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Ask HN: Are there books for mathematics like Feynman's lectures on physics?

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Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#61

Post by mathgenius »

I believe mathematics as a field is really suffering because there is not much in the way of "Feynman"-style books. But people like John Baez and John Conway have countered this trend somewhat. You should definitely try reading anything by these two. Conway does tend to be a bit too brief at times.

And there's this book: "Conceptual mathematics" by Lawvere and Schanuel. It's unlike any other mathematics text I have found. Fundamental and easy to read: yes. Also leads up to some deep ideas in an intuitive way.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#62

Post by the_watcher »

beagle3 wrote: post #19

When I was studying physics, I found Feynman’s books in the library, read them all, and had the feeling I understand everything! But then I tried to solve some final exams from previous years, and realized the feeling is false. These books gave me great intuition - but they made all the math look deceivingly simple, and as a result it is hard to develop the actual problem solving skills and intuition. I know my exper…

I think that's fair for trying to master physics or to become a physicist. But if you're looking for an intuitive understanding of the concepts or relearning it, which seems to be what the OP is looking for, Feynman-style seems like the optimal type of book.

I don't think Feynman's books are a replacement for a more traditional physics textbook as a student looking to pass a class, become a physicist, or a hobbyist trying to master it, but I do think they're pretty ideal for someone who wants to get much stronger grasp of the concepts than a layman without having to go through the struggle associated with solving problems they'll never actually apply.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#63

Post by AlexCoventry »

vymague wrote: post #33
beagle3 wrote: post #19

When I was studying physics, I found Feynman’s books in the library, read them all, and had the feeling I understand everything! But then I tried to solve some final exams from previous years, and realized the feeling is false. These books gave me great intuition - but they made all the math look deceivingly simple, and as a result it is hard to develop the actual problem solving skills and intuition. I know my exper…

Isn't that true for any physics or math texts? You need to do problems. That's why there were exercise books to accompany Feynman's lecture.

I didn't know about the companion exercises. That's great.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#65

Post by tobinfricke »

auntienomen wrote: post #44

Feynman's PhD advisor, John Wheeler, together with Charles Misner and Kip Thorns, wrote a textbook on general relativity called Gravitation. It's gigantic, 1200 pages, and its tone is similar to the Feynman lectures. And it is at least partially a math textbook, as it includes a fairly complete introduction to Riemannian geometry.

I think even among professionals in general relativity, MTW has developed a reputation as being too dense and old-fashioned, certainly so for a beginner. If you're first approaching GR, Sean Carroll's notes or books are much more approachable.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#66

Post by devmacrile »

nicklaf wrote: post #54

Mathematics and Logic by Mark Kac and Stan Ulam (1992 Dover paperback, ISBN 978-0486670850) [1] Mathematics, Form and Function by Saunders Mac Lane (1986 Springer-Verlag hardcover, ISBN 0-387-96217-4) [2] [1]: https://www.cut-the-knot.org/books/kac/index.shtml [2]: https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function

+1 on Mathematics, Form and Function

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#68

Post by elorant »

iamaelephant wrote: post #49
jfarlow wrote: post #38

Penrose's 'Road to Reality' [1] is a kind primer on where the math comes from, as it applies to physics. Kind of a philosophical walkthrough of how math applies to physics. It is nowhere near as concise as Feynman's lectures, but it does complement them pretty well, while getting more into the math, and why the math is needed to describe various aspects of physical reality. [1] https://www.math.columbia.edu/~woit/wor…

As it happens I bought both Road to Reality and Lectures on Physics at the same time, about 14 year ago. I read and re-read Lectures on Physics but I was never able to finish Road to Reality. I have kept my aging copy and hope to one day get through it, but it's a MUCH more difficult read, at least in my opinion.

It definitely is quite difficult, but it's also very inspiring in finding various topics to read more. I must have bought at least 20 books from the vast bibliography in the appendix of the book.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#69

Post by WalterBright »

beagle3 wrote: post #19

When I was studying physics, I found Feynman’s books in the library, read them all, and had the feeling I understand everything! But then I tried to solve some final exams from previous years, and realized the feeling is false. These books gave me great intuition - but they made all the math look deceivingly simple, and as a result it is hard to develop the actual problem solving skills and intuition. I know my exper…

At Caltech (home of Feynman) in the 1970s, his books were not used as the main texts in physics classes, but as supplements.

Re: Ask HN: Are there books for mathematics like Feynman's lectures on physics?

#70

Post by m31415 »

For mathematics, I would recommend:

1. "What Is Mathematics? An Elementary Approach to Ideas and Methods" by Courant and Robbins -- a general book on mathematics in the spirit of Feynman lectures.

2. Strogatz's "Nonlinear Dynamics and Chaos" -- it's a bit narrow in scope (mostly dynamical systems with a little bit of chaos/fractals thrown in) but very good nonetheless.

3. Tristan Needham, "Visual Complex Analysis", beautiful introduction to complex analysis.

4. Cornelius Lanczos, "The Variational Principles of Mechanics" -- this is a physics book, but one of the classics in the subject, and as Gerald Sussman once remarked, you glean new insights each time you read it.

5. Cornelius Lanczos, "Linear Differential Operators" -- an excellent treatment of differential operators, Green's functions, and other things that one encounters in infinite-dimensional vector spaces. This book has some very intuitive explanations, e.g., why d/dx is not self-adjoint (i.e., Hermitian), whereas d^2/dx^2 is.

For chemistry, I would recommend "General Chemistry" by Linus Pauling, even though it's a bit outdated.

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