Sheafification – The optimal path to mathematical mastery: The fast track (2022)

I am not sure if I agree with the list. I mean, one red flag is the frequent mention of Landau & Lifshitz. It is considered a "standard textbook", but I feel it stuck there by inertia. There are quite a few choices of both less boring and more insightful.

(Back when I was reading such stuff, 20 years ago, the Feynman Lectures provided orders magnitude more insight. And fun.)

Shivlov for the one and only text in linear algebra is rough. IMO, it’s a little terse and fast paced. Efficient if you’re already well versed enough to be dangerous, but otherwise I think might slow down the beginner to a crawl in places.

Same for Hartshorne’s Algebraic Geometry. Neither of these are bad textbooks at all, they both have a place on my bookshelf, but certainly better options have appeared through the years (for AG, I’d be remiss to mention Ravi Vakil’s fantastic The Rising Sea, due for a physical publishing October, and Ulrich Görtz & Torsten Wedhorn two part series)

What would you recommend as a supplement to Shilov's LA book?

Linear Algebra and Geometry by Igor Shafarevich, coupled with Linear Algebra by Friedberg, Insel, and Spence; the latter has great problems to work with, whereas the former is for a lucid exposition.

The Feynman Lectures are in a very different category from Landau & Lifshitz. You shouldn’t use L&L as your first university-level physics textbook (too difficult and divorced from the real world), but you probably shouldn’t use the FLP as your second, either, provided your first was good (too easy to be worth the time spent, though it’s still useful as pleasure reading that also fills in things you might have missed).

I have to admit I like the FLP less than the typical reader—it’s immensely fun in the moment, but I’ve always found the material too disjointed to build a coherent picture (ah, and now we have the tools to understand this random fun thing that I’ve never mentioned before and never going to mention after). As far as classic introductory books, the Berkeley course covers less, but the things it does cover fit together much better.

As for L&L, it’s just very uneven in quality. General relativity is great; electromagnetism is kind of bad. (And the two are in the same book!) Theoretical mechanics is adequate but way too much of a slog despite how short it is. Elasticity is surprisingly good. QM is OK but there’s a dozen approaches to QM depending on your background and it’s a toss-up whether this one will work for you. QED is good at the things it covers but like half of those things are relegated to the status of obscure specialist topics these days, while the point of view is something you should be aware of eventually but definitely not at your first go through the subject. And so on.

I dislike Feynman, frankly. So many of his weird hand-wavy metaphorical descriptions of shit obscure more than clarify the really important elements of the physics.

To name an example: Feynman is the source of the popular idea that in special relativity we can think of a particle as having a constant 4-vector with length c and that movement changes the direction of the four vector into the spatial directions, thus "slowing" the speed through time.

This is a very strange way of thinking about this stuff because the entire point of special relativity is that there is no objective state of affairs about velocity at all. It's meaningless to talk about the velocity of a single particle because velocity is a relative quantity. Also, I'm just generally suspicious of all this "hyperbolic rotation" stuff. I mean its true as far as the mathematical structure is concerned, but most of the time metaphors which try to get us to think of a minkowski space as being a lot like a normal 4d euclidean space confuse us or at least hide the real interesting structure, which is that in a minkowski space much of the 4d structure implied by a set of events is redundant. That is, spacetime is less than space and time together, not more.

In a way Feynman was also the 3b1b of his generation. He was very good at coming up with and communicating with visual metaphors. To the laypeople at the receiving end, these give a strong illusion of understanding.

That's ok if you are not going to compute or design or build anything with it. But they are very inadequate when it is time to shut up and compute.

Feynman (and I am sure) Grant Sanderson could/can operate at a virtuoso level at both the visual imagery and the compute layers. But their popularity with the masses is because of the visual imagery they could conjure up.

On the other hand for those who can already compute for themselves, the metaphors can be a big help for building intuition as long they think in the same style.

Sure, if one wants to move deeper then Feynman Lectures are a nice entry point - at least for some people, everyone has different background and taste.

For L&L - well, not sure which ones I read (or: try to read), but likely electromagnetism and classical mechanics.

For quantum mechanics, I used to suggest these: https://p.migdal.pl/blog/2016/08/quantum-mechanics-for-high-...