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.
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.
Thanks for posting. I wish there were many other books done similarly.
Selfishly, I'd love to see statistics, probability and advanced robotics displayed this way.
<3 <3
Now with LLMs it is so much easier and faster. Hopefully books will be rewritten.
The 'tooltips' are also a nice touch. If someone wanted to go nuts with this concept, they could allow the user to highlight any sentence, equation, or individual symbol to bring up an 'Explain this' popup option.