Thinking about Mathematics

What Hacker News says

1. 3PSJan 2021
   In a similar vein, I'm currently halfway through 'Thinking About Mathematics' by Stewart Shapiro. It's a great introduction to the various philosophies of mathematics: logicism, formalism, intuitionism, structuralism, basically all of the different sorts of philosophical positions prominent people have taken on the nature of mathematics, going back to Plato and Aristotle. It's wonderfully approachable as well, I highly recommend it.
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2. archi42Jul 2020
   This is an excellent comment, and I agree on the conclusion that either exists as much as the other.

   However ;-), I dare to say your argument is weak: Assume "I believe in the apple on my desk". But you will find there is neither a fruit nor an Apple branded computer on my desk. So an outside observer is bound to believe I am going mad, hence my belief shapes my social relationship with others around me. Now does this make the apple as real as religion, which becomes real due to it's impact on social relationships? Or are people who let religion shape their social relationships as mad as I am? Or is the argument flawed? (edit: No, I can not answer these question).

   Shapiro's "Thinking about mathematics" springs to my mind, IIRC in the first chapter(s) he gives a nice overview about what philosophers thought about numbers, the realm of numbers and whether they "exist" or not. I think some of that could be applied here. (And, generally, I think it's a great read for computer scientists & mathematicians interested in philosophy, as it gives a great overview across various different schools).

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3. archi42May 2019
   There are those philosophers which are as concerned with logic as you'd expect from a pure mathematician ;-)

   If you're interested, Shapiro's "Thinking about Mathematics: The Philosophy of Mathematics" gives a nice introduction into that topic, discussing several schools of philosophy and their thinkers (without forcing the authors pov on the reader). We had a seminar discussing that book, and while most philosophy students seemed happy to skip that seminar (too much math/logic), those of us with a MINT background (CS major here) found it quite amazing.

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4. mttyngJan 2019
   That depends heavily on your philosophical interpretation of mathematics: Platonism vs. Formalism

   Someone linked the BBC video, which is great, but there’s also a wonderful book that discusses this and many other facets of mathematical philosophy:

   https://www.amazon.com/Thinking-about-Mathematics-Philosophy...

   (Sorry for the link spew) I highly recommend that book to anyone remotely interested in the field.

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5. billybatsonDec 2018
   A Mind for Numbers by Barbara Oakley: Decent. I think this book would best be read in conjunction while working through a textbook. I will admit that it did do quite a bit to help relieve math anxiety, but the nature of the book is practicality.

   Brave New World by Aldous Huxley: A reread. A bit depressing considering the state of the world today. I found myself wondering which reality would be preferable.

   Letters to a Young Mathematician by Ian Stewart: Easy, but fruitful read. I've struggled a lot with math confidence, and this helped alleviate a lot of that.

   How to Speak, How to Listen by Mortimer J. Adler: A lot of practical advice. My biggest takeaway was this: if it's worth talking about, even if the conversation sucks or the other person doesn't understand, any bit of advancement and understanding is worth the effort. Really helped me increase my patience when talking to people.

   Quack This Way by David Foster Wallace and Bryan Garner: Super useful and practical discussion between two lovers of language. I keep a copy with me at all times.

   The Autobiography of Gucci Mane: Just a fun read while on vacation. "If Gucci can do it, you can do it".

   Jesus' Son by Denis Johnson: A nice if brutal read. It was my first foray in DJ. I felt Cormac McCarthyish vibes.

   Blood Meridian by Cormac McCarthy: A classic. The Judge.

   Thinking About Mathematics by Stuart Shapiro: Highly recommended for anyone interested in the philosophical questions of mathematics. Shapiro writes clearly, concisely, and in a manner that is easy to read.

   The Liars' Club by Mary Karr: Pretty great but brutal.

   The Broom of the System by David Foster Wallace: I really enjoyed it. It's ode to Wittgenstein and it helped me cope with a lot of questions that I felt after studying LW.

   The Sorrows of Young Werther by Johann Wolfgang von Goethe: I think we've all been in Werther's shoes. Though I hope that nobody comes to the same conclusion he came to.

   Manage Your Day-To-Day: Build Your Routine, Find Your Focus, & Sharpen Your Creative Mind: A pretty great book. I find myself writing a book report on it to make sure I internalize a lot of the lessons. If you're having trouble doing creative work while working, read this.

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6. black_knightMar 2017
   There is no consensus as to what is the true and correct philosophy of mathematics. People are going to disagree about that, just like they disagree about almost every other part of philosophy. But there are books which give you a survey of different views, such as Shapiro’s “Thinking about mathematics” — which surely will bring you to “I know a bit about the philosophy of mathematics”-level.

   During my time as a master student in mathematics we used to have a joint seminar with students from philosophy where we would take turns reading and presenting topics from philosophy of mathematics. I think it was useful for everyone, and it wasn’t difficult to organise and didn’t take much time (2 hours per week during one term).

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