While not a math wiz myself— I understand why you would want proofs, but that can easily be taken to the extreme. Should you be measuring the gravitational constant every time you need to use it as well?
Seems like a good path to learn high level abstractions. As you progress in understanding you dig deeper.
Maybe I'm even still too much a sprite—but when I first learned anything about computers the first program I wrote was in a high level, simpler language. I wasn't moving bits around with explicit knowledge of where they were going.
Then again, maybe it's not a fair comparison on my part?
To some extent you're right, the benefit of a higher-level abstraction is using it without knowing the details. For standard usage, on the "happy path", this is fine. But if you need to modify techniques, or debug them, it's kind of impossibly frustrating without actually knowing what you're doing!
BTW computers have much cleaner abstractions than mathematics. e.g. the JLS defines Java independently of hardware; IEEE 754 is similar for fp arithmetic. There are specifications all over the place.
But my experience with mathematics is completely different - you have to understand the lower level to understand the next level.
In my personal journey, I started off with your perspective of just learning the higher levels that I directly needed. It was very difficult, but after heroic efforts, I made breakthroughs! After a while, I noticed these "breakthroughs" were mostly entirely to do with material from lower levels... So I went back to them. This happened again and again, going lower and lower. Now I'm basically re-doing high school maths.
Heheh. That’s not too far off from me. Though my progress has been delayed I was starting to circle back through many basics even taking high school courses to prep for a return to university. Hasn’t panned out so far but I’d still like to do it.
Your point about specifications makes sense. I think that was a point that made some aspects of maths harder for me— contextual differences in notation all over the place. Thanks for the input.
Seems like a good path to learn high level abstractions. As you progress in understanding you dig deeper.
Maybe I'm even still too much a sprite—but when I first learned anything about computers the first program I wrote was in a high level, simpler language. I wasn't moving bits around with explicit knowledge of where they were going.
Then again, maybe it's not a fair comparison on my part?