[vatsachak]

I have math papers in top journals and that's exactly how I did math;

Just get a proof of the open problem no matter how sketchy. Then iterate and refine.

But people love to reinvent the wheel without caring about abstractions, resulting in languages like Python being the defacto standard for machine learning

[wiz21c]

Now there's engineering and math. Engineering use maths to solve problems and when writing programs, you usually tinker with your data until the math tools pops in your mind (e.g. first look at your data then conclude that a normal distribution is the way to think about them). BAsically, one uses existing math tools. In math it's more about proving something new, building new tools I guess.

Sidenote: I code fluid dynamics stuff (I'm trained in computer science, not at all in physics). It's funny to see how the math and physics deeply affect the way I code (and not the other way around). Math and physics laws feels unescapable and my code usually have to be extremely accurate to handle these laws correctly. When debugging that code, usually, thinking math/physics first is the way to go as they allow you to narrow the (code) bug more quickly. And if all fails, then usually, it's back to the math/physics drawing board :-)