Philosophies of mathematics
by Alexander George, Daniel J. Velleman · first published 2001
100% recommend
"During the first few decades of the twentieth century, philosophers and mathematicians mounted a sustained effort to clarify the nature of mathematics. This led to considerable discord, even enmity, and yielded fascinating and fruitful work of both a mathematical and philosophical nature. It was one of the most exhilarating intellectual adventures of the century, pursued at an extraordinarily high level of acuity and imagination. Its legacy principally consists of three original and finely articulated programs that seek to view mathematics in the proper light: logicism, intuitionism, and fini
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Velleman's book with Alexander George, Philosophies of Mathematics, is a good introduction to that subject, and has a nice walkthrough of ZFC.
on “Ask HN: good math books” ↗…understood it - obfuscation and abstruseness for their own sake. For actually understanding Godel's work I would recommend Gödel's Proof (Nagel, Newman, somewhat ironically, prefaced by Hofstadter) or Philosophies of Mathematics (George, Velleman).
on “Gödel, Escher, Bach is the most influential book in my life (2022)” ↗…to my mind, these other authors/works also provide fun and/or excellent examples of technical writing: * Neal Stephenson's "In the Beginning was the Command Line" * Velleman's "How To Prove It" and "Philosophies of Mathematics" * Mittelbach & Goosens "The LaTeX Companion" * Waldrop's "The Dream Machine" * Nielsen & Chuang's "Quantum Computation & Quantum Information" * Lakatos's "Proof & Refutations" * Chambers "What is…
on “Ask HN: Examples of good technical writing?” ↗