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A misalignment of AI in mathematics

mathandai.org

991–1000 of 1001 posts

Re: A misalignment of AI in mathematics

#991
Amazing. Comment upon comment, thread upon thread, failing to engage with the substance of the Field medalists' letter and instead going off on tangents about the privileges that mathematicians will lose and how they're bitter about it. There is a shocking inferiority complex on this site towards mathematicians and yet users always seem to think of themselves as smart nerds, all about science and reason and maths and whatever.

I've been disappointed by this community before but this is the first place that there is such unanimous rejection of the very ideals the uses here will claim to represent. The reaction is just... small, tiny, petty.

Re: A misalignment of AI in mathematics

#992

As a software engineer, 6 months ago. I was better than AI in essentially every way except raw typing speed. Now AI has surpassed me in fine-grained problem-solving ability. It can write more reliable code than I can, faster than I can, provided it is given the right guidance. But one thing that I'm still much better at is identifying technical opportunities and choosing the right tradeoffs. My feeling is that fronti…

This mirrors my understanding when I use Claude code for mathematics. I can have deep discussions with it and it can solve my hairy problems. But whenever we go off the beaten track into design new mathematics, it struggles to make conceptual leaps and find the right definitions. Once I give it my ideas, it is back to its super-human pace and top notch intelligence. This situation suits me fine, since I am anyways mo…

Yes very much the same situation in software development.

The people who prided themselves on raw puzzle-solving ability got hit hard. Those who are idea-driven and architecture-oriented feel like they got handed a superpower.

It's quite a big shock at the industry level because the entire software engineering job interview process at essentially all large companies was heavily biased towards well-defined, raw problem-solving under time constraints which is precisely the skill which AI has replaced.

Re: A misalignment of AI in mathematics

#993

Earlier quoted context omitted.

different fields have different communication cultures, that’s not inherently bad. sacrificing inward focus is expensive from the pov of the insider; i see your points but not everything can be written for a general/wide audience. after all, the audience of the author are the specialists, since only specialists spent the effort to be able to engage with the work in depth. perhaps we disagree that mathematics is not a…

> what the work was meant to achieve in the first place is what the work was achieving in the first place. it was developing mathematics. Meant by who? Were the people footing the bill aware of this? People can like and do a lot of things. When money enters the picture it gets more complicated because usually the people who pay do that because they derive some gains from it. Historically scientists and mathematicians…

mathematicians are primarily paid for teaching, and that's their primary function from the pov of the general society. i don't think anybody is debating that part of their profession? i read somewhere that the annual nsf grant budget for mathematics is 57 million, in total. even if it was just spiritual elegance, that's a reasonable number no?

Re: A misalignment of AI in mathematics

#994

Earlier quoted context omitted.

> what the work was meant to achieve in the first place is what the work was achieving in the first place. it was developing mathematics. Meant by who? Were the people footing the bill aware of this? People can like and do a lot of things. When money enters the picture it gets more complicated because usually the people who pay do that because they derive some gains from it. Historically scientists and mathematicians…

mathematicians are primarily paid for teaching, and that's their primary function from the pov of the general society. i don't think anybody is debating that part of their profession? i read somewhere that the annual nsf grant budget for mathematics is 57 million, in total. even if it was just spiritual elegance, that's a reasonable number no?

Yes, that amount seems fine if true. They may be seen as teachers by the outside world yet they hire and promote and award internally based on research. Status and prestige is rarely allocated based on teaching. This is already a discrepancy. And note that the post doesn't much talk about teaching courses, but mentorship of grad student researchers who already work at their labs.

Re: A misalignment of AI in mathematics

#995

Earlier quoted context omitted.

mathematicians are primarily paid for teaching, and that's their primary function from the pov of the general society. i don't think anybody is debating that part of their profession? i read somewhere that the annual nsf grant budget for mathematics is 57 million, in total. even if it was just spiritual elegance, that's a reasonable number no?

Yes, that amount seems fine if true. They may be seen as teachers by the outside world yet they hire and promote and award internally based on research. Status and prestige is rarely allocated based on teaching. This is already a discrepancy. And note that the post doesn't much talk about teaching courses, but mentorship of grad student researchers who already work at their labs.

my response is not to the post, but to the parent comment i replied to. the internal structure of mathematicians is their thing, if someone should step in, who? do you think that discrepancy matters?

Re: A misalignment of AI in mathematics

#996

As 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 aut…

One key idea to understand about human behavior is that people are focused on their status among their peers and their next level superiors with power to lift their status. You are not among either, so you don't matter to them. This is nothing special about mathematicians, though, people work the same way everywhere, in every field, community etc.

Yes, that’s very true. I recognized that in 2014. It was hard, but I stopped doing research on formal proof.

I got an economics degree and found that the City of Austin to pay off its $3 billion dollar pension debt … and encountered the same problem you mentioned, again. Except this time my plan is to run for City Council and be their next-level superior.

Re: A misalignment of AI in mathematics

#997

This 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…

Precisely.

Re: A misalignment of AI in mathematics

#998
I get it that someones annoyed they didn't get credited, but aren't we better off having the solution than not? And surely if the AI rationalised the answer, even off the work previously done by others, then surely it can detail it's solution making it completely comprehensible to others that follow. Storm in a teacup?

Re: A misalignment of AI in mathematics

#999
post #715

Earlier quoted context omitted.

It’s frustrating that this comment is at the top because it, along with lots of the replies it inspired, absolutely misrepresents the actual declaration. The declaration is not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what s…

It includes Terrance Tao who has made the front page several dozen times at this point for his usage of AI such as to help the community write proofs for Erdos problems. But to many commentors he's a now gatekeeping AI-hating Luddite clinging to a dying profession out of bitterness and envy because his position is more nuanced than "throw AI at everything and turn off your brain".

It kind of reminds me of Clay Shirky's predictions about the influence of the internet on society from a few decades ago. To paraphrase what he said: when the printing press was invented, everyone predicted it would lead to world peace, and we got the Thirty Years War instead. When modern mass media was invented people predicted world peace, and instead the Nazis rose to power and we got World War 2.

And yet as a society we typically consider these technologies a net positive these days, because alongside all the political instability and violence that followed them at first, some people were figuring out how to do beneficial things with them along the way that did more good than bad. Because the issue really was that the influx of more voices and ideas shifted the power dynamic, required relearning how to communicate, and in the end be better as a society.

The issue was figuring out how to "domesticate" these wild new communication channels. One successful example of which was the invention of scientific journals and papers.

Shirky predicted the internet would probably lead to a few decades of political instability too (about fifty years was his guess), and we definitely seem to be in the middle of that process.

Now, I haven't checked his stance on LLMs. I also don't know if I would quite call them a medium for mass communication like the others (as used today, they take humans out of the loop rather than let more voices join the public discourse), but I feel like they are similar enough to otherwise fit the pattern.

Tao's stance similarly feels about wanting to domesticate this wild animal before we get mauled by it. And to stick with the metaphor, I feel that most of the time the AI industry is trying to bamboozle us with spectacular rodeo displays instead.

Re: A misalignment of AI in mathematics

#1000
post #951

I know it's incredibly presumptuous for me, a nobody, to say this to 25 Fields Medalists, but: Perhaps you are misaligned. Who decided the goal of math must be human insight? First off, some mathematical truths might simply be far beyond our biological comprehension. Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to ac…

> Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to actually improve our lives. This is just the problem with the Navier-Stokes solution. We now (supposedly) know the truthiness of the statement, but we have no more understanding of why or how it applies to our quality of life. This is exactly the issue Tao is pointing…

What I don’t get: this letter seems to argue that if a human had solved this problem then that wouldn’t be the case (?)
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