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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?

#31

Post by joelaaronseely »

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…

Yeah, he was like that in person as well. When I was an undergraduate, he would "teach" a seminar on Tuesday afternoons called "PhysX" where you could go and ask any question you wanted. He'd go up to the blackboard and extemporaneously write things down and explain things in such a way that thought you really understood. But when you got back to your room and tried to replicate the chain of reasoning, there were always pieces missing or leaps that you now couldn't make. (It felt like the Star Trek Episode, "Spock's Brain".)

But we all took that as an indication of our own lack of knowledge and intuition and would just try harder.

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

#32

Post by bjornsing »

anton_tarasenko wrote: post #26

In terms of depth and breadth, the Princeton companions get close to Feynman.[1][2] A more formal approach appears in handbooks.[3][4] [1] Gowers et al., The Princeton Companion to Mathematics. https://press.princeton.edu/books/hardcover/9780691118802/th... [2] Higham and Dennis, The Princeton Companion to Applied Mathematics. https://press.princeton.edu/books/hardcover/9780691150390/th... [3] Zwillinger, CRC Standar…

But is really breadth and depth what makes Feynman’s approach to physics unique?

To me the unique aspect is more the uncompromising intuitionistic approach with little consideration/adaptation for “shallow/correlative thinkers”...

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

#33

Post by vymague »

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.

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

#34

Post by bjornsing »

WhatIsDukkha wrote: post #29
agentultra wrote: post #15

Earlier quoted context omitted.

I came to add add Introduction to Graph Theory and found it here. I second it! A nice book and I appreciate it's funny introduction as a book designed for liberal arts majors injured by the pedagogy of institutional mathematics (paraphrasing). If you have a grasp of algebra and sets this book is an easy read for the curious or mathematically immature. Edit WhatIsDukkha is correct and their suggestion better reflects…

Innumerate is infrequently used but it's analogous to calling someone illiterate. Someone that can't do their sums. Usually saying someone isn't "mathematically mature" ie able to read and use proofs is what you would want to say.

You can do a lot of graph theory without being able to sum integers. No problem. :)

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

#35

Post by ArtWomb »

anton_tarasenko wrote: post #26

In terms of depth and breadth, the Princeton companions get close to Feynman.[1][2] A more formal approach appears in handbooks.[3][4] [1] Gowers et al., The Princeton Companion to Mathematics. https://press.princeton.edu/books/hardcover/9780691118802/th... [2] Higham and Dennis, The Princeton Companion to Applied Mathematics. https://press.princeton.edu/books/hardcover/9780691150390/th... [3] Zwillinger, CRC Standar…

Good list! I'd also add Mary Boas' Mathematical Methods in the Physical Sciences. A standard textbook for incoming students across disciplines and very accessible

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

#36

Post by thanatropism »

The Princeton Companions to Mathematics and Applied Mathematics are beautiful to leaf through at the library. They're also hardcore heavy-weight (physically) and unlikely to be read twice, so don't buy them.

My personal take is that good linear algebra books at any level are great "tours of mathematics". Start with Strang and never stop. In a few years you'll be balled up with Kreyszig scribbling proof attempts in receipts, flaming unkempt hair and everyone around you will think you're weird but you'll be so, so happy.

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

#37

Post by perlgeek »

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 daresay you would have the same experience with any other book.

If you just read a book and don't work through problems yourself, you simply don't learn enough to do it yourself.

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

#38

Post by jfarlow »

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/wordpress/?p=154

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

#39

Post by ska »

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…

Physics is a bit like that anyway though, you can't learn it by reading or listening to anyone, you have to solve things yourself from scratch, usually multiple times.

Reading good books/having good lecturers certainly helps, but there is no way to replace the work.

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