If there is a prize associated with doing a puzzle, and a machine does it, then what incentive is there to pursue it.
Again, if you are only concerned with the outcome, and you have a preferred answer that you want (in this case "just use AI to advance faster"), then any information that doesn't support that case is useless or misguided at worst.
I am not trying to dissuade you from your preference. I am flagging that there is a set of other factors that influence the behavior of others, how that behavior is critical to the creation of expertise and drive, and thus why others hold different positions.
If another human was likely to get the answer before you would you also discourage them from doing it because they would rob you of the chance to do the thing you're concerned about?
Would it be unethical to dissuade someone else from enjoying the benefits of the process you wish to enjoy ?
Vs
Would it be unethical to stop a machine from data mining all the possible questions you wish to explore/enjoy.
And on another level - I am concerned with a bit more than just the answer. I am concerned with what system is in place to ask more questions and get more answers.
There is nothing in this argument that says that we won’t find some other way to study the subject. Maybe people will become monks and do math as a hobby.
We may end up in a daemon filled world, like 40k, where any hope of understanding the tech around us is impossible. (More impossible that today)
They may very well have learned plenty of things and solved or discovered other puzzles, but if the first puzzle is worth pursuing because the solution is actually useful it seems liked we're better off with the solution than a bunch of failed attempts.
That said, I do question the value of solving many of these types of math problems. I'm no mathematician so I'm assuming I'm wrong here, but on the surface many seem mostly theoretical puzzles with little or no practical use.
I’ve made this point elsewhere but the debate here is between two different philosophical positions. Results vs process.
If all you care about is the results then the process doesn’t matter.
If a person is starving or needs medicine, then a long discussion on process is inhumane. They need results.
If the conversation is about process though, then focusing on the results is missing the point.
I’d say the question for results oriented people is what are the benefits of the process and at what point does it make sense to optimize for results vs process.
When the topic is about careers the question really has to be about results. Even if the results are made by solving different problems discovered along the way towards their original problem, it still has to be about those results.
There is absolutely a question of whether burning these resources is useful when the only outcome is a solution to a potentially obscure math problem, but that is more a question of prompting and goals rather than the use of these tools themselves.
Could you elaborate?
We spend most of our young lives (many of us our entire lives) studying physics, math, etc. that others have solved. (e.g Quantum Mechanics, Relativity, Calculus, etc.)
Biology consists, almost entirely, of studying solved problems in nature.
Aren't AI breakthroughs just more to study?
Terence Tao’s “don’t create the open problem strip miner”
Why is it a problem that the professor is now a robot, and that humans could spend arbitrarily long learning from it and even after 15 years of masters-style advanced graduate lecture courses still have deeper still levels of the topic that the AI could teach them?
And if they never do reach that level of ultra-competence, well, then we found the niche for humans to continue to exist within.