Comment by adrianN
10 hours ago
I wonder how we could formalize the notion of „interesting“ problems in a way that would allow us to automatically generate new interesting questions from the existing corpus of mathematics.
10 hours ago
I wonder how we could formalize the notion of „interesting“ problems in a way that would allow us to automatically generate new interesting questions from the existing corpus of mathematics.
For me this path means that our role as humans is just the understanding of intelligence?
Everything else is secondary (or the last of our priorities) and would be better automated?
This is a hard pill to swallow
We should think about rejecting this AI future.
A simple way is to just measure how long it takes to solve. If it takes more than 5 minutes then we don't have a good understanding of that area and its worth potentially investing into.
Or maybe we should not let pure mathematicians decide which problems are interesting, but reward the practical applications instead.
This is wildly shortsighted view of mathematics. Historically many of the subfields of math which are presently most valuable were considered useless for decades or centuries. Number theory, non-Euclidean geometry, group theory, and Boolean algebra, to name a few.
This is false dichotomy. Many mathematical achievements were produced while looking at practical problems: Fourier is a good one. For every mathematician that accidentally made a practical contribution, there are many more that produced nothing of value, and would have with a better tuned reward function.
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If you only judge by practical applications you eliminate vast swaths of human endeavor.
Human endeavor and achievement does not make number go up for next quarter’s earnings