Keep Calm and Prove On
(Some of) Math is Solved!
There's been a bit of an uproar about AI in mathematics in recent days. If you haven't heard, math is solved! It seems that just last month I was wondering about this, and now here we are! Mathematicians are lamenting the end of mathematics. The Wall Street Journal story AI is Powerful Enough to Crack Our Hardest Math Problems—and Kill Us All explains:
For mathematicians, the developments have raised existential questions—what do you do when you have devoted your life to problems that are now being picked off by AI?
The story goes on to quote Timothy Gowers, a British pure mathematician and winner of a Fields Medal:
"I don't want to say it's all over," Gowers said, "but I certainly don't want to say it's not all over."
Solved ⇒ Job Growth?
Software developers were the first to be taken down by AI. They are truly suffering. In the United States, according to the Bureau of Labor Statistics (BLS), the number of jobs in software development is higher than ever.
Economists use fancier numbers—in this case considering overall employment trends—and still seem to agree. In The jobs apocalypse is postponed. An AI jobs boom is here, the Economist reports:
The Economist tracked employment in professional occupations closest to the AI boom—engineers, software developers, mathematicians and data scientists—and compared their growth since 2022 with professional employment overall. These roles have added roughly 730,000 jobs above trend in recent years.
Software development is changing but not dying. The general feeling among software developers seems to be that AI is great for many tasks, but it does not have the capability to create enterprise software of the quality necessary for any real business. Communications of the ACM recently published AI Didn't Make Programming Easier. It Just Made It Differently Difficult, which concludes
AI does not, therefore, diminish the craft; it widens it, deepens it, and makes more of the work explicitly intellectual. The work becomes differently difficult because it demands more sophisticated forms of expertise: judgment over recall, architecture over syntax, orchestration over implementation. These are not easier skills to develop or demonstrate, they are simply different ones, and perhaps ultimately more demanding.
I expect that mathematics can take a lesson from this. I don't think mathematicians will or should be reduced to verifying AI-generated outputs. Mathematicians have never been simply proof machines, so it is perhaps not such a big deal that proofs can be largely outsourced in the future, if that is indeed the case.
Waiting for Proof of the Proofs
While the solution of hard math problems is impressive, what we're seeing is that some math problems are being solved. A lot of compute has been thrown at a lot of problems, and we're just seeing the few extraordinary results. These are leveraging extant human-created knowledge, and not without significant controversy.
So, while I will certainly grant that AI is succeeding in solving more and more difficult math problems every day, I will withhold final judgment until I see the results of the next few rounds of 1st Proof. The 1st Proof test problems are nothing compared to Navier-Stokes. They already have solutions, and most are estimated to be solvable by a capable graduate student. In the prior round in June 2026, no single system perfectly solved more than 3 of the 10 problems.
It's also worth commenting that a lot of the math problems that are being solved by AI aren't of particular interest outside of pure math. As Steven Strogatz so unabashedly puts it in a recent Wired article, the significance of the Navier-Stokes result is nada:
It's a very theoretical math problem of essentially no interest to a working engineer in civil engineering or aerodynamics. It's a very, very arcane question.
The AI companies' only interest in these problems is proving their capabilities. They have no qualms about salting the earth of research mathematics. As Thomas Wolf, co-founder of Hugging Face, put it:
I just hope [that AI] companies stop using mathematics primarily as a demonstration of prowess in their private race.
Sabine Hossenfelder had a great video recently titled AI Has Eaten Maths. Physics Is Next. She captured the mathematical mood well, and I'll adapt her quote about physicists to be instead about my image of applied mathematicians working with AI:
Pure mathematicians see artificial intelligence and ask whether mathematics will survive. Applied mathematicians ask whether it can finish the calculation by Friday. — Adapted from a quote by Sabine Hossenfelder
To be fair, not all mathematicians are in despair. See "After Math" by Silvia De Toffoli and Eamon Duede on Terry Tao's blog for a more hopeful take on this existential crisis.
Indeed, I would be quite happy if AI could solve my math problems, which it usually cannot do. Admittedly, it has solved one of my problems, if you count finding someone else's solution and passing it off as its own. I prefer Claude Max, though my coauthors use other tools and don't seem to be faring any better. Perhaps the problem is that I don't believe in it enough.
AI Disclosure: All the writing is my own. I used AI for downloading BLS data and drafting some TikZ figures (later overhauled), discussing image ideas, and grammar checking.