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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#871

Post by breezybottom »

tmhn2 wrote: post #198

As 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

#872

Post by int_19h »

black_knight wrote: post #813
socketcluster wrote: post #809

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…

> Once I give it my ideas, it is back to its super-human pace and top notch intelligence.

That's the real benefit of AI today: you can test your ideas almost as fast as you can generate them, in parallel even. If you have a crazy idea that is unlikely to work but has massive advantages if it does, you just set an agent to explore and prototype it while you focus your main attention elsewhere. And so on.

It's still GIGO, though! An AI can make a bad idea work (and will do so if you don't carefully prompt it to not be so sycophantic!) but it won't work well. Knowing when the idea is bad and should be abandoned is also the part that currently requires human judgment.

That said, given the pace at which models have been improving so far, I can't help but think that this is a transient state of affairs.

Re: A misalignment of AI in mathematics

#873

Post by MelonUsk »

tim333 wrote: post #863

It 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

#874

Post by mdnahas »

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 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

#875

Post by nateburke »

Animats wrote: post #690

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…

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

#876

Post by int_19h »

Animats wrote: post #690

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…

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

#878

Post by int_19h »

lll-o-lll wrote: post #730
noslenwerdna wrote: post #706

Earlier quoted context omitted.

Good? Those people were in the field for the wrong reasons. No reason to mourn them leaving

> in the field for the wrong reasons It’s an interesting view-point. What are the “right reasons” to pursue an intellectual discipline? To selflessly further the total sum of knowledge? > No reason to mourn them leaving What field? Who’s leaving? The conclusion has to be that human involvement in these pursuits is facing existential crisis. “Teach me, oh Oracle, the mysteries of the Universe”. “For a fee”. Both the g…

You don't have to ask the machine, if you value the process of obtaining the answer rather than the answer itself.

Re: A misalignment of AI in mathematics

#879

Post by int_19h »

drdeca wrote: post #326
sim04ful wrote: post #218

Earlier quoted context omitted.

Playing a devil's advocate. Why do we need understanding ? To take an example i would say ~99% of the population do not understand how combustion engines or how semiconductors work, what say another 1% ? Is the fear post-apocalyptic in nature ? We need some human priesthood to carry on tradition ? why ? Let's assume in the next decade GPT-7 PRO Ultra is cheaply ubiquitous, inspectable, reproducible, transferable, rea…

There ought to be more to life than sitting in a pod receiving sufficient nutrients from a tube, even if there was no doubt that humanity would in this way survive until the sun expands and makes the earth uninhabitable.

> There ought to be more to life than sitting in a pod receiving sufficient nutrients from a tube

Even in a hypothetical world where AGI can do everything that humans do better, this would still be a choice to make, not an inevitable consequence for everyone.

And life doesn't require suffering to have meaning.

Re: A misalignment of AI in mathematics

#880

Post by DoctorOetker »

zozbot234 wrote: post #822
freehorse wrote: post #816

Earlier quoted context omitted.

> his prose is directly implying that evil superintelligent AIs are deliberately writing obscure proofs in order to harm the community of human mathematicians That is probably the wildest misinterpretation of sth I have ever read here. Misalignment is used as in the goals and interests of ai COMPANIES are not the same as the ones of the mathematical community. It is very proper use of the word, and if anything imo th…

The point stands whether you attribute agency to AIs themselves or to AI companies. The companies are not deliberately sabotaging human mathematical understanding by writing up purposely inscrutable results, either (which is what the word 'misalignment' would imply in this context): they are merely working with frontier tools that have a very limited capability for human-like understanding. It's left to human mathema…

I wouldn't call the situation settled, nor do I expect we will ever find out what truly happened:

- a rare low likelihood sequence of coincidences

- deliberate frontier lab behavior, setting intellectual interrupts on LLM "aha"-moments, so that when some mathematician explains for the umpteenth time the approach they want to take "stop paraphrasing my approach, start the actual calculation!" and when the chatbot eventually groks it, they can scoop in, possibly with live dash-board and interrupt priority levels ranging from "ensure this sample gets into the new dataset" to "Millenium Prize Scoop Opportunity Imminent, call Sam"...

There is always an alignment problem, incentives to ideals, behavior to incentives, ...

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