Name: What is mathematics, really?
ISBN: 9780195130874

What is mathematics, really?

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 science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. The humanist standpoint helps him to resolve ancient controversies about proof, certainty, and invention versus discovery. The second half of the book provides a fascinating history of the "mainstream" of philosophy - ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, Hilbert, Carnap, and Quine. Then come the mavericks who saw mathematics as a human artifact - Aristotle, Locke, Hume, Mill, Peirce, Dewey, Wittgenstein. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. Platonism and elitism fit together naturally.

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exprofmaddyNov 2024

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

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ggmMar 2022

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.

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actually_a_dogDec 2021

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.

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yantramsSep 2020

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/...

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ggmJul 2023

Richard Rhodes' monumental work on the A and H bomb mentions that from Thompson onward, "being heard" Was a problem. Juniors often struggled to be taken seriously, sometimes seniors ostentatiously "spoke for them" to have new ideas given credence and women were doubly disabled on the "taken seriously" front.

Right up until Murray Gell-Mann and beyond, speaking outside the current limitations to knowledge was hard. I don't want this to descent into AGW and antivaxx denialism, this is inside classic science but considering radical theory/paradigm shifts which were still testable propositions. New models are hard on early stage career.

Blinded peer review was partly designed to help some 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, testable work. Theoreticians.. harder to test sometimes.

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yruiDec 2022

I recommend reading 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, even in part, history of math becomes important.

A few words on your questions:

Mathematics is no different from any other field except that its objects of interest are all abstractions. As an engineer you use it, so it appears to be about number and symbol pushing, but the theory of how and where to push the numbers and symbols and why it works was discovered by a mathematician at some point. The proofs are not ultimate but hopefully convincing given certain usually acceptable assumptions or axioms. We like the axiomatic method because axioms are usually not controversial and everything proceeds from them using strict logical reasoning.

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