Mathematical breakthroughs with commercial relevance are few and far between, and often depend on dusting off old results which were, at the time of discovery, "solutions nobody asked for."
The NS counterxample is actually, by any market measure, a "problem nobody asked for" in the sense that its existence doesn't have any commercial relevance (beyond juicing OpenAI's IPO). So the only long-term value solving it could have is by virtue of whatever reusable theory/insights were generated along the way to the counterexample itself. The letter is absolutely right on that point.
It's not actually clear that those insights will come faster from reverse engineering this LLM proof vs. humans building theory to solve the problem themselves. So what you're saying may or may not even be an efficient way of operating. Also, it implicitly depends on mathematicians to do the hard work of creating problems and then deciphering LLM hieroglyphics for essentially free while the only immediately profitable component gets outsourced to a frontier lab. In what world is that model going to work?
Reading between the lines, it seems like maybe you have a personal grudge for some reason and simply think the technology will advance enough to where we won't need academics at all. But you should say that in the first place.
I just wonder whether a lot of smart people who never needed to go beyond the "solve for X" algorithmic math of a typical calculus sequence are actually reading the declaration the way the signatories wrote it. The Navier-Stokes problem is not exhausted by a simple 'no' counterexample (which most people familiar with the equations already expected to exist). In fact, I haven't heard a single person's explanation for what relevance this counterexample has for humankind. It is something impossible in our physical reality so we have gained zero insight into anything we actually model with NS.
Mathematicians agree that "solving the problem is aligned with humankind." They disagree that releasing a counterexample this way actually constitutes "solving the problem" precisely because there is now little incentive to do the hard theory-building work that actually has the track record of leading to human advancement.
The NS counterxample is actually, by any market measure, a "problem nobody asked for" in the sense that its existence doesn't have any commercial relevance (beyond juicing OpenAI's IPO). So the only long-term value solving it could have is by virtue of whatever reusable theory/insights were generated along the way to the counterexample itself. The letter is absolutely right on that point.
It's not actually clear that those insights will come faster from reverse engineering this LLM proof vs. humans building theory to solve the problem themselves. So what you're saying may or may not even be an efficient way of operating. Also, it implicitly depends on mathematicians to do the hard work of creating problems and then deciphering LLM hieroglyphics for essentially free while the only immediately profitable component gets outsourced to a frontier lab. In what world is that model going to work?
Reading between the lines, it seems like maybe you have a personal grudge for some reason and simply think the technology will advance enough to where we won't need academics at all. But you should say that in the first place.