It is often echoed that mathematicians make excellent software engineers, and that their logic-adjacent work will translate efficiently into coding and designing.
I have found this to be almost universally untrue. I might even say the inverse is true.
While I and many of my peers have capacity to navigate the mathematical world, it certainly is not what sets us (at least me) apart when designing clever algorithms and software tricks.
Point being: I dont think the property/trait that makes good programmers is mathematical literacy.
I would love to hear what others experience is regarding this.
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.
As a person who went to Math Olympiads and then switched to programming (with a math flavour) I am talking this personal.
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 = 1or 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.
Your first paragraph likely also applies to many senior software developers, especially if they primarily worked in small companies / freelance.
For real, though, I wish maths in general, in all fields, adopted the way things are written in programming.
So, instead of something like:
e = mc²Just write it out:
energy = mass * speed_causality²And I mean, that’s still a harmless formula. I’ve had to learn so many formulas, where not the formulas were the problem, rather it was knowing what φ means in this field/context. So many scientific papers are just extremely hard to read for anyone from a different field, because the formulas are obfuscated like that.
And the thing is, I get that pure mathematicians don’t care. Their formula inputs usually truly don’t have much of a meaning beyond
aandb.
But their conventions, in particular multiplication being implied when two random letters are written next to each other, that just fucks up the option for anyone in any other field to use legible variable names.You’re absolutely correct, and in my experience authors with physics background are even worse.
I’ve seen algorithms that I know by heart, understand fully and have implemented tens of times represented in such a way that I can’t even recognise them.
“So many papers are extremely hard to read because the formulas are obfuscated like that”
This isn’t really an issue though, of you don’t have enough foundational knowledge to understand what the formula means or how it could be conceivably derived, does knowing how it’s calculated matter?
I do think so, yes.
For one, not everyone needs to be an absolute expert. You do want some person with expert knowledge to sanity check what you’re doing, but ultimately you’ll have engineers, programmers etc. that are tasked with putting a formula into reality. If they can intuitively read formulas and more easily read up on the surrounding context, that helps a lot.
In that sense, I may also be very programmer-biased in how I read papers, but generally I prefer to look at a given formula and then read up on why it is formulated like that. Maybe I also have some form of ADS, but for the life of me, I cannot linearly read a paper front to back. And I’m not alone in that.
From computer science papers / academic texts, I know that this method of reading works perfectly fine. But if I try to delve into any other fields, it’s always a matter of first decoding the formula before I can try to figure out what it means.
Ultimately, it just feels like unnecessary hindrance of understanding, even if theoretically you’re just hindering those who supposedly wouldn’t understand anyways.
“From computer science papers/academic texts I know this method of reading works perfectly”
This is almost certainly due to pure familiarity. CS papers are just as indecipherable to unfamiliar persons. Possibly even more since things like complexity are heavily used, without any explanation of what it is. Data structures are another common one that the vast majority of non-CS people would not understand when referenced.
I know because this is exactly how I felt coming from an intermediate mathematics background.
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.
Mathematicians are good at writing algorithms, but not at the development aspect, which is basically building for different systems, packaging software and documentation.
I would disagree on the performance part, the vast majority of software developers aren’t writing high performance software and the ones that are tend to be computational mathematicians or physicists.
Just because you’re not writing high performance software doesn’t mean it shouldn’t be a consideration. Sure, I’m not gonna micro-optimize memory when I’m writing an API in Python, but that doesn’t mean I’m not going to write it efficiently.
If I have to store and then do lookups on some structured data I’m gonna use a hash table to store it instead of an array. If I need to contact a DB multiple times I’m only gonna close my connection after the last query. None of this is particularly difficult, but knowing when to use certain DSA principles efficiently falls pretty firmly into the computer science realm.
If you need someone to hyper-optimize some computations then a mathematician might be a better bet, but even those problems are rarely mathematician level difficult. Generally software engineers have taken multivariate calculus/differential equations/linear algebra, so we’re decently well versed in math. Doesn’t mean we don’t hate the one time a year we have to pull out some gradients or matrices though.
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.
Yeah, the ability to just sit in that chair until the code problem is solved is something that requires much more than just math… stubbornness+perseverance+bravery to try out some weird stuff
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!”
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 agree. I think we elevated Computer Science’s importance early on in the industry, and that has stuck around. If you’re a University researcher trying to make a better compression algorithm or whatever, then yeah you’ve got a lot of overlap with mathematicians. But if you’re out in the industry building CRUD apps to fit some business use case, all that theory isn’t going to matter much in your day to day.
It’s still just one of those mostly-bureaucratic hurdles where you need a CS degree to get your first job, and you need to be good at math to get the CS degree.
That said, there are definitely crucial moments where regular projects can still hit scalability boundaries, and a solid understanding of math and CS fundamentals can get you through that. Every single developer doesn’t need to know that stuff, but it’s occasionally good to have access to somebody who does.
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.
