“Mathematicians have to grapple with being replaced by AI.”
This has become a constant refrain among the media and concerned mathematicians alike. For example, the article “THE CRISIS OF AI-GENERATED MATHEMATICS” (all caps) went viral, as further evidence of how we’re living in an “everything crisis.” Even arXiv, once known only for scientific preprints, has effectively become an extension of the mainstream media now, with the expected alarmist language and bold proclamations.
My opinion has not changed: nothing will happen. To the best of my knowledge, no job category has been replaced by AI. Automating manual and service-sector labor at scale isn’t possible, due to overhead costs and technological limitations. Coordination is hard to automate. Same for dealing with edge cases (the so-called “health insurance problem,” where you have circumstances unique to each policy holder). At some point, humans have to make judgment calls. AI cannot do this.
Math is the same, but different filtering mechanisms are at play. By definition, status is scarce and zero-sum, regardless of how capable AI becomes. So this means institutions and individuals will seek to allocate it judiciously. The media assumes that AI will bypass or overturn the traditional status quo in mathematics. I don’t see much, if any, evidence of this occurring, or any compelling reason that it will.
As for trying to simply ban AI, that’s impossible to enforce. AI-assisted math is here to stay. Not using AI puts one at a huge career disadvantage in what is a hyper-competitive academic job market. People will just use AI and then fail to cite it, or rewrite their papers in such a way as to conceal it.
The new bottleneck will be finding worthwhile problems and prompts, conditional on constraints (e.g. usage costs). This includes knowing when to abandon a problem or which problems are most amenable to AI. Otherwise, you risk burning money on dead-end approaches. Those who have better math intuition will focus on problems and prompts that optimize resources.
Journals will adapt to the deluge of AI-generated papers by rejecting more papers, as AI will raise the bar for quality. So it’s not as if having a math career becomes easier, even though AI helps at the same time. This ties in with status being scarce and finite, and how relative innate differences of ability will still persist and matter. The people who were smart and talented before AI will adapt and still come out on top.
Of course, it’s possible an outsider will use AI to upend the “math status quo,” but this seems quite unlikely. If this happens at any scale, then we can entertain the possibility of mathematicians being obsoleted by AI. But so far, it has only been credentialed professionals (either at universities or research labs) using AI to produce new results.
Again, no amateur has successfully published an AI-produced math paper in a peer-reviewed journal. This would be the equivalent of publishing AI slop to a literary journal or magazine, which has actually happened on a few occasions. Experts, by their very profession, are good at sniffing it out, though.
ArXiv is easier, and this is doable with an endorsement. But journals have higher standards for correctness and novelty, and amateurs are not good at either, even with AI. Their results tend to fall into one of two categories: uninteresting but ostensibly correct, or interesting and wrong. So, all the claimed fallacious proofs of famous conjectures fall into that second category.
To belabor the point, AI cannot tell you if a math proof is correct or not. The only consensus mechanism in math is humans. A math result is considered correct when enough peers agree it is. What happens when a preprint drops claiming to resolve some important open problem? Humans, not AI, pounce to check it. And if it passes this scrutiny, then it’s considered correct.
What about Lean? A lot of people think you just upload the pdf/latex to Lean and it tells you if the entire paper is correct or not. This couldn’t be further from the truth. I blame the science media for poorly communicating how proof checkers actually work. A Lean proof requires rewriting the paper in the complicated Lean language to ensure that the concatenation of lemmas and theorems actually proves the original claim of the author. The question “is the translation faithful to the author’s intent” is subjective and requires human appraisal.