Most mathematicians do compete for funding, based essentially on how many articles they can publish and where. Publication strongly favors problem solving. Universities are ranked on the same criteria.
What we see is a panic reaction to the fact that problem solving is "easy", which affects the future of the management of mathematics, not of mathematics itself.
Mathematicians are not luddites afraid of AI, is the academic publishing industry mixed with management interests speaking here.
- that it was stirred by the International Mathematical Union Committee on Publishing
- that is a mixture of the older San Francisco Declaration on Research Assessment DORA https://sfdora.org/read/ and recent fear of commercial AI competition
The academic system developed in the last ~50 years will crumble. On the broad scale of human intellectual history, this was a blip and not even the most productive phase. But it provided mass office employment and so this is all much more about the general knowledge work job replacement issue than anything specific to math. All desk/computer/office jobs will face the same fate. Math is just easier to verify. But engineering design, architecture, lower levels of lawyers and accountants where the selling point isn't charm and connections, they will all have this moment soon.
The is no "the mathematicians". Some mathematicians, very influent ones, are mad at AI, for social reasons, because it shows problem solving is "easy".
Mathematics is fine and will be fine in the future.
Mathematics called and says she's fine. She's curious about how is that possible.
Misaligned are the present academic merit system hand in hand with financial interests of academic publishing industry.
The system will be exploited and there will be an inflation of problem solving articles produced with AI. Nobodies will be more productive than 10 Fields medal recipients, each year.
So of course that the ones at the top of this system are scared.
This is a social problem of the present system, not a problem of mathematics.
Mathematicians will do mathematics and politicians will do politics, what's new?
Second, I think very relevant that the original meaning of "encyclopedia" is "recurrent education".
So I arrived to think that the present and future forms of AI in mathematics and sciences should be seen as modern day encyclopedic efforts.
Once we pass over the flurry of solving famous open problems (and wouldn't you like to know?) the next natural step is an audit of the ehole corpus of mathematics and sciences accumulated until now.
And then pass further on a saner basis and damn about problem solvers and unhappy publishers and management.
I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy. ignoring the attribution issue, there is a real concern that the process of math has been somewhat undermined. so we have a giant lean proof that shows that there is a solution to an important problem. but we didn't find the solution, and we didn't get it expressed in such a way that it helps develop the common language of mathematics, and thus isn't a very useful building block for later work (like the actual solution).
the math people seem to really keep an eye on what's important, so I'm sure this isn't going to lead to fields medalists hanging around in dive bars all afternoon stretching out cheap pitchers of beer. but this is kind of a slop problem.
> I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy.
If advancement comes at the expense of having fewer (or no) humans left in the field, then no.
They're eating the seed-corn, and you're cheering them on. Don't be so short-sighted. There's a reason farmers keep seed corn, and it's because they'd like to eat again next year.
We're singing and cheering our way into an intellectual famine.
Concrete example: Navier-Stokes. I don't make any claims about the truth of the announcement of the proof. But for the sake of the argument le't just suppose we know now that there is a smooth solution with smooth boundary and initial data which blows out in finite time.
Navier-Stokes is the simplest among evolution problems for continuum media, because it has maximal material symmetry (that's the mathematical meaning of a fluid).
If this is solved then go to a harder one, Coulomb friction. As a real life phenomenon, friction is very interesting to explore and mathematically is much harder than NS.
So it is not like we will ever be left without things to think about.
Oh, you want another? The present AIs are things made of mathematics. I would like to understand as a mathematician how and why they can beat human problem solvers?
Is that because mathematics is in some precise, interesting sense, more "computable" than it seems?
What we see is a panic reaction to the fact that problem solving is "easy", which affects the future of the management of mathematics, not of mathematics itself.
Mathematicians are not luddites afraid of AI, is the academic publishing industry mixed with management interests speaking here.
If you look at the Leiden Declaration https://leidendeclaration.ai/ then you notice two weird IMO facts:
- that it was stirred by the International Mathematical Union Committee on Publishing
- that is a mixture of the older San Francisco Declaration on Research Assessment DORA https://sfdora.org/read/ and recent fear of commercial AI competition
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