It would be cool if some prestigious such program revamped itself to be AI-focused, maybe in collaboration with a CS department.
2) TFA argues golden age, provided LLM infrastructure is independent.
3) Tao just opened a new SAIR AI platform.
4) Tao just opened a journal for papers with Lean proofs.
5) Academics are known to play both sides of the fence.
It is absolutely bewildering how some people miss the finer points.
By all means, please read the article if it's interesting to you and ignore it if it isn't. But I believe that it's mostly directed to those already within the research math community, with a far more important purpose than to be interesting.
As the post itself explains, we (research mathematicians, as a profession) need to coordinate on deciding what a bright future will look like in a world with powerful AI, and in plotting a course to get there. And we need to do it fast, or circumstances might decide for us.
Historically, we've rather sucked at coordination. We need leadership -- we need someone to step forward, and begin by floating ideas and getting the conversation rolling. Personally I am very grateful for what Tao is doing here.
The author spends a lot of time trying to suggest that LLMs are not the end all be all and humans are still needed for understanding etc. Fine. I understand.
If it is so the case that LLMs don't help that much, surely it doesn't matter if LLMs are privately controlled?
How come LLMs are important enough that private control matters but also not enough for actually advancing mathematics significantly on its own?
In other words, you are almost always better off with LLMs even if it is privately controlled. The mathematics community can just ignore LLMs for the base case or use ChatGPT if they want. In either case, it is strange to suggest that things will get worse for them. Its as if they don't have the coordination or agency to adapt.
One big problem here is that OpenAI would be hoarding this ability by 1) not releasing their top models for public use,as we have already seen them do, and 2) limiting the capability of the public API, which we have also seem them do.
This not only kills incentive for math, it means that OpenAI becomes the arbiter of math and research for the world. The research that will be done is the research OpenAI decides to do.
This seems very dangerous to me.
Another path forward is distributed local models. Professors can do research on their HPC machines, individuals can have full access to their models. It's a much more democratic approach.
One in particular, about sharing secrets, that had not crossed my mind (I have found that virtually no one ticks the "do not train on my data" box...):
> Similarly, it seems that mathematicians already concerned and guarded about what they write in research statements and research proposals. After all, an administrator or a reviewer may upload those documents into an LLM to get help in writing a report, thus potentially compromising the confidentiality of unpublished research.
When said button is in the basement, at the bottom of a broken set of stairs, locked behind a door that says "beware of the leopard", inside a filing cabinet, and implemented as
dontTrain() { //NYI
}
I don't think technology will fizzle out in either scenario. In the 'dark age' highly competitive scenario, you will still have those who 'understand what is produced' seeking progress and advancement. They will cohort with whoever/whichever organization is producing the best, most validated results.
I don't think knowledge would be become alien to human understanding, it would just become highly concentrated again as it was in the past. In the past, only the wealthy and noble could afford to spend time on education.
And usually, those who went deep into any field and provided contributions to science were those who had time to devote entire lives to the study or pursuit of knowledge. We still have these issues today, and these issues will always be present.
There is a supply chain of economy, and we provide different rewards based on the value of what is produced. The jobs never go away, the desire for prestige, greed, etc., never goes away. It's why economies exist, and it's why everyone is considering the value of LLMs, and their place in economies, and academies (presumably which exist to advance human understanding/appreciation, but also to prepare younger generations for future work).
This is just incoherent. Even if we "agree" (we don't but...) not to "abandon" math, how does it follow that "we need a lot more mathematicians" exactly?
Even if you reject the idea that AI can displace the current top quartile/percentile of human mathematicians, wouldn't it be reasonable to assume that it will at least displace some parts of math so that there'll be less demand for mathematicians overall, not more? The mental gymnastics are astounding here.
It'll not necessarily be that great for every mathematician or scientist.
I’m not bitter about this anymore — it’s been a long time. But the story holds something.
Back in the day, I knew I was talented at mathematics, and I wanted to pursue a research career. For a freshman research class, I selected a problem that was intentionally outside my comfort zone, and came up with some cool ideas. It wasn’t publication quality, though the course wasn’t really expecting publications.
Framing the problem in a way that it could be solved with calculus turned out to be a key insight. I turned to Wolfram, since the integrals were beyond what I as a freshman could have done myself, and I understood that the insight that produced the solution was my original work. I don’t think anyone in the class could have done those integrals. The instructor himself couldn’t tell me what was wrong with them if anything. Yet, he was unimpressed and subtly dismissive or critical.
Today, I might have been in the wave of researchers developing AI for mathematics work. The instructor could have been proud of shaping mathematics through his mentorship. The university might have invited me for talks. Instead, I ended up leaving mathematics as a field altogether. Now, I write software for a bank.
The world is as rich as we make it. Don’t let your opportunities and potential expire. Embrace the materials that are available to work with, or someone else will and they will out compete you and you will have missed the moment.
I get that there’s a romantic idea of what mathematicians do, and the field changing creates a sort of identity crisis. I would argue that the field has entered a new era. Exploring and shaping this era of mathematics is the opportunity of a lifetime. Embrace it, drive it, and make your mark.
In other words, the crisis in mathematics (as I read it) is that AI can solve without teaching. The result may be impressive, but if the only beings that can move math forward in future are machines grinding away on billions of scenarios that no human would have the patience to undertake, this leaves those in the profession wondering about their place in it.
Frontier models can easily one shot what I ask for, and make adjustments as ask to quickly make an app that meets what I wanted.
But often when I programmed outside of work (and at work too) I learnt something.
Quite often that my favourite pattern is an antipattern in some use cases.
That might never happen again at the rate of development.
> The result may be impressive, but if the only beings that can move math forward in future are machines grinding away on billions of scenarios that no human would have the patience to undertake
Seems like the same thing as neural networks. You have something like a few thousand parameters for computer that works well, but no underlying algorithms and formulas, like the shaders.
IMO this is probably not an accurate assessment of Tao in particular at this time.
But in the general case, I think most people have a set of blinders on that will result in a predictable reassessment of AI with the following steps as AI progresses when applied to whatever it is they do:
1) AI is useless and doesn't impact me at all. Look at how bad it is! (Most developers up until late 2025)
2) Ok, now AI is useful but will not replace me. Sucks for the juniors in the field but I am still needed to guide the AI. AI will never be capable of my judgement (or whatever). (Most developers now)
3) Oh shit, I've been replaced in terms of economically valuable utility by AI. (tbd, but likely sooner than is comfortable)
And not everyone will experience #3, there will be a top 1% or so for most fields where #3 remains true for them, but it is likely that for most people #3 comes eventually.
> Universities, professional societies, funding agencies, and scientific foundations should coordinate the development and governance of competitive LLMs. Scientists will need access to frontier capabilities, transparency about their operation and use of research data, strong confidentiality protections, and the ability to test and reproduce research claims independently.
> The massive computing resources, specialized personnel, data infrastructure, and ongoing investments needed to support this kind of initiative are not within the reach of a single institution, and a huge leadership effort will be necessary to conjure the combination of independent model development, guaranteed access to commercial systems, public computing infrastructure, and open research resources that could do the job.
the post is calling for....an enormous investment in LLM infrastructure.
bananaflag•58m ago
tim-kt•52m ago
bananaflag•44m ago
https://proofsandprompts.com/
tim-kt•38m ago