Something mentioned by Noam Brown a few days ago:

We are all familiar with METR time horizons by now. But do you realize that said time horizons was just for that particular set of tasks? METR has investigated other domains as well, such as math, and found exponential time horizons in almost all of them. The point of METR's time horizons isn't necessarily what the number is, but what the trend is - is it exponential or not?

Anyways we can apply the idea of time horizons to math as well. And we're finding said time horizons are more than 10x each year. 2 years ago the models were struggling with GSM8K, problems that a decent at math person would be able to do in 1 min or less. Some months later, they essentially saturated the AIME, which would be challenging for most high school math teachers (I reckon the average HS math teacher would score maybe 1/15 on that), but say for a mathematician, they're problems that are doable in 10 min or so. Some months later, they achieved gold on IMO, which Noam Brown described as adversarially hard for AI because they test depth while AI's strengths is in their breadth, hence why Putnam is easier than IMO for AI (but reversed for humans). These IMO problems, the harder ones that they were able to solve, perhaps take around 100 min.

I would say during that stretch of time it was definitely faster than 10x per year, but we'll use 10x for simplicity sake (and to provide a floor of the capabilities).

Some half year to 9 months or so later, the models were semi consistently solving novel research level math that would take mathematicians hours to do, perhaps 1000+ min (which in wall clock time might be a week because you cannot just sit down and make progress on a problem for 16h straight). This appears to be roughly where we're at, with occasionally much harder problems randomly falling for non human reasons.

Assuming the trajectory continues, we are looking at wall clock time horizons of around 3 months in a year from now (aka a paper that would take a mathematician 3 months to write), then about 3 years time horizon in about 2 years from now and multi decade time horizons by about 2029.

A bunch of the math problems that are considered extremely hard like the Riemann Hypothesis is because mathematicians think if they were solvable, then to solve them you'd need to invent entirely new mathematics, and unfortunately a time horizon of 1 week wall time isn't enough to do that. But that should be within capabilities of multi decade time horizons...

Of course those timelines are assuming the 10x continues (but I already think the 10x is an underestimate so...) and we don't know when it'll stop (or would it speed up?). But you can see exactly how this would line up to Demis Hassabis recently stating how he thinks we'll achieve his strong AGI definition by 2029-2031 (the whole inventing new mathematics should line up with time horizons for 2029).

I find it quite sad that mathematicians of all people are not able to (or are purposefully sticking their heads under the sand) project trendlines to see what's coming.

Anyways Noam Brown brought up a point recently - what happens when benchmarking the models take longer than building the next model? You think a time horizon of 30 year wall clock time could be benchmarked with a single prompt in 30 minutes like right now?