Comment by YeGoblynQueenne
>> If there happen to have been as many as four humans working on Navier-Stokes at any given time since the year 2000, then that's more human-years applied to the problem than agent-years.My bad for not showing my work and inadvertently leading you down the garden path, but the "~100 agent-years" calculation goes like this:
10,000 agents * 88 hours = 880,000 agent-hours
88,000 agent-hours / 24 hours = 36,666.7 agent-days
36,666.7 agent-days / 365 days = 100.5 agent-years.
That's what you get for working 24 hours a day, 7 days a week, 365 days a year. Realistically speaking, that's not a work schedule any human can follow.
It's hard to make a realistic estimate because normally even a very dedicated mathematician will not be working exclusively on one problem all their waking time, or even all their working time. But, let's ignore this and assume a pretty standard work schedule of 8 working hours, five working days a week, and 52 working weeks a year.
Now, that's:
8 hours * 5 days = 40 working hours a week
40 hours * 52 weeks a year = 2080 hours a year
880,000 agent-hours / 4 humans = 220,000 hours per human
220,000 hours per human / 2080 hours a year = ~105.8 years
To clarify, that's how I estimate the number of years it would take a mathematician to do a quarter of the work of the 10k OpenAI agents if that mathematician worked only on solving Navier-Stokes and did nothing else in their entire career.
That's just not a realistic work schedule for any human. You can adjust the working hours if you want but I don't believe you'll get any realistic estimate. Don't forget that most academics' careers last around 30 years from PhD to Professor Emeritus. If you want a more realistic estimate of how much time it would take how many humans to do the work of the 10k OpenAI agents, you can start from that assumption and work your way up from that.
>> That would be a more convincing argument if the AIs, like the humans, had been around and trying to solve those problems for the last 2k years. However, as you might have noticed, the state of the art in AI was rather primitive 2000 years ago.
Sure. But the thing is agents can run 24/7, 365/365 in parallel and as you see above they can cover 2000 years of human work in much less time. I'm not going to estimate how much because the only bottleneck is the amount of compute and money that an AI company wishes to spend, and that depends on their motivation to solve a particular problem. However, with sufficient motivation 2k years of human research (keeping mind that's not 2k years of continuous work) can be covered in a few ... months? Probably.