Mechanizing mathematics — the delegation to machines of part or all of what mathematicians are imagined to do — has been an obsession of computer scientists and a target for artificial intelligence since the very beginnings of digital computing. Until recently this has been a marginal concern for mathematicians, but this is changing rapidly. To convince yourself of this it’s enough to look at the list of plenary talks scheduled for next year’s International Congress of Mathematicians (ICM) in St. Petersburg. Computing was the theme of two plenary lectures at the 2018 ICM, notably Sanjeev Arora’s talk on machine learning. At the 2014 ICM there were none. Next year, on the other hand, 4 of the 21 plenary lectures, or 19%, are likely to be related to computers. Kevin Buzzard’s abstract announces the stakes:
Now Buzzard is figuring out whether it is possible to “teach” mathematics to a computer so that it helps to prove mathematical theorems or even does it on its own.
This newsletter will not try to evaluate answers to the question that Buzzard is figuring out; that is a task for which I am thoroughly unqualified. Instead I will explore what might be meant by the question. I have read a fair amount of what other authors — mathematicians and computer scientists, in particular — have written on this and related questions, and I find that my understanding of the nature of these questions is quite different from theirs. But I find it hard to put these differences into words; my aim in this newsletter is to do just that, to my own satisfaction and, hopefully, to the satisfaction of at least some readers.
I will do so using the methods I improvised when I wrote Mathematics without Apologies. This newsletter is in a sense a continuation of my blog, also entitled “Mathematics without Apologies.” But where the earlier blog, like the book, was a wide-ranging exploration of “what do mathematicians do, and why do they do it?” this newsletter will have a single-minded focus on mechanization.
In one respect, however, the newsletter will be literally a continuation of the blog. Readers’ comments will be disabled on this newsletter, at least initially; but readers will be invited to submit comments to a page on the blog dedicated to that purpose.
This “About page” is and is likely to remain indefinitely under construction. Much more information about its author than you can possibly want to know can be found on my Columbia home page.
