What is Mathematics, Really?

What Is Mathematics, Really? examines the foundations and philosophy of mathematics from a humanist perspective. Mathematics philosopher Reuben Hersh challenges both Platonist and formalist views of mathematical truth and existence. The book analyzes key questions about the nature of mathematical objects, proofs, and knowledge through historical and contemporary examples. Hersh draws on developments in mathematics, philosophy, cognitive science, and anthropology to build his case. Through discussions of mathematical practice and education, Hersh explores how mathematics functions as a social and cultural activity rather than an abstract, otherworldly realm. The text incorporates dialogues between different viewpoints and examines common objections to humanist mathematics. This work presents mathematics as a human creation that exists in the shared understanding and activities of the mathematical community. The philosophical framework developed has implications for how mathematics is taught, learned, and understood by both practitioners and the public.

Readers describe this as a philosophy-focused examination of mathematics rather than a math textbook. Most reviews indicate it's best suited for those interested in mathematical philosophy and foundations rather than practical mathematics. Readers appreciated: - Clear explanations of different philosophical views of mathematics - Accessible writing style for non-philosophers - Thorough discussion of social and human aspects of math Common criticisms: - Too much focus on arguing against Platonism - Not enough concrete mathematical examples - Some repetitive arguments and points - Writing can be dense in certain sections Ratings: Goodreads: 3.9/5 (84 ratings) Amazon: 4.1/5 (31 ratings) One reader noted: "Hersh effectively challenges the myth of mathematical certainty but spends too much time attacking Platonic views." Another wrote: "Good introduction to mathematical philosophy, though it could use more mathematical substance to support its arguments."

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🔢 Despite being a mathematician, Reuben Hersh trained as a lawyer before switching careers and earning his Ph.D. in mathematics at age 35. 📚 The book challenges the traditional Platonist view of mathematics, arguing that mathematical concepts are human-made cultural constructs rather than eternal truths existing in an abstract realm. 🎓 Hersh studied under Peter Lax at New York University and went on to become a professor at the University of New Mexico, where he taught for over three decades. 🏆 The book received the 1999 CHOICE Outstanding Academic Title Award and has been translated into several languages, including Chinese, Spanish, and Japanese. 🤝 Hersh collaborated frequently with Philip J. Davis, and together they wrote "The Mathematical Experience," which won the 1983 National Book Award for Science.