{"id":22984,"date":"2026-08-02T00:00:00","date_gmt":"2026-08-02T00:00:00","guid":{"rendered":"https:\/\/scannn.com\/mathematics-without-mathematicians\/"},"modified":"2026-08-02T00:00:00","modified_gmt":"2026-08-02T00:00:00","slug":"mathematics-without-mathematicians","status":"publish","type":"post","link":"https:\/\/scannn.com\/lv\/mathematics-without-mathematicians\/","title":{"rendered":"Mathematics Without Mathematicians"},"content":{"rendered":"\n
\n

Yesterday, OpenAI announced<\/a> the solution to ten open problems in
\nmathematics, all discovered by a yet-unreleased model. There\u2019s only one, the
\ncoding theory one, where I know enough to say \u201chuh, that\u2019s important\u201d, but
\naccording to the mathematicians I trust this is important.<\/p>\n

Inevitably, people will spin some sophistry to cope, to convince themselves
\nnothing will change. And that\u2019s fine. People need to cope. But we can\u2019t put our
\nheads in the sand forever while the world is transformed around us. So, here is
\na list of ways people will cope about AI taking over mathematics, and how each
\ncope is likely to be refuted by reality.<\/p>\n

My intent is not to horribly depress everyone but rather to help them metabolize
\nthe implications of this technology. The arguments here are somewhat portable:
\nreplace \u201cmathematics\u201d with \u201cbotany\u201d or whatever as needed.<\/p>\n

Moving the goalposts.<\/strong><\/p>\n

Obvious and not worth addressing.<\/p>\n

\u201cWe will direct the AIs, point them at problems and research areas
\nto solve.\u201d<\/strong><\/p>\n

The AIs will exceed humans in taste<\/a> and intuition. At some point, the
\nhuman pointing the way will get worse results than the human saying \u201chere\u2019s a
\nproof checker, have fun\u201d and paying for the tokens.<\/p>\n

\u201cWe will teach the mathematics AI discovers.\u201d<\/strong><\/p>\n

The AIs will be better teachers than the humans. In any case, there won\u2019t be a
\nhuman audience for expository work of frontier math.<\/p>\n

\u201cWe will choose how to canonize the results AI discovers.\u201d<\/strong><\/p>\n

This is a nice cope. The AIs are explorers out in the frontiers, the humans
\ngratefully receive their Lean proofs, and then discourse over them, choose which
\nresults are relevant, shape those results into a little brick for the great
\ncathedral of algebra<\/a>. Analogous to the above: the AIs will build the
\ncathedral on their own. They will be better architects than us.<\/p>\n

\u201cWe will become students of AI mathematics.\u201d<\/strong><\/p>\n

This works until the AIs have blasted so deep into the deductive closure of
\nmathlib that the distance from elementary mathematics to the frontier exceeds
\nwhat any human can hope to learn in their lifetime, no matter how narrow their
\nfocus.<\/p>\n

\u201cWe need humans to understand the results AI discovers.\u201d<\/strong><\/p>\n

We won\u2019t! This misunderstands who the audience will be. AIs will do frontier
\nmath, downstream, AIs will use the new math to do frontier science, finally, AIs
\nwill use the new science to do frontier engineering. No human needs to
\nunderstand any of it, firms that put humans in the loop to understand the
\nresults will be outcompeted by those which don\u2019t.<\/p>\n

The result is that we will live in a demon-haunted world, full of marvelous
\ndevices whose operation we will not understand, based on engineering principles
\nwe will not understand, discovered using formalisms we will not understand.<\/p>\n

\u201cComputers are already superhuman at chess, yet we still play chess.\u201d<\/strong><\/p>\n

Unlike most copes, I think this one is interesting. Computers are superhuman
\nchess players, yet we don\u2019t care, and continue playing as normal. Why should
\nmathematics be different?<\/p>\n

The main reason, I think, is that chess is self-contained: results from chess
\ndon\u2019t help us understand the orbits of the planets or the binding of drugs to
\nprotein surfaces. But mathematics, famously<\/a>, is the great dynamo of
\nscience, the best language and method for understanding the world. A machine
\nthat can replace a human mathematician, but better and faster and cheaper, is
\nmaterially useful; a better chess engine is not.<\/p>\n

If two computers which are superhuman at chess play against each other, who
\ncares? There is little demand for this, so there is no-one to outcompete. A
\nsuperhuman mathematician is different.<\/p>\n

\u201cMathematics will change, but mathematicians and the mathematically-inclined
\nwill still do math on their own.\u201d<\/strong><\/p>\n

I think this ignores that mathematics is embedded in a social context. As an
\nexample: when it became clear that AI would eat software, my cope was: \u201cI\u2019m
\nperfectly happy to become an engineering manager to agents in my professional
\nlife; in my off time, I can still write code<\/a> for the pleasure of it.\u201d<\/p>\n

And I do. But this cope ignores the effect AI has had on the social context of
\nwriting code: the discourse has gotten worse, and vastly more anti-intellectual;
\npeople who used to talk about type systems and compilers now talk about \u201cloops\u201d
\nand \u201charnesses\u201d; you put a hand-created project on GitHub and you get slop PRs;
\nyou open a link to an interesting-looking project and find the README is
\nunreadable AI slop. And in the long-term, it is demoralizing to ponder: will
\nanyone design a new programming language? Dually, if I design a new language,
\nwill anyone care? If I write a library that introduces an elegant new formalism
\nto solve a particular problem, will anyone use it?<\/p>\n

Which is to say: no man is an island. You can do mathematics on your own, but
\nyou\u2019ll find that very, very few people can sustain any activity long-term on the
\nbasis of intrinsic motivation alone. We are social animals: we care about being
\nuseful, about status, about outcomes in the world.<\/p>\n

I think I should end on a cheerful note. So let me try. Personally, I don\u2019t
\nbelieve technology is inevitable. \u201cInevitable\u201d is a word reserved for the orbits
\nof the planets. Nothing that is the product of human action is inevitable. We
\ncan choose to obsolete ourselves, and we can choose not to. We can realize that
\nAGI is a devil\u2019s bargain: we may<\/em> accelerate technical progress, we may<\/em>
\nunlock all kinds of wonderful tech tree nodes like life extension earlier than
\nwe would otherwise; but the result, in the long run, is that humans become, at
\nbest, like pets under the care of vastly more powerful entities.<\/p>\n

The future is not certain, but I\u2019ve phrased everything above as definitive for
\nsimplicity. If we take the possibility of AGI and ASI seriously, if AI continues
\nto progress as it has for the past ~6 years, I think this is a reasonable view
\nof where things will go.<\/p>\n

Probably the best argument against AI progress is \u201cRL doesn\u2019t generalize well,
\nwe have seen immense progress in verifiable domains like formalized mathematics
\nand coding, we will see less progress in domains that are intuitive or
\nunformalizable\u201d. Maybe true. But billions of dollars and thousands of very smart
\npeople\u2014and, increasingly, very smart models\u2014are being thrown at this
\nproblem. How long does this cope last?<\/p>\n<\/div>\n

Source link <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Yesterday, OpenAI announced the solution to ten open problems in mathematics, all discovered by a yet-unreleased model. There\u2019s only one, the coding theory one, where I know enough to say \u201chuh, that\u2019s important\u201d, but according to the mathematicians I trust this is important. Inevitably, people will spin some sophistry to cope, to convince themselves nothing […]<\/p>\n","protected":false},"author":16,"featured_media":22985,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[143],"tags":[],"class_list":["post-22984","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai"],"_links":{"self":[{"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/posts\/22984","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/comments?post=22984"}],"version-history":[{"count":0,"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/posts\/22984\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/media\/22985"}],"wp:attachment":[{"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/media?parent=22984"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/categories?post=22984"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scannn.com\/lv\/wp-json\/wp\/v2\/tags?post=22984"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}