What is mathematics, really?
by Reuben Hersh · first published 1997
80% recommend20% neutral
Virtually all philosophers treat mathematics as isolated, timeless, ahistorical, inhuman. In What Is Mathematics, Really? renowned mathematician Reuben Hersh argues the contrary. In a subversive attack on traditional philosophies of mathematics, most notably Platonism and formalism, he shows that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of sci
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For anyone interested in the topics discussed here, I highly recommend What is Mathematics, Really? [1] by Reuben Hersh [1] https://www.amazon.com/What-Mathematics-Really-Reuben-Hersh/...
on “What Is Math?” ↗Some very nice related works that dispel widespread math myths: (1) What Is Mathematics, Really? Hersh, 1997. https://books.google.com/books/about/What_is_Mathematics_Rea... (2) Where Mathematics Comes From. Lakoff and Nunez, 2000. https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
on “Everyone is capable of, and can benefit from, mathematical thinking” ↗Here's a list of 10 good, popular mathematics books: https://www.theguardian.com/books/2012/jan/18/ian-stewart-to... Of the list, I've read Goedel, Escher, Bach", and What is Mathematics Really* and can recommend them wholeheartedly. GEB is a bit of a project, but it will bend your mind in a good, math-y way. I first read it in high school, so the material should be pretty accessible.
on “Ask HN: Books Similar to Code by Charles Petzold?” ↗Davis and Davis/Hirsch wrote the book(s) on this. The mathematical experience (1981) is a great read. What is mathematics really? (1997) also fine.
on “What is mathematical thinking? (2012)” ↗I think Davis and Hersh say this. Ruben Hersh "what is mathematics really" felt like it was opening the door to the sausage factory.
on “In Search of Proofs from “The Book”” ↗…histories of mathematics including more recent histories like Morris Kline's "Mathematics: the loss of certainty." According to other books by Reuben Hersh, such as "the Mathematical Experience" and "What is mathematics really?", mathematics can be seen as a social activity where what gets studied and what gets accepted as proven has a definite relationship to human existence and human social life. If you agree with this,…
on “Ask HN: I want to learn what mathematics is really about” ↗…of that. In a narrow enough field it's impossible for reviewer and submittor not to know each other. There may only be 3-4 people who understand your niche fully. Rueben Hersh discusses that a bit in "what is mathematics really" (I think, could be another book of his, "the mathematical experience") Rhodes discusses Michael Polyani's theory of science as old fashioned apprenticeship. Journeyman scientists publish reproducible,…
on “Argonne National Lab is attempting to replicate LK-99” ↗