FrogReaver
The most respectful and polite poster ever
The bigger issue isn’t the monetary expense anyway. There are only so many mathematicians in the world who can legitimately contribute to problems at this level, and allocating their time to one problem means forgoing the work those mathematicians could have done on other problems.No more than you would like to back up yous I imagine. Calculating the financial benefit of knowledge acquisition has always been terribly complicated because its hard for us to predict what knowledge will actually be useful. Lasers went from pet project fringe sceience to one of the most important underpinnings of modern technology. Meanwhile, we have spent decades on string theory without a lot of commercial application.
So would 176 man-years of mathematican time bore better fruit than the solution to this Navier-Stokes millenium problem? Maybe, maybe not.
Of course.
Yes to my recent point...unfortunately this particular example is not the best when it comes to saying "how much is the AI thinking" because its still hard to parse out what the AI did on its own versus just walked the path already laid before it. Its very unfortunate, so we have to look to other examples for the debate.
Overall, I have seen you bring up this point a few times regarding the "cost" of AI intellligence in terms of money, resources, etc. Your point being that AI is simply too expensive which therefore nullifies it as a viable option for thought expansion. My point is, all new technologies start that way. We are already seeing signs that AI can solve problems that traditional have taken very intelligent very educated people to solve. And the difference is, the AI is getting smarter every year, whereas mathematicians still require decades of schooling to get to the point where they contribute meaningfully to their areas. If AI is capable of doing that work, than it becomes an efficiency problem....we need more intelligence per dollar. That's an engineering and computer science problem, and we have traditionally been very good at taking new technologies and making them more efficient once they hit the threshold of true utility. there is nothing to me that AI is any different in this repect than the hundreds of ground breaking techs that have come before it.
Now I can respect that we have taken such an "inefficienT" technology and expanded it way too quickly before its proven itself, that I could fully respect and agree with. But it doesn't detract from the more fundamental point that the AI IS able to do work that even a few years ago would have been a pipe dream...work that has traditionally been considered very "thoughful" work.
And mathematical progress isn’t necessarily additive in person hours. Many problems are only solvable once someone develops a genuinely new technique or insight. You can’t necessarily compensate for the absence of that insight by throwing more mathematician hours at the problem.
So I think the relevant comparison isn’t simply mathematician expense versus however much compute cost the AI used. It’s also what else could those mathematicians have accomplished with their time on other problems. And that opportunity cost is much harder to quantify.







