> but it is very productive in terms of hundreds of proofs being produced that had previously consumed uncountable hours of the brightest minds
You’re making the following assumptions:
1. the exercise of struggling to find proofs was not productive, but this is precisely how new techniques in math were produced. Brute forcing solutions doesn’t lend itself to the creation of much new mathematics (except maybe the exercise of developing verifiable proofs)
2. the point of doing mathematics is to be “productive” in the first place. This is silly. Many people get into mathematics because of the beauty of understanding, for example.
> 2. the point of doing mathematics is to be “productive” in the first place. This is silly. Many people get into mathematics because of the beauty of understanding, for example.
Are they independently wealthy? Or do they have a deal with their local supermarket that they can take food for free?
What economic system do you recommend instead? Marxist-Leninist communism? Anarchism? Feudalism? I guess none of these will be fitting for what's coming...
It’s definitely interesting to think about how all of this would play out.
To slightly deflect your question, what do you think will arise naturally?
I’d put my money on feudalism if SOTA model providers can stay far ahead of open weights models. However if that proves infeasible and everyone ends up having access to local AGI does that serve to level the playing field? What resources are still going to be scarce in the coming decades?
Very few people will pay mathematicians to produce as if they were making art. The big problem here is that counting proofs is how mathematicians historically have created legitimacy for the universities they work for. Mathematicians in the past 100 years have been paid solely for the prestige they generate, the work itself is irrelevant to the university. If the prestige signal dies universities will spend less on math departments. Every math professor will be expected to teach undergrads as well as a stable of grad students. That’s the value they are actually able to provide to universities.
> The big problem here is that counting proofs is how mathematicians historically have created legitimacy for the universities they work for
This is a really interesting point. This is almost analogous to a metric in software engineering like lines of code which is a proxy for something we actually want to measure.
In a way, the SOTA model providers are cargo culting what appears to be what mathematics is.
You’re making the following assumptions:
1. the exercise of struggling to find proofs was not productive, but this is precisely how new techniques in math were produced. Brute forcing solutions doesn’t lend itself to the creation of much new mathematics (except maybe the exercise of developing verifiable proofs)
2. the point of doing mathematics is to be “productive” in the first place. This is silly. Many people get into mathematics because of the beauty of understanding, for example.