I have a mathematics PhD and have worked in academic research, industrial mathematics and software development. I agree with Princess_Stargirl that mathematics and programming feel quite similar, but for me mathematics is less relaxing because it's harder. Yes, it's great when you "have an argument that works and isn't insanely complicated", but until you get one you don't even know that it exists. Which is stressful if your pay, or reputation, or career prospects, happen to be governed by your success in finding such things.

(Whether, and how far, the same is true in programming depends on exactly how you define "programming". If you take it to mean the whole process of going from nothing at all to high-quality software, then it does share that characteristic with mathematics. But the very researchy open-ended work is a smaller fraction of programming than of mathematics, and there are people happily and productively employed as programmers who do scarcely any of it at all.)