As a programmer who uses math heavily, I can answer this. As a programmer, your intuitive understanding of the world is infinitely important. You use it to formulate ideas, rule out solutions that would not be feasible, have an estimate of the expected cost and quality of solutions, etc.

Being able to dig deeper is important, but what's more important is to have an intuitive understanding of many many things: psychology, economy, finance, physics, art, etc. It's important to know the limits of your familiarity with any of these. For instance, my understanding of the fundamental practices in Accounting is really good (I've led a budget aggregation software for a huge conglomerate), but details is bad (tax rules for each industry, etc).

When I needed to create a software for optimizing stone cutting, I needed to know enough from computer vision, computational geometry, and optimization to know that our solution is feasible, task team members to learn what they need to do, and get into implementation, debugging and optimizing with them when needed.

After that, I still can't write code in computational geometry that handles all corner cases.

It's really good if we know everything with infinite precision, but for a programmer it's not efficient. We need to know where to stop.

In my experience, mathematicians are attracted by over-simplified/lightweight versions of programming. I think "just tell me what I need to do my job" is a universal human principle.

I don’t think they are simplified but they are an introduction course for sure. I think what’s usually missing is integrating (heh) linear algebra with calculus for solving more interesting problems but I think the audience for that needs to have a big appetite first. And those are hard to come by unless it’s pushed on you to finish your degree. And even then, people barely scrape by in those classes.

All this LLM stuff uses pretty basic linear algebra, and that’s a hot topic these days (not to turn my nose up at it, doing easy linear algebra at massive scales turned out to be a really good idea). Maybe that explains some of the attraction?

Because, realistically that's all programmers ever need, would be my guess. I do think linear algebra is an extremely interesting topic in its own right / outside, but yeah.

For the same reason mathematicians who aren't computer scientists or logicians are attracted to proof assistants implementing ZFC object languages while ignoring the stuff underneath (type theory, systems theory, etc.)

Have you opened the book? There are both theorems and proofs there.

Why do you consider a "real" textbook for linear algebra?

Can you read your own writing?

What makes someone a "programmer" vs a mathematician? If you suspended your arrogance for a few moments you might realize you've wasted our time with a question that answers itself.

I mean it's also a generalization of very little value. Is someone doing linear algebra in lean not doing "the real stuff"? What is a programmer to you? Your question is why do some people not follow an area that is tangential to them to the maximal extent? Or to some arbitrary level of "real" as you subjectively define it? Is your claim that the level of linear algebra offered here is inherently useless unless paired with the "real stuff"?

Or did you just want us all to know you are a practitioner of such arts? Gold star for you.

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