My point is just that I feel a little optimistic that the human culture around math ("ideas we disseminate in talks, private discussions and careful writeups, connecting them to the previous ideas of others" and so on, to quote the declaration) is robust even against relatively irresponsible use of AI (i.e., an onslaught of proof-slop).

And I guess we'd better try to be optimistic, because even if the declaration results in some realignment between the community and big AI companies, the models capable of this work are not always going to be exclusively under the control of those aligned parties.

That said, I think the declaration is great and I support it--let's see what comes out of it.

I think it's OK that there are some materials designed for a specialist audience, and some materials designed for a wider audience. Technical density serves a real purpose in the former (I'd like to just say "stack" without including an explanation 10 times longer than the rest of my paper about what a stack is and why we are talking about them), and some people expend a lot of effort on the latter (think lectures, lecture notes, textbooks, seminars, blogs, etc--totally appropriate to dig into the motivations here).

It's just the fact that it's a really vertical field, not some cultural failing, that results in pretty opaque stuff sometimes.

> why bother grinding through all the material of climbing Mt. Everest and then attempting it if the helicopter ride is how things are done now?

I think you answered this yourself earlier:

> I think progress is really measured by what humans are able to do and understand

People want to make this progress. Therefore people will "grind Everest" as a mathematical community, and that is maybe not so hugely different from a lot of previous mathematical work.

There's still ample room for creativity: simplifying, generalizing, asking new questions humans are interested in, ...

(Well that's my hopeful, optimistic take, anyway.)

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 skepticism, but it also generated conferences, papers, talks in the hallway, discussions with students, and so on--a flurry of exactly that kind of community process that the declaration says is the main driver of mathematics.

Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize, etc).

Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc.

It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generations of mathematicians. (See also his article about "non-renewable mining" of good problems.)

Reducing mathematics to "let's just generate results through an isolated and automated system" is a misalignment since it bypasses those processes.

The goal is more to understand why something is true than just whether it is true. To oversimplify a lot, it's the difference between industry versus academic motivation. In the former case you have a point, but not so much in the latter. We really need both modes of work going on.

> As a not math person, seems strictly good that AI can solve more problems.

As a math person I think that's probably true, though it's not that simple. We do still have to understand the solutions to the problems, and take time to explore. That's how we figure out what problems should be solved in the first place. Cognitive debt is bad enough in your codebase, but you don't really want it to overwhelm entire academic disciplines.

[1] https://mathstodon.xyz/@tao/115420236285085121 [2] https://xcancel.com/wtgowers/status/1984340182351634571

It's probably sort of being mixed up with the transitive verb "to circle", which goes the other way, with the subject ending up in a state of circling.

Guns per 100 people - Finland 2017: 32.49 (total of 1.79 million) [1] - US 2017: 120.5 (total of 393 million) [2]

All gun deaths - Finland 2017: 138 [1] (~77.09 deaths per million guns) - US 2017: 39773 [2] (~101.2 deaths per million guns) <- A bit higher

Mean death rate per million in mass shootings, 2009-2015 [3] - Finland: 0.132 <- A bit higher - US: 0.089

[1] https://www.gunpolicy.org/firearms/region/finland [2] https://www.gunpolicy.org/firearms/region/united-states [3] https://worldpopulationreview.com/country-rankings/mass-shoo...

The data seems to suggest that the number of deaths and mass shootings sort of tracks with the number of guns, and that Finland isn't particularly better off "per gun".

Unless the environmental changes happen too fast for adaptation to keep up with--the tree of life can have dead ends.