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> Mathematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them, often in the context of their own autonomously guided research. This expert knowledge is essential, both to effectively use mathematics, and to continue to articulate new and significant research questions.
In a word, the job of the mathematics department is not only to produce mathematics, but mathematicians.
Similarly, the output of programming is not only a program, but also a programmer. It is you.
Outsourcing the work deprives you of who you become by writing it.
The foundations of a great our mathematics came from landed gentry who enjoyed the work and were not paid for it. Today we prosper in our technologies and algorithms (not talking about recsystems) because of them. If math should once again become the pusuit of the curious and free but with even greater "skills", that does not seem to be an issue for math, or for those of us who benefit from math. An issue for people as a concept and for mathemeticians, yes. But that's a separate topic, like the anguish of not getting into the Premier league.
>>Similarly, the output of programming is not only a program, but also a programmer. It is you.
This can be said about pretty much any job on earth.
By that definition nothing should ever be automated.
Everything thinks they are special, actually no one is. You become special by being rare. Find something that can be done by no one or only a scant few.
> Outsourcing the work deprives you of who you become by writing it.
Just because AI can do something that resembles work should not mean outsourcing work to it. Mathematicians should not outsource their work to AI just like programmers should not outsource programming to AI.
Humans working with AIs in a tight loop means intellectual work becomes more high-level and creative, but a human should always own the work, validate it and stake their reputation to it. Simply ban any humans who produce low quality work using AI.
While you are right in a way, I think you miss the point. In the past "computer" was a job description and mechanical power came from serfs. They surely developed skills we are lacking today but I'd argue that overall the world is a better place with digital computers and electrical motors. It frees up these people to do something else, something of higher value.
Much of math (or science) research has the strange quality of being mostly curiosity-driven, but having giant benefits that occasionally spin out to the public.
Some questions are more urgent and practical. My feeling is that the more directly practical a question is, the more likely the research community is to support AI usage in that question.
The annoying thing about recent AI advances is that they target questions on the wrong end of the spectrum: Erdos problems are exactly the sort of "useless" questions that people might answer purely for the love of the game. The sort of questions that a young person might cut their teeth on and gain confidence.
Solving questions like these automatically, I think, is not good for the long-term health of research. At least for the foreseeable future you still would like people to become interested and develop skills in these fields. These developments, and especially how they are presented, directly discourage that.
To me, the most interesting feature of the OpenAI solution of the Unit Distance (Erdös) Problem is that the solution - using deep algebraic number theory as a source of extremal combinatorial/geometric constructions - is much more interesting than the problem’s elementary statement might lead one to expect.
Writing off Erdös’s problems as random, useless, or meaningless dismisses his mathematical intuition, second-to-none, and strikes me as somewhat uncharitable.
Finally, I agree that AI threatens mathematical training by rendering an entire class of acolyte-level research problems solvable by prompt. But the Unit Distance Problem is not of this class.
>> At least for the foreseeable future you still would like people to become interested and develop skills in these fields. These developments, and especially how they are presented, directly discourage that.
This assumption may well turn out to be correct, but it is not self-evident.
Nearly everyone who has ever got interested in mathematics got discouraged at some point and they left the field. Mathematics is very hard. Those very few that remained certainly have talent, but they also have characteristics that are necessary for success in a competitive field, which are perhaps less valuable per se. Such characteristics as may be over-represented in males for instance. This is not a point about gender differences, but about the intrinsic merit of different success factors.
It seems equally possible that the above assumption will turn out to be diametrically incorrect. People that would have been discouraged before LLMs will now retain their curiosity longer. Democratisation is surely a possible outcome.
Arguably, chess has never been as popular and accessible. And that discipline fell to AI three decades ago.
I've been spending 3 weeks, as a non mathemetician, chasing down a particular, very simply-stated, but secretly quite complex problem, and AI has been _so incredibly helpful_, not just in making progress on it, and doing obvious stuff like formalizing in lean, doing literature searches, reading through 10 or 15 papers and summarizing the results for me and how they apply to what I'm doing, giving me enough of an introduction to _entire fields_, that I can talk intelligently about it (I've had email correspondence with a couple of professional mathematicians in a few different fields about it, who agreed that it's an interesting, simple, but difficult problem). I've gone from "this should be easy", to "okay, I've almost got a proof", to "this is impossible", to literally just nailing down a few remaining sub-cases out of an infinite family.
I don't want to call anyone out, but I emailed one fairly famous mathemetician, and he literally said: "This is very interesting, I thought about it for a while, couldn't figure it out, but I thought ChatGPT had an interesting response..." and he linked me to his chatgpt transcript... (which, was actually helpful, because he asked it a better question than I was asking).
I have a suspicion that math will quite soon be exactly like programming and fall to the same machinery that coding is.
One thing that I noticed is that a common workflow I had was isolating hard subquestions in a self contained way and then "surveying" multiple different LLMs in a totally clean context. They would often say: "Oh, this is a obvious example of such-and-such" and immediately clear the barrier.
Do you not think that solutions to erdos problems might end up stepping stones to other important problems?
Either by introducing new tools, or by proving things that were previously unproven that end up helping in unexpected ways?
That's often how math goes, isn't it?
Sounds like yet another example of how AI is kneecapping industries from the bottom by "removing the barrier to entry" but really just removing the training path by doing the work itself with no guidance for juniors.
For every interesting problem AI solves there are a long tail of really dumb things that AI performs that humans would never do. Some days I am in awe of one-shot magic eight-ball output and other days I'm so frustrated by the sheer stupidity of what it produces. It remains to be seen whether that long tail of stupidity can ever be resolved in the current form of LLMs.
Accelerationists may argue that the eroding of proper attribution and proof verification by humans is a meaningless short term struggle of a dying field.
Mathematics seems to be entering an era where human + machine maximizes performance, much like chess in the 1990s. However, imagine a future where even talented mathematicians are nothing but noise in the machine (as is the case in chess now). A future where AI generates and verifies proofs without humans in the loop. Where the mathematics may be beyond human comprehension.
In that future, does it matter that early career mathematicians are inhibited by these developments? Perhaps not. Programming faces the same issue. As AI crawls up the competence ladder, does it matter that fewer people have opportunities to develop the skillset of a senior engineer? Perhaps not.
Anyone else draw similarities with this and the artists and authors who complained when gen ai first came out. I think a lot of people don't realise the disruption ai will cause to many industries, until its directly impacting them, basically personal fable at scale (https://en.wikipedia.org/wiki/Personal_fable).
> However, the declaration argues math is more than a machine for producing correct answers.
There might be more to maths than that, but that is definitely the most important part. I love science funding. But not because it's a jobs program for nerds.
> “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University
As a former physicist and current data scientist/engineer, I know for a fact that commercial utility drives math research and researchers.
Math is a tool to solve problems. Some mathematicians might only love the process of using the tool, but commercial logic absolutely drives mathematician attention to develop commercially useful tools.
One of the reasons why over a decade ago, I dived deeply into the OSS world instead of mathematics was that it was so much more accessible: there were docs for everything, and I got direct feedback when something worked vs when something didn't work. Most of my questions had answers on stack overflow, and once I joined Rust (which back then in 2015 didn't have a big stackoverflow presence) I had a community who answered them for me (and in maths I didn't have that).
AI makes the math world more accessible than before. If you have a question about a proof in the lecture, you can just ask it. Of course, one can't trust it blindly, but fundamentally it's amazing.
I think that's a good thing, but of course this means that a lot has to change in culture and behaviors, also in the research world.
The software engineering world is more or less in the same situation, it's also changing. But for now I think it still holds true that someone who knows maths plus an LLM is better than someone who doesn't know maths plus LLM. At least in software it does.
Mathematician Ken Ono (https://en.wikipedia.org/wiki/Ken_Ono) gives a well nuanced viewpoint on AI in Mathematics (and more) - https://www.youtube.com/watch?v=jGZOi-7haCw
He states that he struggled to come up with problems which would be challenging for AI to solve (at the below site) and thus forced to accept that mathematicians have to rethink their profession.
FrontierMath: Benchmarking AI against advanced mathematical research by Epoch AI - https://epoch.ai/frontiermath
As a follow up to the above, see "First Proof: Mathematicians Putting AI to the Test" featuring eminent mathematicians - https://www.youtube.com/watch?v=AaICCTpkI7Q
My vague prediction right now is that in five years LLMs will be heavily used by universities in grant-funded math research but nobody else will be able to afford it, much like supercomputer clusters 25 years ago.
From the article:
> However, the declaration argues math is more than a machine for producing correct answers. The discipline, its authors believe, is a deeply human endeavor built on creativity, understanding, collaboration, and the pursuit of knowledge for its own sake.
Generation X was the last generation that had 'general knowledge', as in an abundance of fairly useful information stored in 'grey matter' that could be recalled quickly. When search engines came along there really wasn't much need to know anything since most things could be looked up. However, you still had to think.
With LLMs, thinking is kind-of optional. This really is an existential threat to our intelligence since 'use it or lose it applies'. I am glad these mathematicians are doing their duty as canary in the coal mine.
Math for non mathematicians is a tool. Math for mathemeticians is an art in the same way an artisan takes pride in his work.
That's why there's a disconnect when you go from math for engineers to the stuff above it. It feels less useful and very different
Understanding is and always has been the "hard" bottleneck. In programming work, if one drops understanding and eg let's an agent write code with only superficial human review or none at all, I believe that they can easily get 100x fast or more, the main question being whether the process collapses some point due to sloppy code. In research fields like mathematics, skipping understanding is not something that can be done without a radical reconstruction of what mathematics (as a process/activity/field) is.
It sounds plausible that LLMs help generate insights that humans have missed. But there are many open questions, eg the rate of generating insightful vs uninsightful but plausible statements, which can affect how useful they will be, and of course "open"ai has no incentive to share how much effort/cost (tokens and/or human-review) had been put into investigating erdos problems before coming up with this solution.
> AI-generated papers could overwhelm peer-review systems with low-quality work
That's not a problem unique to math, or even to academia. It's a problem in every context in human life where people communicate via written documents.
Is it possible they feel threatened their jobs are at stake?
I've said it before, but there's a massive risk that we simply stop educating researchers. So much of a Ph.D revolves around the person learning how to do research.
They learn how to read papers and literature rigorously. They get low-hanging fruits to practice on, which can take months. Their funding doesn't come from thin air either.
So what happens when the group leaders would rather spend money on compute, and get models to solve the low-hanging fruit? Which the models could very well do in mere hours, compared to months.
Nor does it help that publishing is the number 1 measure in academia. Furthermore, the access to compute and capital could end up be the defining factor between researchers and research groups.
It is basically the "junior problem", but even more severe.
> This story is part of Science’s AI in Science Reporting Initiative, which is supported by Ray Rothrock & family.
This excessively pro-AI article brought to you by private equity.
Are maths AI models now using "tools", aka formal solvers?
I understand that the "language interface" of a "maths AI" could be some specialized trained LLM (Large Language Model) that to convey, with human language, "high level" mathematical mental contructs and intuition.
But then, you would need some models which does the reasoning using formal mathematical solvers (and probably a ton of "scratch" memory, it would be interesting to see how those models end up storing "mathematical" lema data). I guess you can have ML (Machine Learning) for those models on 'general maths', but also we can think about more mathematically focused ML for a specific problem, area, etc. And in the end, ML for maths, would it be mostly permutations of truth statements fed to a neural net?
When we were talking about "AI", one decade ago, that was what most had in mind (it may help a bit in physics, but it seems less likely, because reality/experiments are hard to teach to "AI"s).
If that becomes a reality (aka easy hardware access, and some "working" models), mathematicians will have to be as good in maths than in maths ML. And this is were there is an issue: training honestely good mathematical human brains may become very hard with some broad availability of good general maths reasoning "AIs".
>and the pursuit of knowledge for its own sake
Except when someone hands you a magic button that just gives you knowledge?[at least in the framing of this "warning"] Then it's about peoples' livelihoods, about "culture", etc?
"Computer" used to be a job. Did science on the whole lose or gain by making these clerks obsolete?
I see any kind automation as a good thing as long as it is reliable enough. We stopped copying books manually a long time ago, and the craft was lost, most of us can't do complex calculations manually etc. but it does not matter as long as we can rely on calculators and computers to do it.
At this stage, the current wave of AI is not reliable enough that it would be safe to lose the abilities it can replace.
The failures modes are often turned into memes and jokes, but they are the thing we should really pay attention to, IMO.
The way humans beat AI, at least until AGI, is to innovate conceptually. If what you do is simply rearrange existing concepts then your work will likely get replaced by AI. Coding is a good example of this, you put documented commands, with known behaviours, in sequences that produce defined outcomes. That is the perfect job for AI, if we can solve their irrational desire to please and hallucinate along the way.
AI is simply not able to innovate, only combine.
AI is the interpolation of the human corpus. Is it suprising AI recombines sucessfully where human attention has not explored all plausible solutions? N,o not especially. The key fallacy is that AI is other than human. This is really no different from computer proofs, e.g. 4 color theorem. The fact the prompt is not linked to the solution by individual human intention alone does not make the solution less human in origin.
I'm curious about whether we will start discovering new maths in the next few years that provide insight into unsolved CS or Physics problems!
Actual "warning":
Far more interesting as it's outlaying a set of principles for using AI to augment human involvement and science, rather than replacement.
As a mathematician by trade I think they’re overblowing it. You can choose to use it or not. I choose not to because I enjoy the process. But I’m not doing formal research or getting paid to do it these days.
I will note that the average corporate mathematical modelling is usually a fucking circus so adding AI might make it better.
I think we just haven’t spent enough time creating the systems to help people learn faster - so far, only the systems that teach AI to know more and for people to rely on AI to retrieve information.
I still don't understand how "AI" is ready for serious use beyond entertainment purposes
Every time I ask ChatGPT to make a table for a subject I know well, I will find an error in one of the results and it is very confident about it until I question it in detail
Every time I ask ChatGPT for nutritional breakdown of some dense food source and give it a quantity like 8 ounces and ask for the weight of each ingredient, the weights will be wrong and add up to more than the original weight of 8 ounces
These are variations of the old "how many Rs in strawberry" problem, it's still not solved, "AI" cannot reassemble a complex problem properly
A lot of what it tells me in detail about some subjects sounds suspiciously like Reddit posts reassembled out of order
People talk about research mathematics being a science or an art, but it's also a sport. AI will kill the sport aspect of it. The art will survive. The science will thrive.
Why is it wrong to expect humans (mathematicians) to adapt here? AI is already producing solutions to problems that humans could not find. Culture holds value until it does not.
"""
However, the declaration argues math is more than a machine for producing correct answers. The discipline, its authors believe, is a deeply human endeavor built on creativity, understanding, collaboration, and the pursuit of knowledge for its own sake. Those values often clash with the incentives driving AI development. “The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” declaration co-author Michael Harris of Columbia University told The New York Times.
"""
I mean, what field doesn't? Everyone works to make money.
Slightly unrelated, but, their website "https://leidendeclaration.ai/" itself gives an eerie feeling of being built by Sonnet. That color scheme and the layout is what Sonnet chooses by default most of the times.
> However, the declaration argues math is more than a machine for producing correct answers. The discipline, its authors believe, is a deeply human endeavor built on creativity, understanding, collaboration
Mathematicians of all people should be free from such emotion-driven thinking. I guess people’s self interest in continuing to make an income trumps all.
> For years, AI researchers have used math as a proving ground for their models.
For years?
>My job is uniquely creative and human, other jobs can be automated away but mine is just so special.
If you love mathematics so much, and it's not the prestige and accolades that drive you, then what stops you from just solving problems on your free time even if they are already solved by AI?
Why does your field have to remain economically viable for you, why does this not apply to textile manufacturing or something? Someone's positions in society is owed to textile manufacturing too, and it has a culture that some people would lament the loss of and so on.(See guild system, craftsmanship in Europe).
I can't predict whether this will be a good thing in the long run, but this is literally the same complaint that every industry affected by automation ever had, and many who are now complaining would dismiss it if it were about something they personally do not care about or isn't sufficiently "noble" or intellectual.
I know it hurts, but the core complaint is just economic displacement, many have had to deal with that before. Most people who have something they love have to do that on their free time because it's not economically viable as a job, tough luck.
In a year, none of this will really matter. Intelligence is now a scalable resource independent of biological constraints. Everyone will use it because the system will no longer afford them the luxury of time. In a decade (maybe sooner), references won’t matter either.
Cry-babies. They want to stay back in the stone-age.
I will argue that AI and flood of low quality slop makes genuine human work more valuable, not less.
The ability to clearly outmatch trillion dollar machines is a very unique satisfaction. I even write ordinary internet comments with an intention to make them clearly better and more fun to read than boring Claude output.
Imagine Claude coming up with a solution to the Grand Unified Theory and also proved that P = NP, would we see physicist write an angry letter saying that we should ignore these results because they weren't derived by artesian hands? Give me a break.
Isn't the whole point of the field of mathematics in a theoretical sense the pursuit of formal solutions?
So, why would they be advocating for limitations on arriving at solutions?