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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#901

Post by casey2 »

If the goal of math is to communicate results it has utterly failed long before AI and they are in a weak position to defend this view. Every researcher is only taught a handful of DSLs and their papers are written in PSL(problem specific language). That may be necessary for a human to actually make forward progress in math, but it's certainly not conducive to reading (and certainly not when symbols are favored over English)

I think the mathematics community should realign their goals with humanities, not just declare themselves a "mini humanity", this means expanding human taste, intuition and communicating systems and their associated structural truths in a human friendly way. Bye-bye standardized education you won't be missed.

Re: A misalignment of AI in mathematics

#902

Post by largbae »

We need a new way to describe "alignment". The term "misalignment" assumes that there is some perfect set of beliefs or practices to be out of alignment with. Do Atheists, Christians, Jews and Muslims agree on what is perfect alignment? How about Europeans, Americans and Chinese? Humans, Dolphins, Rabbits and Fruit Flies?

Alignment alone is not enough. Aligned with _what_?

Re: A misalignment of AI in mathematics

#904

Post by gregdeon »

socketcluster wrote: post #798

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 is exactly how I feel about the recent ChatGPT models. It feels like I'm working with an incredibly enthusiastic junior student who listens to everything I say, checks it against my entire codebase, and thinks through all of the possible connections 1000x faster than I can. But it doesn't spot the ideas first. It actually makes work quite fun, since I can spend so much more time in "idea space" instead of "implementation space".

Re: A misalignment of AI in mathematics

#906

Post by dwa3592 »

int_19h wrote: post #893
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

#908

Post by GPerson »

40four wrote: post #870
GPerson wrote: post #703

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

#909

Post by GPerson »

looofooo0 wrote: post #873
40four wrote: post #870

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

#910

Post by dgreensp »

GPerson wrote: post #703
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.

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