Some initial thoughts, and a complicated mix of feelings

Some initial thoughts, and a complicated mix of feelings.

1. Wow. I mean, Erdos problems are cool (I genuinely mean that), I didn't know about the Jacobian conjecture before it got disproved. But this newest batch from OpenAI hits home in a way the previous announcements did not.

New circuit lower bounds? A simple, easy-to-describe non-sofic group? Hardness of approximation for CVP without needing a unique games-like conjecture? I didn't just hear about these problems from my friends or from seminars. I feel their importance in my bones; I deeply care about the answers to these questions.

• 2. And then -- the kicker -- something that I personally spent a couple years on in grad school, leading to some of my proudest work: quantum parallel repetition theorems. I spent many hours, days, nights, weekends in cafes, in my office, at home, trying to understand Ran Raz's3. Now, to the math. In 2016 I proved a polynomial-decay theorem; the exponential-decay theorem was left open and has since remained one of my favorite problems. I always intended to come back to it. Actually, a month ago I tried to set GPT 5.5 on it, and it didn't make very much4. I am disappointed by the writeup of this proof (sorry Lijie -- I should've taken a look at it earlier!). It writes in a way that's characteristic of a lot of ChatGPT-generated proofs, in which it elaborates at length on "boilerplate" setup, but then nonchalantly introduces5. I'm in awe, and excited to see what other things we will learn from the AIs. There are a number of problems I've spent a long time thinking about, and maybe I will learn how to answer them soon.6. But -- what then? What happens when AI has answered the handful of my favorite problems that I've spent the last 15 years thinking about? There are a lot of nice problems that I like, but it's not so easy to find a favorite problem.7. There's a lot more to say here, but I think we mathematicians and theoreticians will have our work cut out for us: to keep a leash on these collossi of thought and reasoning, and to keep their abilities intelligible to humankind.
• sounds like your Lee Sedol moment for math. interesting read. thanks for being honest. sounds like we are reaching AGI/ASI soon, especially for math..