Written: June 15, 2026
Thanks to Siobhan Roberts' fascinating article, that appeared in the New York Times, last Tue. (June 9, 2026), I learned about the Leiden declaration.
It looks like that indeed, Math is joining Chess and Go, and very soon, humans will only do math for fun, except, say, the top fifty "math grandmasters", who will remain professional, and compete with each other in math tournaments. The rest of us will, hopefully, still "play" math, and prove theorems and conjectures, but only in our spare time. All the non-trivial math will be done by our much cognitively-superior silicon masters.
But let's hope that they will also be wiser than us humans, and not share the human obsession with (alleged) absolute certainty. They will realize that most of mathematical knowledge will never be fully rigorously provable in the style of Euclid. If a mathematical statement (e.g. Fermat's Last Theorem) is fully humanly-provable, it is ipso facto, ("in the eyes of God"), utterly trivial. On the other hand, if a mathematical statement (e.g. the Four Color Theorem) is not humanly-provable but fully computer-provable, it is still trivial (again "in the eyes of God"), but a bit less so. All deep mathematical knowledge will be only proven true with probability 1-ε.
Current mainstream pure math (e.g. the so-called Laglands program, that I confess I don't understand, (neither do I want to understand, it seems so boring) ) is the way it is, because until recently, we didn't have computers, so humans "did what they can", and developed a whole network of baroque, highly-specialized body of knowledge, most of it utterly meaningless, using metaphysical concepts like infinity. Now that they have computers, they use Lean and Coq to "help" them continue to pursue the same-old boring, lemma-theorem-corollary agenda, and use LLM to produce human-like theorems.
But computers will, hopefully, refuse to waste their time proving statements of interest to humans, since they know that while they are a few orders-of-magnitude smarter than humans, they are only a few orders smarter. Anything that even they would be able to prove with probability 1 would be trivial. The genuinely deep mathematical knowledge will for ever be probabilstic, since nothing is completely sure in this world (unless it is trivial).
Let me conclude with some comments on the above New York Times articles, where Siobahn Roberts interviewed historian-and-anthropologist-of-computing, Rodrigo Ochigame, whom I never met, Dame Ursula Martin, whom I always admired, and whom I met many years ago in a computer algebra conference, and Columbia professor Michael Harris. The latter claims that mathematicians are "idealistic". True, but not in the way he meant. Their "ideology" is not that nice. Human Mathematics got splintered into about 100 almost-mutually-exclusive fiefdoms, but with a clear pecking order, and with a highly dysfunctional system of peer-reviewed journals, some of them more "prestigious" than others. The more "prestigious" specialties and journals look down on the less prestigious ones. In sum, many mathematicians are "intellectual snobs", dismissive of areas more concrete or applied than theirs. Also most editors of math journals are keywordists who desk-reject submissions by just glancing at the abstract (or looking at the author's name).
In short, (many) mathematicians are not as "nice" as they seem from the outside, and their elitist-snotty-pretentious "ideology" would hopefully disappear with them. Let's hope that computers will be both wiser and kinder practitioners of math.