Disarming the AI Bomb

It's been about a month since the OpenAI drop. Many people have been asking, how should mathematics look in the future? I wanted to offer my take.

First, let me tell you what was the reaction I saw to the OpenAI drop. Not the initial upset, shock, or excitement that rippled through the community. But what came afterwards. Nobody picked up their stuff and left, but most people I've talked to (inside and outside of set theory, that was relatively unscathed by that drop) are not particularly in a rush to read those papers. Instead, people are annoyed by the action, and there are debates on whether or not we need to decipher what's in those pdf files and lean proofs, or if we need to just move on, etc.

In a short summary of my previous posts on this matter, OpenAI tried to muscle a disruption on mathematics. They tried to create a perception in the public that they can do it better than us, and they may or may not have succeeded on some of these fronts to varying degrees. I think nobody doubts that the AI models of today, or at least those of next year, will be able to do some very complicated things. But the way that OpenAI dropped those solutions, that was just an act of war on the mathematical community. If the true goal was to advance it, they would have tasked an agent to figure out who are the top 5 experts on a problem, and consult with those experts as a first step. They would collaborate, and slowly produce digestible outputs.

So. What should a mathematical community do? Well. Here is what I understand is the prevailing mood, which I am very much a part of. If OpenAI tried to scoop us, we need a scoop-proof mathematics. This means, redesigning the notion of "credit".

Very often we tend to give credit to the person who had placed the capstone on the top of the pyramid. The person who connected the dots, and made the final deductions. But mathematics is not done in isolation. It is an impressive pyramid because so many people contributed to its enormous height. And sometimes, maybe, much of the pyramid is buried under the sand and is invisible to us. But a capstone on top of a buried pyramid is just a lonely stone in the desert. Mathematics is, by all accounts, a social activity. We work together, to make each other understand better.

The goal of mathematics is to promote understanding, not solve equations of sorts.

So, how does AI fit into this? AI is a new tool. And it will be able to solve all manner of things for us, just like a calculator saves us time in computing logarithms or the values of sine, or even multiplication and addition. Just like Wolfram Alpha and MATLAB allowed us to compute integrals, etc. etc. etc. Those are tools, just like AI helpers.

When calculating machinces became more widespread, easy to use, and convenient, people stopped spending their careers computing stuff. When computers because convenient, we started using code to search for various solutions instead of doing it by hand, or by just guessing possible values and checking. But in these cases, we understand the machine, it is transparent to us. Even if I can't (or won't) calculate \(\log 2\) to the 20th digit, I know how to do it: pick a convenient Taylor series, compute the \(n\) you need to get the level of approximation, and do a bit of arithmetic. Even if I will never, in my life, be able to check all numbers below \(2^{34}\) on whether or not they are twin primes, I understand how the algorithm goes: write down the numbers, use a sieve algorithm to weed out the composite, check if \(n\) and \(n+2\) are still on the table.

But how does an AI agent come up with an idea for a proof? How does anyone come up with an idea, though? Well, the idea for the lifting criterion that Yair and I found came from trying to understand how to modify Silver's criterion for a new context. The idea for critical and weakly critical cardinals came from trying to focus on embeddings and not ultrafilters. The idea for the construction of a critical cardinal with a singular successor came from analysing similar proofs done in the past. I had a long chat with Andreas Lietz yesterday, where he explained to me part of his Ph.D. work. And he did a great job conveying the origin of the idea "in this context, you want to think about this and that". That was wonderful. But do androids dream of electric sheep? What moved an AI to think of a solution? We don't know.

So, we can wait until the technology ripens enough and we can trust it to produce correct results and be able to explain the train of thought. And I am sure that for some problems, we are already there. But this depends on the specifics.

Here is my take. The credit should go to everyone involved. An in particular, to the people who spend time not only connecting the dots, but explaining to us why they connected these specific dots.

We need to work together to strive for understanding. Mathematics without understanding is not interesting, nor it is really useful. And we need to understand how to promote that understanding, and how to reward people who contribute to the understanding.

Nobody knows what mathematics is going to look like in 2121. We are in times of such rapid change, that we can't even say how it will look like in 2030. But we can still take control over how we consider results generated by AI, the explicit goals of mathematical research, and how we build our culture around it.

As an immediate action in the short-term, I think that journals should require AI-assisted papers to come with the logs, available (at least) to the editorial board and the reviewers. I think this way we can judge who contributed what. And each journal can make their own decision about what are the comfortable ratio between human and AI contributions.

And for the love of god, ban the sentence "the authors take full responsibility on the results". If you put your name on something, you're already taking responsibility on it.