Computers helping Mathematicians

So I wrote this for the FOM (Foundations of Mathematics) mailing list. There has been some discussions on the topic there, and the discussion was quite silly. It veered off way too quickly into when will computers "replace" mathematicians by doing what they do now, i.e. all the creative, insightful parts. Enjoy.

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I honestly think that a lot of you are looking in the wrong places to find “computers helping mathematicians”!

Example: it was not that long ago that ‘human computers’ were used to create large tables of logarithms and other functions. The first editions of Abramowitz & Stegun (A&S) were all done by humans, after all. Slowly, we learned to automate a lot of the more tedious parts of A&S.  Today, there is active work in automatic almost all of the content of A&S. This is because our understanding of ‘special functions’ has grown so much that the vast majority of that book, including the pages upon pages of symbolic identities, are now automatable. A lot of mathematics, including oddball things like Ore Rings, went into automatic what a priori looked like analysis.

Another example: LaTeX. It is a tool used by the vast majority of mathematicians, and has greatly helped make the typesetting of papers come out of the awfulness that was the 1960s and 70s. It is a mathematically boring tool, but its effect is very large indeed.

More recently, web sites like MathOverlow, and math-aware web technology, and even just standard support for Unicode in web browsers and chat apps like Zulip, have made the act of communicating among a much larger community massively easier.  Various such technologies, and others, also helped the Polymath projects into existence.  Git and github is also playing a highly non-trivial role in the speed at which systems like Lean and its growing mathlib can proceed.  Without the underlying tools, all of that would be too painful to proceed at the current speed.

The place to look for “computers helping mathematicians” is: the boring stuff. All the stuff that just needs done, requires time, but not active brain cells to perform. The more we can automate that, the more time we can rescue for human mathematics to THINK about all the fun stuff. What is considered “boring” can evolve over time. I certainly have my pet peeves of things still done by hand which shouldn’t [and am working on it.]

One day computers can actually play a more active supporting role in the ‘fun’, creative stuff of mathematics. And we should be working towards that too.

A few of us deign to work “down in the weeds”, to automate the boring stuff, as that’s the only way that the rest will eventually happen.  No, it’s not math. No, it’s not glamorous. It’s even hard work.  But, please, don’t under-estimate its value.