anything else I'm aware of. I've always liked it, but long thought it to be a too niche for general consumption. However, a few years ago I was shocked to found that the poet/memoirist Mary Karr not only really loves this work, but even hands a copy to her students as they graduate, as a reminder that "we're all in the same arena" when it comes to the creative struggle. Since then I've been recommending it more freely.