Henry Yuen on X: "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." / X<br>Post

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Henry Yuen

@henryquantum

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.<br>span:not(:empty)~span:not(:empty)]:before:content-['·'] [&>span:not(:empty)~span:not(:empty)]:before:px-1 [&>span:not(:empty)~span:not(:empty)]:before:shrink-0">6:39 PM · Aug 1, 202654.8KViews

10<br>68<br>799<br>193

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@henryquantum

4h

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's Show more

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@henryquantum

4h

3. 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 much Show more

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@henryquantum

4h

4. 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 introduces Show more

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@henryquantum

4h

5. 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.

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