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Looks like we're getting another big load of solutions soon from OpenAI, this time at least with more consideration for human mathematicians https://openai.com/index/advisory-group-on-mathematics-and-ai/ :
Exciting times, as they say. Their new group:
As an ex-mathematician who now works in a field with no time for sentimentality (if it works, we use it, if it doesn't, we throw it out) I'm quite happy to see AI push the boundaries of the field. My mathematician friends are understandably more reserved about things, but apart from those who literally wanted to just be an academic they're all at least somewhat interested. Equally though another part of me is quite pissed off that we now have a gaggle of commissaries who decide on when and how the top labs will be doling out crumbs of mathematical insight to the general public. This kind of crap, if anything, is what leads to the creation of the "permanent underclass", to use a phrase that is currently a la mode with the AI types. What next, a committee for AI and law? A committee for AI and medicine? A committee for AI and finance (I shudder)???
I wish OpenAI would just disclose these results. Even assuming their strategy is benevolent, I’m still uncomfortable with the company keeping such artifacts secret.
If OpenAI has a proof of (e.g.) the Riemann Hypothesis, then that seems like part of our shared human cultural heritage. I’d feel similarly if some private collector discovered a trove of lost Shakespeare plays and declined to share them.
I decided long ago that if I stumbled upon a proof of P=NP that I'd decline to publish it, quit my job, and find a cabin in the wilderness like Uncle Ted (without the explosives). If P!=NP, publish away. But "actually asymmetric cryptography is fundamentally broken" seems like something to really think through the disclosure of, given it's ubiquity. I would not trade that for the ability to optimize travel routes for the sales department.
Imagine the conspiracy theories though. “OpenAI has cracked all public-key cryptography via proving that P=NP internally. Only the secret superprimes generated via their own proprietary Riemann Hypothesis counterexamples are secure.”
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Proving P=NP doesn't break all asymmetric crypto. Factoring probably isn't even NP-hard, nor is discrete log on a Galois field or an elliptic curve. You need both more and less to break asymmetric crypto. More, in that you need a practical break; if you can factor numbers or extract discrete logs in polynomial time but the minimum exponent is 1000, you've got nothing useful. Less, in that you could theoretically come up with a polynomial-time solution while leaving NP-complete problems without them.
If you do find a practical break, obtaining a few "orphaned" bitcoins and selling them might be the best thing to do. But the NSA might be watching for that.
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