alt Hacker NewsI’m wondering why frontier labs haven’t done that.
A few possibilities I can think of are:
A. The capability is just not there. OpenAI and Anthropic can produce a brute-force Lean proof, but their models aren’t capable enough to digest the proof as human mathematicians do.
B. They haven’t seriously tried it yet. They prioritized grabbing the land first, and have not spent much effort to polish things up.
C. It’s fundamentally impossible. These theorems are provable only in a very ugly manner. This is the reason why human mathematicians haven’t been able to crack them before AI in the first place.
As a programmer, what I’m seeing is (C). Many recent cyber hacks are products of AI trying & combining every possible tricks, and I don’t think there is any elegant short path that human engineers can replicate.
Replies
D. They seek disruption as way to market dominance and worldly power. It's not unfortunate, in their minds, but the means to their ends.
Disruption has been a SV buzzword for a long time now. It's not a byproduct but a strategy for your new technology product. SV has long perfected disruption and the people behind the AI products are masters at it.
How can so many who have seen it (and used it) for so long be so taken in by this well-worn tactic. Over and over, they choose what is most disruptive. They could have dealt with the mathematical output in many ways, including working with mathematicians to polish and publish; you see what OpenAI chose.
Similarly was the recent events where AI software 'broke containment' and hacked others. Obviously they could have controlled it if they valued it; they got the result they wanted. Notice how Anthropic (or were they first and OpenAI followed?) urgently publicized that their product, too, 'broke containment'. 'We're disruptive too!'
The four-color theorem appears to be case C. That was the first really long computer-assisted proof. No one has since found a concise way to do that proof, and it's been half a century now.