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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?

#141
post #125

Earlier quoted context omitted.

Learning requires a lots of false starts, traps, etc. Once one has mastered, he/she can provide an intuitive explanation (a path through the wild forest that learning is).

After doing the hard learning, you can lecture your intuitive mental model you have. But it's difficult to install that mental model into a beginner's mind. Often the intuitions are illusory mnemonics for the deeper understanding, which if you never learned in the first place would just point to nothing. You have to do the hard learning to arrive at the "intuitive" mental model.

While i see where you are coming from; i feel that you are putting the cart before the horse. While Intuition by itself is not enough, it should absolutely be the first thing you should focus on before doing the hard work through rigor and formalisms. The former can be "grasped" while the latter needs "practice and applications". This is how Science itself developed (a good example is Faraday vs. Maxwell's approaches). Intuition/Rigor are analogous (in a certain sense) to Theory/Practice. You need both, each amplifying the other's effects at various stages.

Here is a neat communication from Faraday to Maxwell on receiving one of Maxwell's paper;

“Maxwell sent this paper to Faraday, who replied: "I was at first almost frightened when I saw so much mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well." Faraday to Maxwell, March 25, 1857. Campbell, Life, p. 200.

In a later letter, Faraday elaborated:

I hang on to your words because they are to me weighty.... There is one thing I would be glad to ask you. When a mathematician engaged in investigating physical actions and results has arrived at his conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formulae? If so, would it not be a great boon to such as I to express them so? translating them out of their hieroglyphics ... I have always found that you could convey to me a perfectly clear idea of your conclusions ... neither above nor below the truth, and so clear in character that I can think and work from them. [Faraday to Maxwell, November 13, 1857. Life, p. 206]”

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

#142
post #121
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…

People want intuitive explanations because it seems the easiest. It is, that's the problem. Learning is supposed to be painful. You have to get your hands dirty. It's easier to feel that you know something than to actually know it.

> It's easier to feel that you know something than to actually know it.

Well said! All students need to keep this in mind.

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

#145

I know you asked for books, but I have to mention the videos of Grant Sanderson (3Blue1Brown) [1]. His explanations of mathematics are the only ones I can think of that have given me the same sort of piercing clarity and insight that one gets from reading Feynman on physics. [1]: https://www.youtube.com/c/3blue1brown

I agree that he's a great educator. I wonder if a book by him would work as well, though. A lot of his explanations depend on the animations he makes.

Maybe if schools and colleges had off-the-shelf software that was 80% as good at making explanatory animations as his Python lib is we would see a huge boost in the understanding of maths.

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

#146

Earlier quoted context omitted.

Came here to say this. The professors I've learned the most from were the ones who weren't awesome at explaining things. I didn't understand them and had to struggle through the material. That struggle made the material stick more. I think ideally you want a professor who's 80% good at explaining things, but leaves enough gaps and says things just confusingly enough that you have to engage your brain. Feynman was too…

disagree here. you're judging society on the most naive ranking a student would give. in an ideal world you can optimize for the perfect amount of understanding and imperfect leaps for each student to best address long term understanding and success.

You're right that in principle it's possible. But say you were a great teacher, and knew that clear teaching was worse than imperfect teaching. Could you actually make your lectures less clear on purpose?

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

#147
post #89

Earlier quoted context omitted.

There is some quality in Russian math books that western authors seem to lack.

Somebody from Russia/Former Soviet Countries from Eastern Europe ABSOLUTELY NEEDS to setup a publishing company (eg. Dover Publications) to bring all of their Science/Engineering books back into print. They will do very well in today's education market where the emphasis seems to have shifted to huge tomes/useless multiple editions/pretty colouring etc. rather than succinctly presenting the knowledge itself. The Mir…

I absolutely agree about the quality of Russian math books. "Bronshtein and Semendyayev" and "Abramowitz and Stegun" come to my mind.

I doubt that a publishing company bringing back those titles into print would be very successful. One thing is that many of these titles are mostly of historical value. Who needs a book with mathematical tables nowadays? Many of the books are still available as used books too.

The most compelling argument though is that they are easily available on libgen (like this very post proves). So in a sense the publisher you wish for already exists, just not in a the form you probably thought of.

EDIT: Oops, I just learned that Milton Abramowitz and Irene Stegun are actually Americans.

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

#148
post #51

"Mathematics : Its Content, Methods and Meaning" by A. D. Aleksandrov, A. N. Kolmogorov ,M. A. Lavrent'ev. (3 Volumes) This is a classic and exactly what you are seeking for. I think it was originally published in 1962. https://www.goodreads.com/book/show/405880.Mathematics https://www.amazon.com/Mathematics-Content-Methods-Meaning-V...

I love this one, it's from 1962 but already had a chapter on

ELECTRONIC COMPUTING MACHINES

§1. Purposes and Basic Principles of the Operation of Electronic Computers

§2. Programming and Coding for High-Speed Electronic Machines

§3. Technical Principles of the Various Units of a High-Speed Computing Machine

§4. Prospects for the Development and Use of Electronic Computing Machines

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

#149
post #91
post #89

Earlier quoted context omitted.

There is some quality in Russian math books that western authors seem to lack.

Yes, and quite a few Mir books are available freely [1] [1] https://mirtitles.org

Thank you for the link. A treasure trove. Their archive page [1].

[1] https://archive.org/details/%40mirtitles?&sort=-publicdate&p...

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

#150
post #89

Earlier quoted context omitted.

There is some quality in Russian math books that western authors seem to lack.

Somebody from Russia/Former Soviet Countries from Eastern Europe ABSOLUTELY NEEDS to setup a publishing company (eg. Dover Publications) to bring all of their Science/Engineering books back into print. They will do very well in today's education market where the emphasis seems to have shifted to huge tomes/useless multiple editions/pretty colouring etc. rather than succinctly presenting the knowledge itself. The Mir…

I remember when one of my professors told me how AVL trees were invented by mathematicians in the Soviet Union. It was in a paper titled “An algorithm for organizing information”. It was a side project for them, and it’s humbling to hear how simple the idea was to geniuses.
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