another story about the lack of chain-of-thought reasoning traces in frontier models...
[deleted]
A misalignment of AI in mathematics
401–410 of 451 posts
Re: A misalignment of AI in mathematics
#402Having an oracle that answers yes/no to mathematical questions is very valuable even if there aren't ever any explanation. I don't see how having an answer influences the process of making sense o it negatively. If anything it will save a lot of time - you won't spend time trying to prove something that's not true.
I get that mathematicians and other academics have their social structure and mechanism to create social hierarchies but those aren't very important to interest of general population that funds them.
If the process of making sense of the results, finding structure that humans can understand and writing explanations that allows for wider understanding is valuable it will still be valuable and there will be need for people able to provide it. If it makes higher mathematics accessible to more people then it's even better. I am hope they will not manage to sacrifice that for the sake of their little society in society.
Re: A misalignment of AI in mathematics
#403As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…
I agree. What would stop the AI from explaining the proof in a way human mathematicians can understand, and then giving them a roadmap for spreading it through the community via textbooks, conferences, and so on?
Re: A misalignment of AI in mathematics
#404This is quite fascinating as it looks like the esteemed professors run into a problem of runaway capitalism for the first time. Guess what? The corporations involved don't really care about your feelings or how pursuing their goals affects your life, your well being, anything at all here. Talking with them is kinda moot, this is full on adversarial as countless people around the world, say the nigerians dealing with oil spills would tell you.
Re: A misalignment of AI in mathematics
#405As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…
How do you write a grant for that though? "I plan to prompt Claude until it eventually spits out an answer"?
Re: A misalignment of AI in mathematics
#406It reminds me of Frédéric Bastiat's Candle Makers' Petition. It satirised protectionism in the 1800s: >We candlemakers are suffering from the unfair competition of a foreign rival. This foreign manufacturer of light has such an advantage over us that he floods our domestic markets with his product. And he offers it at a fantastically low price. The moment this foreigner appears in our country, all our customers des…
This is a straw men argument
The petition is about a much broader problem: if we’ll demotivate people from understanding math, vibe math in a rush without making it understandable - math becomes useless
Basically with pic generation at least we all understand what is on a pic - some cat or something
With math it is trivial to generate a lot of stuff that is half-assed and just gives a plain yes/no but doesn’t get absorbed into human technology and better math
Basically it is not inly about the answer 42, it is about the questions, _meaningful_ _full_ answers and empowering people
By giving a short answer AI can burn the find and make it boring, hide the fertile ground around that answer that any human would’ve highlighted
If you have Einstein - it is not just relativity he did - you can continue asking him questions and he continues the research direction, teaches students, etc
With AI it is often 100% gate keeped (most of the time experimental AIs do the stuff, you have no access even for 200 bucks/month or more) slave that was killed after finishing - hard to “compete” with that and it is not very inspiring approach to researchers ;-)
Re: A misalignment of AI in mathematics
#407As a consumer of mathematics, I want to attack the author’s idea of “what that work was meant to achieve in the first place”.
I do a lot of programming that uses mathematics. I designed the error recovery file format “par2”. I worked as a quantitative trader.
What do I want from math? To be able to search math results, understand them, and apply them. But academic mathematicians are so inwardly focused - as these authors so obviously are - that it does all of these badly! Search is still with words, not symbols and formulae. As for comprehension, many math papers are unreadable to those not in the cliche of mathematicians in that specialty. And even applied math papers don’t ship code or specify the operations explicitly.
I wanted to fix this and in 2013 I worked on formal proof. It makes symbol search and application easy. I found out that the tools had been usable for decades at that point. But mathematicians didn’t use them because they had that inward focus and didn’t give a damn about math consumers.
AI is enabling formal proof. It will carry mathematics into the computer age, which the field should have joined with every other industry in the 1970’s! I welcome it. Math will get used more and that is what the work was meant to achieve in the first place.
Re: A misalignment of AI in mathematics
#408This is a PR problem, not a mathematical problem. It's possibly the worst PR problem mathematics has faced since the execution of Hippasus for whistleblowing on the cover-up of the regular dodecahedron. It's still a PR problem. So what went wrong? Mathematics education. Math below grad school is all about solving stated problems. Credit is given for solving puzzles successfully. Homework is problem sets. Everybody be…
They are defending the value of their achievements!
They should explicitly advocate for the Fields Medal to weight teaching achievement more heavily going forward.
Re: A misalignment of AI in mathematics
#409This is a PR problem, not a mathematical problem. It's possibly the worst PR problem mathematics has faced since the execution of Hippasus for whistleblowing on the cover-up of the regular dodecahedron. It's still a PR problem. So what went wrong? Mathematics education. Math below grad school is all about solving stated problems. Credit is given for solving puzzles successfully. Homework is problem sets. Everybody be…
It's not just math, though.
In general, in our existing society, status matters, and it is tied to achievements. Therefore a thing that devalues the achievement is also causing people to lose status, and everything that comes with it (income etc). Of course they are mad.
But maybe the answer to that is to acknowledge that our civilization is basically a dick measuring contest at scale, and try something else for a change? Starting with the part where people don't have to be "productive" to have intrinsic value as a person?
Re: A misalignment of AI in mathematics
#410[flagged]