How is CS/programming used by mathematicians in industry? I am currently writing about the relationship and I've read a lot about the relationship going the other way. However, it's usually about how mathematics taught in CS and nothing about the relationship in for example research or by mathematicians in white-collar jobs.
I would also appreciate any articles about the subject for the proper reference.
 A: Computers can be used to form conjectures such as the Birch and Swinnerton-Dyer Conjecture. You calculate a large number of values and look for patterns to form conjectures.
Another use can be to find counter-examples. One such case was Euler's Sum of Powers conjecture which was disproven by a brute force computer search.
A third use can be to prove theorems by checking a large number, but finite number of cases. One such case is the Four Color Theorem, which has only proven using a computer verified proof which could not be accomplished by humans. Software can be used to prove theorems directly as well.
But I think we should address one other point which is that the Curry-Howard
Correspondence shows that all proofs are programs and all programs are proofs. This means the idea that math being used for computer science and vice-versa might not be a meaningful question in the first place. They're both the same thing, so you're always using both of them. They're entangled with each other inherently.
