Programming

I think the same can be said for a lot of fields. E.g., just because someone’s an excellent architect doesn’t make them a good animator by default.

There’s also so many variations on the types of programming. Maybe a mathematician might be better suited for data science rather than frontend stuff. And even then, each person is different and has their own set of skills part from whatever their formal training is.

What I think makes good programmers is having the ability to bash your head against your desk while debugging, but still walking away at the end of the day loving the job and problem solving. Persistence and creativity go a long way in programming.

I've known a lot of math people, and /on average/ I think they're more capable of programming useful code than the other college graduate groups I've spent a lot of time working with (psychology, economics, physics) /on average/.

That said, the best mathematicians I've known were mostly rubbish at real programming, and the best programmers I've known have come out of computer engineering or computer science.

If you need a correct, but otherwise useless implementation, a mathematician is a pretty good bet. If you need performance, readability, documentation, I'd look elsewhere most of the time.

In my (anecdotal) experience, software is best approached as an engineering pursuit. Almost anyone can write code, but building code that is maintainable, scalable, and reliable has a lot in common with building other things that we want to see similar features in.

There are plenty of math people who are good at this, but there are lots of other fields of study that are just as adjacent (philosophy and communication both come to mind).

I would say, having an affinity for math can be a sign of affinity for programming.

Logical abstract thinking, order of operations, and problem solving all transfer. A for loop is just a summation equation for example.

But id say in today's high level development, being math centric is less important.

To be good at programming, a lot of knowledge is needed, but "accidental". From practical ones like how to use git, to conceptual ones like cache performance mental model. It's perfectly possible that git is designed with a different CLI, or the common cache line size being 512 bytes. Mathematicians usually don't care about these things, since they are accidental. So they are bad at writing programs that's far away from math.

It's a completely different story when they are writing programs about math. If the tool is good enough, i.e. allowing them to express math ideas in familiar terms, mathematicians are very good at writing math programs. As can be observed in Lean and mathlib.

I tend to agree. I think this attitude is something of a holdover from the early days of computer science, when of academics from all the other, existing fields, mathematicians were usually the best fit. Now that we have formal computer scientists, computer engineers, and software engineers, this is no longer the case.

In my experience, when someone from a purely mathematical background tries to program or explain something for programmers, they often (but not always, to be fair) insist vehemently on sticking to methods and algorithms that at best confuse the issue in a programming setting, and sometimes even run counter to how the computing hardware works, reducing performance. In these situations the rationale given is usually something along the lines of, "Listen, we mathematicians have been doing it this way for X hundred years, so that's the way it should be done!"

I definitely concur. Scientists often write functional but abominable code that follow no style-guide, no conventions, no rules, just "get'er dun" mentality. Short obfuscated variable names, enormous functions, no comments, no build instructions, no tests, no edge case handling, no modules, no separation of concerns, etc.

They often write the most job secure code on the planet.

I get it, it's because they come from a world of f(h) = g(h) + i(h) -> assoc = 1 or whatever. Maths, physics, biology, computer science, etc. all have the most obtuse, unvarnished, terse expressions ever. They aren't teachers (most professors have no didactic training whatsoever), nor do they write stuff that has to be understood by anybody outside of their field.
Especially if people from that field become researchers, only their results and number of papers for their peers count. They spend most of their time getting grant money and under pressure to release something that passes peer review.
Their entire system is more about money than actually expanding our realm of understanding and they are caught up inside of that.

IMO, the most dangerous specimens to exit that system are mathematicians as they believe maths is the purest form of science (everything is maths after all), that they are smart, logical, and can solve anything. They treat software development as a practical application of their formulas and, in my experience, see it as beneath them to follow rules they consider superficial.
Code doesn't have to readable, it has to be correct, functional, and at best pure. It's why functional languages, especially Haskell, attract them so much. There are those of course who just want something that works and feel like they're in the rat race of research.

That's been my experience anyway with making code written by scientific minds production-ready (tested, maintainable, documented, functional, extendable). It's a task I actually do wish upon my worst enemies because I want them to suffer like I did.

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I’m a mathematician by training who has worked extensively (and exclusively) in the software field. While I realize I’m probably biased here, I think I write very solid code and have rarely received any complaints from trained software engineers about it.

I did however also take quite a few computer science classes in college and have spent a lot of time learning how to write better, more readable and maintainable code. Having had quite a few jobs at the start of my career where I was the only programmer on a project and therefore forced to eat my own dog food has certainly also helped.

Yeah this is generally true in my experience. I have a colleague who is a mathematician, and they write completely uncreative code most of the time, often with logical flaws.

Maybe you’re confusing engineering with programming.

Although everyone uses both interchangeably, software programmers aren’t more engineer than ‘sound engineers’. Engineers are good at structuring and optimizing. Programmers, though, are much better at finishing the job.

Math people don't have time to delve into modular code with the right amount of encapsulation/abstractions. Their money making is via testing hypotheses by constructing models and experiments.

If you want good code look at people making money writing code.

I think Haskell was created by mathematicians and it feels exactly like that: Clever and elegant language, but no normal programmer would stick with it as it's unpractical to write