Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A misalignment of AI in mathematics

mathandai.org

Post reply on HN
Print view View original

921–930 of 1001 posts

Re: A misalignment of AI in mathematics

#921

Post by dwa3592 »

int_19h wrote: post #908
dwa3592 wrote: post #42

While I agree with this and appreciate Tao and other mathematicians to take the time to do this. There are similar concerns for many many other fields aka there is a general misalignment of technology. Take Software engineering for example, I can't believe there is a class of software engineers who wake up everyday and tell themselves, "today is the day I am going to automate the rest of my job". Lets forget the hype…

> can't believe there is a class of software engineers who wake up everyday and tell themselves, "today is the day I am going to automate the rest of my job". The whole point of software engineering is automating processes; it's literally all that we do. Not only that, but the endgame has been explicitly stated by Our Lady Ada of Lovelace herself: > [The Analytical Engine] might act upon other things besides number,…

>>can't believe there is a class of software engineers who wake up everyday and tell themselves, "today is the day I am going to automate the rest of my job"

>>The whole point of software engineering is automating processes

There is a difference between 'automating a process' and 'automating oneself' and making one obsolete a benchmark. I can sympathize if it's confusing for you to understand that.

Re: A misalignment of AI in mathematics

#923

Post by GPerson »

40four wrote: post #885
GPerson wrote: post #710

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…

I don’t see why the two are mutually exclusive to be honest. I’m not a mathematician, but I’m a software engineer and whether I like it or not, AI has changed my field dramatically forever. I understand the distaste for the way AI might be affecting the field of mathematics, but the genie is out of the bottle, and it will never be the same. It just took a little longer for it to hit the math community. Software engin…

Mathematicians are not idiots! They’ve been living on the same planet as you for the last few years and everyone in any thinking profession has been debating and coming to terms with reality over the same period. People who aren’t involved in mathematics might see a big headline and come to the conclusion that mathematicians haven’t seen this coming, but that’s a completely ignorant position.

Re: A misalignment of AI in mathematics

#924

Post by GPerson »

looofooo0 wrote: post #888
40four wrote: post #885

Earlier quoted context omitted.

I don’t see why the two are mutually exclusive to be honest. I’m not a mathematician, but I’m a software engineer and whether I like it or not, AI has changed my field dramatically forever. I understand the distaste for the way AI might be affecting the field of mathematics, but the genie is out of the bottle, and it will never be the same. It just took a little longer for it to hit the math community. Software engin…

Soon AI mathematics will be 10x or 100x or 1000x more productive than humans in the proofing theorems business. Mathematics of old style is dead, they should develop ideas how to deal with that as a math community.

> But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal.

Re: A misalignment of AI in mathematics

#925

Post by dgreensp »

GPerson wrote: post #710
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…

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…

The declaration literally opens by writing that AI companies (or really anybody) saying, “Hey, let’s see if this powerful reasoning engine can solve an open problem in mathematics” is “detrimental” to the “science” of mathematics. Full stop. So I don’t think it’s being misrepresented. If it’s a science, why isn’t progress good in itself? You can’t have it both ways.

The online comments I’ve read that side with the letter explain that the problem is AI proofs are inscrutable and useless, but the reality is using computers to brute-force things has long been part of proofs in one way or another, and AI proofs range in legibility up to 100% (like pointing out a proof exists in a long-lost paper, or writing something that is basically correct and just needs a human reviewer to fix it up). People are probably defending the declaration inaccurately, but I think that’s because the real argument or arguments are unclear.

Is it that students won’t learn math if there’s ChatGPT? That could be discussed.

To a non-mathematician (MIT physics and CS ‘06), the letter sounds like, “We have a fun job. Sometimes there are no practical applications of the work, so it’s just kind of like a sport, er I mean science. If someone solves a problem that has stumped mathematicians for decades or centuries, we worship them as a great mathematician. It’s a status thing. So we don’t like some guy with a computer coming along and solving our problems. The way things unfold with all the ideas coming from humans, over time, maybe it’s slower, but it’s nice.”

I don’t think anyone can really stop someone from using a computer capable of solving unsolved problems to solve unsolved problems, and there are always going to be mathematicians who DO think it’s fun to try to figure out what a computer is doing (if the computer isn’t already explaining it in English, which it generally can), and make progress that way, and it obviously will lead to mathematical advances in human understanding, from my point of view. So the whole thing is a non-issue that no one can do anything about anyway.

Re: A misalignment of AI in mathematics

#926

Post by jacquesm »

eru wrote: post #754
robotpepi wrote: post #444

Earlier quoted context omitted.

It makes no sense to compare mathematics with chess. Chess is a sport. No one is interested in watching two machines compete. Chess doesn't have a practical impact. Etc. What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. It could be the case in the future, but no one knows right now, and more importantly: tech companies don't even think about it! they…

Well, what you are saying that the situation is even better for math than for chess? Chess is only valuable as an entertainment. So no one really gains anything from computers becoming really good at chess. But with math, everyone in the world would gain from computers becoming really, really good at it.

> But with math, everyone in the world would gain from computers becoming really, really good at it.

I'm not convinced of that.

It is one possible outcome but there are also other possible outcomes.

Re: A misalignment of AI in mathematics

#927

Post by cagz »

I wish this were a document that clearly described how mathematicians expect AI to behave, rather than how it is misaligned. I can kind of decipher the expectation from the declaration, but it still sounds a bit like "it would be better if AI didn't meddle with mathematics", instead of "we want AI to approach problems like this and that way".

Re: A misalignment of AI in mathematics

#928

Post by lukeplato »

Many comments seem to be misinterpreting this, but all this seems to be suggesting is that the AI companies should not be treating mathematical milestones as benchmark targets but need to release the cumulative findings in a human interpretable and digestible way that enriches and develops the field. See Thurston quote on Tao's banner:

> We are not trying to meet some abstract production quota of definitions, theorems and proofs. The measure of our success is whether what we do enables people to understand and think more clearly and effectively about mathematics.

Re: A misalignment of AI in mathematics

#930

Post by 8n4vidtmkvmk »

SavageNoble wrote: post #678
breezybottom wrote: post #670

Earlier quoted context omitted.

How could you possibly know if it has potential or not? Sounds like AI psychosis setting in.

Because every test I run with it is telling me so? The great thing about math is it can be externally validated.

Yeah, but you're missing a gut intuition if something is off.

I wrote a fancy polygon decomposition algorithm in university (pre-AI) which my professor didn't seem very impressed by because it was missing some sort of mathematical rigor. Yet everything I threw at it worked! Even he couldn't find a counter example.

It took a while for me to find some failing cases but it turned out they did exist.

But hey, maybe all I was missing is an AI-written lean proof.

Post reply on HN