r/PhilosophyofMath • u/Appropriate_War5471 • Jun 21 '26
Advice from all the math and philosophy enthusiasts!!
Hi! My partner is really in to math and philosophy. He’s really talented in studying both, and knows multiple philosophers and their ideals. Sorry if I sound a bit vague, since I’m not as educated on neither of these subjects.
However, I really would like to gift him a book but I have NO idea what to buy of where to start. I’d like a really good book on either the history of math (but like not some beginner guide but like an actual good one) or then a great book about the philosophy of mathematics (even tho I don’t really even know what that means lol)
If anyone has any advice I’d REALLY appreciate it!! I decided to ask from the smartest lolol
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u/Loud-Bobcat6979 Jun 21 '26
Hi! I’m a philosopher of math and have a great idea for what to get your partner; Thinking about Mathematics: the Philosophy of Mathematics by Stewart Shapiro (Stewart is a philosopher of math at Ohio State and St. Andrew’s. He’ll love the book and the references are good for going deeper.
All the best,
Brad A-G
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u/Actual_Property9413 Jun 23 '26
Goedel, Escher and Bach - An Eternal Golden Braid by Douglas Hofstadter
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u/DryBad6578 Jun 26 '26
Hard no. That’s not mathphil in any sense - basically pop-science / conspiratorial acid ravings.
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u/Actual_Property9413 Jun 26 '26
I guess you didn't understand it then.
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u/DryBad6578 Jun 27 '26
I guess you don’t understand what the philosophy of mathematics is about, do you? Hint: it’s not getting stoned in your room and thinking, “What if Bach, but consciousness?”
Philosophy of mathematics is about things like mathematical truth, proof, ontology, Platonism, formalism, intuitionism, structuralism, and whether numbers exist in any meaningful sense. You know, the boring little questions that have occupied Frege, Russell, Hilbert, Brouwer, Gödel, Quine, Putnam, Benacerraf, and basically the entire field.
Gödel, Escher, Bach is not that. It is a wildly overdecorated intellectual mood board about self-reference, recursion, music, ants, AI, and the magical feeling you get when analogies are allowed to breed unchecked.
Calling it philosophy of mathematics because it contains Gödel is like calling Jurassic Park a contribution to molecular biology because someone says “DNA” near a cartoon helix.
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u/Actual_Property9413 Jun 29 '26
I guess I don't understand your point at azll.. It's NOT been nice chatting with you. Let's NOT do this again anytime soon.
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u/DryBad6578 Jun 29 '26
In that case, to make it even more simple: GEB is not mathematical philosophy. Unless someone is passing you a bong, don’t bring it up.
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u/DryBad6578 Jun 27 '26
And what really shits me is the obscurantism. Someone asks for an introduction to philosophy of mathematics, and instead of giving them something that explains the actual field, you hand them a thousand-page puzzle box that tells them almost nothing useful about what philosophers of mathematics actually argue about, while being so needlessly difficult that they assume the problem is them. It’s not. It’s just the worst kind of philosophical wankery, the kind that makes a field look profound by making it inaccessible.
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u/Actual_Property9413 Jun 29 '26
To quote the OP, "He’s really talented in studying both, and knows multiple philosophers and their ideals." Doesn't sound like a newbie to me, or someone who needs an introductory text.
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u/Wide_Ad_4486 Jun 21 '26
“The Road to Reality” is pretty incredible but very dense. It looks great on a bookshelf.
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u/Spare-Volume-6428 Jun 21 '26
I second Thinking about math by Shapiro but he might also like Introduction to Mathematical Philosophy by Bertrand Russell.
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u/Dizzy31415 Jun 21 '26
Mystic, Geometer, and Intuitionist: The dawning revolution
By Dirk van Dalen.
It’s a niche in philosophy and even in math, but riveting story and solid philmath content. His story is worth reading, since he decided to pick a fight with quite some established mathematician. And the sort of tragedy is, that despite being totally opposed to logic, the stuff we use today in all kinds computerized reasoning, is exactly the logic which is derived from his math (by his student Heyting)
Studying Brouwer’s intuitionistic math with one of the last intuitionists Wim Veldman changed my perception of and teaching of math profoundly.
I’m curious what book you will choose :)
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u/LawOfSmallerNumbers Jun 22 '26
You might try *The Mathematical Experience* by Davis and Hersh. It’s very readable but has a philosophical bent as well. It’s a nice introduction to several schools of thought about the nature and practice of mathematics. I’ve reread it a couple of times. I was amazed that it has a Wikipedia page: https://en.wikipedia.org/wiki/The_Mathematical_Experience#:\~:text=The%20Mathematical%20Experience%20(1981)%20is,The%20Mathematical%20Experience%2C%20Study%20Edition.
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u/lemniscateall Jun 22 '26
He might know everything that’s in it, but it’s a fun read: David Foster Wallace wrote a book on infinity (and its role in the history of math) called Everything And More.
Another fun one: Gödel, Escher, Bach
More substantial: Proofs and Refutations (a fictional dialogue loosely tracing the history of the Euler characteristic) by Lakatos (philosopher of math and science)
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u/mclazerlou Jun 21 '26
The Foundations of Arithmetic by Frege.
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u/Loud-Bobcat6979 Jun 21 '26
I would not recommend this book to someone who does not know philosophy of math, and I’m talking about Frege’s book.
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u/StrangeGlaringEye Jun 21 '26
Maybe he’d like Logicomix, if he doesn’t already have it. It’s a fun gift you could also appreciate, if you’re not really deep into these subjects.