Interesting problems are not the ones which are useful, but the ones which are difficult, which allow you to show what you can do.
Soon enough instead of Millennium Prize Problems we will have a list of problem AI has not been able to solve, with even bigger reputational reward for humans
Why should any mathematician invest decades of their life working on one of them, knowing that all their efforts could be vanified by the release of the N+1-th version of a LLM, or by the usage of 10x compute resources by companies with infinite dollars? It was VERY different when the only competition came from other biological brains that had to invest the same amount of time and effort.
According to "3blue1brwn" (I'm aliasing here, no disrespect intended by not recalling his legal name), it is because of the sensation of aesthesis in understand, having your mind form the abstract structure etc. In the end I did not pursue some form of mathemathesis, but I did tip my toe in and think I know what he's talking about and his description resonates with me personal. And the way understanding changes reality is still quite informative in a lot of other engagements with the world. (Also the virtuality of me being someone who has pursued a deeper mathematical faculty is still sometimes intriguing, more on the side of applicability though.) What is curious to me with pure math is how the aesthesis could potentially happen at all, when one is dealing with stuff that isn't representable in the usual mental faculties of spatial reasoning and time. I got some impression of dealing with infinities, but wonder if anyone could try to lay out an account how something like an intuituon for something really abstract (say dealing with quantum mechanical mathematical formalisms like the schroedinger stuff) presents itself as a qualia/phenomenological) or high dimensional non euclidean spaces or what have you. (My understanding here of what potentially exist is already limited I have to admit for the sake og being humble).
Is there some visual/spatial sensation with it? Some abstract anticipation of continuity in thought? I have to think of accounts of aphantasia (not as a correlation on the register of the individual capable of something as a form of naturalism, but as an analogy to the pursuit of engaging with a form of experience that is not ones own and (presumably) can't be ones own.
Mathematics is humanity's current best approximation to a universal language, capable of expressing conscious thought precisely.
It's a "programming language for the human brain" that lets you describe reality exactly and thereby make predictions about it.
Without people (humans) knowing and understanding it, society is incapable of grasping reality in any meaningful way, unable to shape it in order to achieve a better tomorrow.
Most never realize that, because society is compartmentalized to the point of people never witnessing how it actually works under the hood. "Experts" do things for you that you never heard of, but that your very life depends upon.
While the majority of people thus lives a kind of "simulated" reality, the mechanisms underpinning that cushioned fantasy land aren't infallible. You cannot uphold an economy nor even a social structure without understanding and modeling it to a sufficient degree.
What the vast majority employs as "rational thought" isn't sufficient.
Careers in the real world are always about winning competitions, no matter what the field of mathematics is supposed to be. If not about competing for tenure, then it's a competition to publish.
And if AI can also make use of the math, then the AI is all you need in order to grasp a better tomorrow. If AI poops out a warp drive, you don't need to understand it to use it. The argument about humans needing to understand anything only holds true as long as humans have something unique to contribute, which might not be the case even a year or two from now.
Competitions are a way to motivate people. What do you believe, why they get set up in the first place? Because rich people have fun seeing you run in circles?
Competition for tenure and publishing metrics has been detrimental to science in general.
Your idea of life being about grabbing whatever comes your way and consuming it first says a lot about you, but not about life.
What do you suppose happens in a society where the constituents of that society "have nothing to contribute"? Your habit of over-simplification will come to bite you.
Well, I agree with publishing metrics being detrimental! On your other points, you're arguing against a strawman. I didn't say anything about life just being a snatch and grab, nor do I hold this belief. But university admissions, job interviews, buying non-plentiful resources...all of these are competitions. Competition permeates the very foundation of our education and financial systems. Many of our greatest virtues as a species are not competition based, but it is a large part of the reality we live in, for better or worse.
And about what happens in a society where constituents have nothing to contribute... I have no idea. But we might find out within a decade or so. The fact that what happens might not all be great is unlikely to stop any of the AI labs.
Those competitions get set up because some people understand the importance of mathematical knowledge and want their names attached to advances in it, even if they can't do the work themselves.
Clearly, it would be far better to make the public understand how the world, and society in particular, actually works. Only, those with the money profit from that not happening.
Regardless of credentials you certainly appear to have entirely missed his point. Imagine if someone suggested that cars existed for the sake of competition. But they don't, right? They exist because in our society we've organized the bulk of transportation around them. The fact that formula 1 exists, or that delivery drivers can be rated on performance relative to one another, those are not (at least in and of themselves) arguments against this basic fact.
> Imagine if someone suggested that cars existed for the sake of competition
are the mathematicians the cars here? what are you even saying? the question is whether elite mathematicians do the work they do primarily for competition and compensation or for the love of the field. now ask yourself: do F1 drivers do it primarily for the love of the sport or for the money?
> delivery drivers
people getting scooped by OAI are not the "delivery drivers" of the math world.
> we will have a list of problem AI has not been able to solve, with even bigger reputational reward for humans
we will have a list of problems that AI has not been able to solve _yet_
anyone who attempts to solve it will do so knowing that there will be thousands of agents working on the same problem, so they may not be motivated to try if they think the AI swarm will get there first and have their time wasted
Soon enough instead of Millennium Prize Problems we will have a list of problems AI has not been able to solve, with even bigger reputational reward for humans
True, but will those be problems for mathematicians to solve, or for AI developers?
It's possible that the best thing a mathematician can do for their field is to drop what they're doing and work on AI instead.
I expect Centaur Field Medals to be awarded. It's not clear how much steering Levent Alpöge did to get the result. In math it's very common to hide the search pattern and show only a simplified path to reach the final result.
Oh, GPT-3.5, recognizable in so many old screenshots by the green icon. If ever a popular model deserved the term "stochastic parrot", it was GPT-3.5. I wonder what percentage of people today still base their opinions of AI capabilities on their experiences with that model. That model was the only option for free ChatGPT users for the first year and a half of ChatGPT's existence, from November 2022 to May 2024.
GPT-3.5 was so nice because the safeguards were so easy to bypass and it wasn't lobotomized by RLHF. Newer models really don't hit the same spot and I'm not sure what I liked so much about that initial release. I look back at conversation logs I saved and I just can't replicate them nowadays.
It looks like the practical limit for that on my hardware is ~130 t/s, which is just okay. Makes reasoning mode quite painful though.
(llama.cpp can't seem to exceed 30 t/s, I had Fable make me custom inference. that's why it took me a day to get back to you)
GPT-3.5 would repeat my prompt back in its own words for me to confirm. This model immediately runs with it and generates a lot of output. I would definitely need to use a harness that allows editing / cutting off generations.
Something I've noticed about models that have been specifically uncensored or trained to generate content is that they aren't very engaging to chat with. Maybe this is just because they weren't trained to chat at all (base models) but, it's hard to find a chat model that's been trained properly.
Soon enough instead of Millennium Prize Problems we will have a list of problem AI has not been able to solve, with even bigger reputational reward for humans
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