The Mathematical Experience

What Hacker News says

1. TimK65Sep 2024
   I recognize this content from Hersh and Davis's later book "The Mathematical Experience," which I really like.
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2. ykonstantJul 2023
   How to Prove it by George Pólya gave me good foundations and perspective on mathematical problem solving. The Mathematical Experience by Davis and Hersh was a fascinating introduction to the way mathematicians think and their perspective on mathematical challenges.

   Just be warned that classics like the Mathematical Experience and Men of Mathematics by E.T. Bell tend to give a romanticized view of mathematical research, with anecdotes mostly by high profile mathematicians doing high profile mathematics, and with up-to-20th Century perspectives that don't always hold up.

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3. mrazomorJan 2023
   The Mathematical Experience -- https://www.goodreads.com/book/show/1113522.The_Mathematical...

   It's touching many areas. For some it explains how they were developed or the controversy around them (e.g. the definition and use of infinity).

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4. mpweiherNov 2022
   The proof is not a social construct.

   The truth is.

   The proof is a mechanism to reach that consensus, by convincing other mathematicians of a specific truth. That is all it is.

   There is a naive idea that a proof is a purely mechanical series of steps that provides access to truth. Last I checked, this isn't so for the vast majority of proofs in math. Such a proof would be way too tedious to construct or check by mathematicians. And if it isn't checkable, how do we know it is actually true?

   Automated proofs are a subfield, and (again, last I checked) controversial because they can often not be checked by humans.

   So for example, if the proof doesn't convince other mathematicians, then it's not a a proof.

   Or it might convince other mathematicians and later turn out to be wrong after all.

   For more on the practical aspects of math, I highly recommend The Mathematical Experience.

   https://www.amazon.com/Mathematical-Experience-Phillip-J-Dav...

   I read it in German:

   https://www.amazon.com/Erfahrung-Mathematik-German-P-J-Davis...

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5. 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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6. rg111Feb 2022
   - The Innovators: How a Group of Hackers, Geniuses, and Geeks Created the Digital Revolution by Walter Isaacson is a great book that taught me a lot. It covers the gradual discovery of computers from Babbage and comes to modern ages. I highly recommend it. This book is also very fun to read.

   - Seven Brief Lessons in Physics by Carlo Rovelli is a brief, enjoyable, and great read. This book is good for both layperson and experts.

   - Albert Einstein is Einstein's biography by Walter Isaacson. Really nice book.

   - The Life and Science of Richard Feynman by James Gleick (author of Chaos and The Information) is another great biography. This biography shows the evolution of his science as well as evolution of his person and thoughts. Great book. Background in Physics will be very helpful if you want to read this one.

   - The Mathematical Experience David, Hersh is a very succinct and pleasant book on the history of Maths. Will recommend.

   - Alan Turing: The Enigma by Andrew Hodges is a good mathematician's biography. I have not finished it, but fully intend to.

   - I have just read some of The Man from the Future by Ananyo Bhattyacharya is a biography of John von Neumann. It already seems very good and I plan to read through the end.

   - The Annotated Turing deals a lot with history and is a read of a lifetime.

   ____

   - I have not read A Mind at Work yet. It is a biography of Claude Shanon. I would recommend you to check it out.

   - Sylvia Nasar's A Beautiful Mind is also recommended highly. I plan to read it.

   ____

   I have recently watched a BBC Documentary that I thoroughly liked. One of its themes that had striken me was the change of science from fully deterministic to probabilistic. It's an extremely important paradigm shift for all of science.

   The name is Dangerous Knowledge (2007).

   The people covered are- Cantor, Boltzmann, Godel, and Turing.

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