Why don’t mathematicians write great code?

In the discussion surrounding a series of recent articles on the question of how mathematics relates to programming (one of my favorite navel-gazing topics), the following question was raised multiple times

If mathematics is so closely related to programming, why don’t professional (research) mathematicians produce great code?

The answer is quite a simple one: they have no incentive to.

It’s pretty ridiculous to claim that a mathematician, someone who typically lives and breathes abstractions, could not learn to write well-organized and thoughtful programs. To give a simple example, I once showed my advisor a little bit about the HTML/CSS logical flow/style separation paradigm for webpages, and he found it extremely natural and elegant. And the next thing he said was along the lines of, “Of course, I would have no time to really learn and practice this stuff.” (And he says this as a relatively experienced programmer)

That’s the attitude of most researchers. Most programming tools are cool and would be good to have expertise in, but it’s not worth the investment. Mostly that comes off as, “this is a waste of time,” but what’s keeping them from writing great code is their career.

Mathematics and theoretical computer science researchers (and many other researchers) are rewarded for one thing: publications. There is no structure in place to reward building great software, and theoretical computer scientists in particular are very aware of this. There have even been some informal proposals to change that, because everyone understands how valuable good software libraries are to progress in our fields.

But as it currently stands, the incentives for mathematicians reward one thing and one thing only: publishing influential papers. There are very small emphasis given to things like teaching, software, or administrative duties. But the problem is that they don’t replace publications. So spending work time on things that are not publications takes away from time that could be spend on papers. Everyone understands this about the job market. Say you have two candidates of equally good work, but the first candidate has one more top-tier paper and the second has contributed an equal amount of work to open source software. Though I have never seen this happen first hand, every career panel I have posed this question to has agreed the first candidate would be chosen with high probability.

So when mathematicians or theoretical computer scientists do write code, they have an incentive to get it working as quickly and cheaply as possible. They need the results for their paper and, as long as it’s correct, all filthy hacks are fair game. This is most clearly illustrated by the relationship between mathematicians and their primary paper-writing tool, the typesetting language TeX. All mathematicians are proficient with it, but almost no mathematicians actually learn TeX. Despite everyone knowing that TeX is a true programming language (it has a compiler and a Turing-complete macro system), everyone prefers to play guess-and-check with the compiler or find a workaround because it’s way faster than determining the root problem.

With this in mind, it’s hard to imagine your average mathematician having a deep enough understanding of a general-purpose language to produce code that software engineers would respect. So something like adequate testing, version control, or documentation is that much more unlikely. Even if they do write programs, most of it is exploratory, discarded once a proof is found achieving the same result. Modern software engineering practices just don’t apply.

For the majority of mathematicians, I claim this is mostly as it should be. Building industry-strength tools is not the core purpose of academic research, and much of mathematical research is not immediately (or ever) applicable to software. And most large companies who want to utilize bleeding-edge research for practical purposes form research teams. For example, Google does this, and from what I’ve heard many of their researchers spend a lot of time working with engineers to test and deploy new research. At places like Google (and Yahoo, Microsoft, IBM, Toyota), researchers negotiate with their company how their time is split between academic-style paper writing and engineering pursuits, and there are researchers at both extremes.

But even there, where coding is part of the goal, the best industry research teams still hire based on publication history. I can only hypothesize why: a great researcher can be taught programming practices trivially, so a strong research history is more important.


Now read this

Things mathematicians know but most people don’t: proofs are what’s beautiful

The depiction of mathematics in popular science often falls woefully short of reality. Authors tend to prance around the “beauty” of numbers like e, π, and the golden ratio φ, but in all honesty numbers are only one part of mathematics,... Continue →