Mathematical discovery
by George Pólya · first published 1962
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…their existing methods. Even advanced undergraduate math students who read it aren’t going to fully understand the book IMO; I would recommend Pólya’s other books (Mathematics and Plausible Reasoning, Mathematical Discovery), or maybe start with a gentler book like Mason, Burton, & Stacey, Mathematical Thinking.
on “Book: Mathematics for Machine Learning” ↗…a first step in my opinion is to think about problem solving per se. E.g. see: Mason, Burton, & Stacey, Thinking Mathematically Pólya, How to Solve It; Mathematics and Plausible Reasoning (2 vols); Mathematical Discovery (2 vols) Schoenfeld, Mathematical Problem Solving Larson, Problem-Solving Through Problems
on “How to Study Mathematics (2017)” ↗…dictionary–style with short sections on particular named problem solving topics, and is somewhat hard to interpret for novices without guidance, let me recommend Polya’s other two books (each 2 volumes), Mathematical Discovery and Mathematics and Plausible Reasoning.
on “Ask HN: Recommend a maths book for a teenager?” ↗Read 'Proofs and Refutations, The Logic of Mathematical Discovery' by Imre Lakatos. That may provide a good answer to your question.
on “The Man Who Knew Infinity: A Life of the Genius Ramanujan [pdf]” ↗…introduction with Pascal's triangle and some of Polya' legendary problem solving insights (paraphrased from my memory: "you are on to something once you find a pattern") are definitely highlights in this book. Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving by George Polya. Based on the previous book and my fond memories of reading "How to Solve it", I got this one from the library. Again I can't attest…
on “Ask HN: Best books you read in 2012” ↗…student group in the lead-up to the 1956 Hungarian Revolution. > ... He received a PhD in philosophy in 1961 from the University of Cambridge; his doctoral thesis was entitled Essays in the Logic of Mathematical Discovery, and his doctoral advisor was R. B. Braithwaite. The book Proofs and Refutations: The Logic of Mathematical Discovery, published after his death, is based on this work.
on “How to think in writing” ↗