| A strongly-related topic would be Curry–Howard correspondence, that is to say that programs and mathematical proofs have a lot in common. Proving an assertion is chaining transformations, without managing some underlying state / side-effects. Big difference is that concepts in Mathematics are very immutable -- it's unlikely for us to redefine what Euclidean Space is and if we find some other framework to be more useful, we'd rather give it a new name. I am inclined to say it's a difference in discipline and conventions and in the scope and span. Programmers will create more when Mathematicians will try to cram their discovery into an already packed library, rather than open a new one -- the latter happens by accident in the world of Maths. The workplace of a programmer differs in such a way that a lot more mutation (codebase, not just variables) is going on, the work isn't purely novel, e.g. will contain mundane parts [2]. Also, contractual obligation is different from formalism and it does appear that programmers work in strictly formal environment to achieve goals while mathematicians have goals and vibe but have to become correct machinelike interpreters and conjure up a formally valid extension on the basis of accepted assumptions. Furthermore, there is a disconnect and reconsiliation between code and processes, because code resides on layers of abstraction. Mathematicians work more cleanly with abstraction because immutability allows you to do so. Programming does toy with pragmatism because the assumption is that problems can only be discovered once a prototype is made -- an earlier version of code is the instrument that enables deeper insight and understanding of the underlying project.
Math has a weird "human brain fetish" that's a bit difficult for me to articulate. Those would be my 2cc to this discussion. I think the overall picture has become more clear about what programming and 'theory building' is, comapred to the 80s. As computation "broke off" from Math and had to reconsile with physics a bit, it's starting to enrich the parent discipline a lot more by providing avenues and interesting fields of research. [1]: https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspon... [2]: writing LaTeX and verifying would be mundane but it isn't doing maths per se as one could get away with handwritten text, unlike programmers having to ultimately compile their code into binary and making sure all env variables are set up correctly. |