Books That Shaped My Thinking in 2024
A few books I read last year that left a mark — on how I think about mathematics, computation, and their limits.
Not a comprehensive list. Just the ones I keep thinking about.
Computability and Logic — Boolos, Burgess & Jeffrey
This is the book. If you want to understand Gödel, Turing, and Tarski in one place, rigorously but without unnecessary abstraction, this is it. I read it cover to cover and then immediately started over. The chapter on the arithmetization of syntax is one of the clearest expositions I’ve encountered of a deeply subtle idea.
The Annotated Turing — Charles Petzold
A line-by-line walk through Turing’s 1936 paper. What I did not expect was how much historical and philosophical context Petzold weaves in. Turing was not solving a problem in a vacuum — he was responding to Hilbert, to formalism, to a specific intellectual tradition. Understanding that makes the result feel less like a trick and more like an inevitability.
Homotopy Type Theory — The HoTT Book
I will not pretend I understood all of it. But reading the first few chapters gave me a completely new way to think about identity, equality, and what it means for two mathematical objects to be “the same.” The univalence axiom alone generated three weeks of obsessive thinking. Worth it.
Gödel, Escher, Bach — Hofstadter
Everyone reads this eventually. I came to it late, which I think was the right order — having read actual logic first meant I could separate the mathematical content from the philosophy (which Hofstadter himself blurs somewhat). The dialogues are still delightful. The central argument is more suggestive than rigorous, but some ideas are better as puzzles than as theorems.