Automating Mathematicians

The New York Times published an article with the ominous title A.I. Is Coming for Mathematics, Too. We know by the work of Gödel and Turing that we can't automate mathematics. But can we automate mathematicians? Is AI coming for us?

Reading the article I'm not immediately scared. The focus is on logical systems like like the Lean theorem prover and SAT solvers. 

Developed at Microsoft by Leonardo de Moura, a computer scientist now with Amazon, Lean uses automated reasoning, which is powered by what is known as good old-fashioned artificial intelligence, or GOFAI — symbolic A.I., inspired by logic. So far the Lean community has verified an intriguing theorem about turning a sphere inside out as well as a pivotal theorem in a scheme for unifying mathematical realms, among other gambits.

So Lean is being used mainly to logically verify known theorems. This could actually make life harder for mathematicians, if journals start requiring formal verification for submitted papers.

I'd love a higher-level AI. One that takes a journal-style proof and verifies it, or even better takes a proof sketch and fills in the details (and write it up in LaTeX) . In other words, let me think of high level ideas and leave the messiness to AI. 

I'm won't be holding my breath. Right now, generative AI has limits in its ability to reason, and reasoning is at the heart of mathematics. 

On the other hand, AI now plays a mean game of chess and go, which we also think of reasoning. So maybe automating mathematicians is closer than we think. It might go further and start suggesting new theorems and proving them on their own.

Ultimately like most other fields AI won't eliminate the need for mathematicians. But like nearly every career moving forward, those who will succeed will not be the ones that push back on AI but those who work smarter and harder to use AI as a tool to do even greater things. Best to think about how to do that now before it's too late.