Sharing AI progress in mathematics

The problem isn't effort, though. All of the things I mentioned constitute effort and could be rewarded. The job economy was created by mathematicians incentivizing the proof of difficult theorems above all else and valuing all other work at approximately zero as far as career advancement was concerned. Now they're pulling a 180 and claiming that math was never really about proving theorems, but that's contradicted by their revealed preferences. The strip-mining problem only exists if they continue with the status quo ante.

> the incentive to mine that particular area drops considerably, dropping the chance to discover potentially brand new materials that would have been found the normal way.

FWIW, I think the metaphor breaks down with this framing. This isn't really a problem associated with strip mining, what's left behind is generally low or negative value (toxic). I'd suggest a different metaphor, from Wikipedia:

> This process involves the removal of all ground vegetation in the area, which is a detriment to the environment.[19] Topsoil may be placed over the tailing along with planting trees and other vegetation. Another reclamation method involves filling in the hole with water to create an artificial lake. Large tailing piles left behind may contain heavy metals which can leach out acids such as lead and copper and enter into water systems.

This feels very similar to the issues with algorithmic problem "mining". It has the potential to destroy the human ecosystems surrounding these problems, leaving barren wasteland behind where nothing can grow or flourish.

That's an empirical claim. I could equally well say that doing an automated search of the problem space and having a database of results and open problems will identify vastly more interesting and valuable areas. Again, the idea that math is some exhaustible material is a metaphor, not an established fact. I'm willing to change my view as new evidence comes in, but I think we're going to have to wait and see what the landscape looks like in a few years.

You're right, and that's a bad thing. AI is nothing fundamentally new, but its extremity is making many people aware of the truth that's been there all along. There's no contradiction in that.

> Do we see strong moats that are going to cause monopoly in AI?

Ownership of the capital assets used to train and inference new models. Yes, we may end up with more than one firm. But as we see with big tech today, a small number of fantastically wealthy firms in "competition" does not an open market make.

And incentives are sovereign over the humans. The humans leading the AI labs have every incentive in the world to move quickly without any restraint.

I am not sure how convinced I am by that argument. A gun is also a particular kind of tool, and it makes the person at the handle end sovereign, and the person at the pointy-shooty end subjugated.

When you blanket a set of things with a pejorative, and it turns out that some of the members of that set are demonstrably and definitively NOT covered by that pejorative, and that all the pejorative means at bottom is "I don't like", all you've accomplished in the long run is to call into question any future legitimate use of that pejorative. It is tempting, especially when heated, to stretch an invective, but it will ironically only lead to the death of its utility over time.

I've read some of the results papers (the Einstein condensate one and the pi exponential one). I'm not an expert but it definitely wasn't AI slop. The introduction sections were particularly well framed and informative.

Also you can see in the papers where an idea is introduced but in the bibliography you can see where the foundational idea comes from. So the narratives are not unmotivated as some claim (proof without intuition claims).

In the context of maths papers, the term has come to refer to papers having the shortcomings that are, for whatever reason, typical of LLM out, including things like using non-standard terminology all over the place, emphasizing easy steps while leaping over harder ones, having bizarre organisation, and, importantly, failing to properly cover existing work and as a result being hard to tell from plagiarism.

The degree to which these issues feature will differ, but it is generally the case that converting the output to proper research requires significant effort, hence the AGMAI recommendations being what they are, and not performing that effort tends to come off as laziness or incompetence, so I can see how slop has become the popular term.

> We can't just call any output slop, or it loses all meaning.

The term “ai slop” is not supposed to discriminate good ai output from bad, the entire purpose of the phrase is a blanket term that delegitimizes all ai output.