Re:How I learned to love and fear the Riemann Hypothesis
by PartiallyTyped on Wednesday January 06, 2021 @04:39AM
(#25656125)
I would like to bring up Gödel and his idea that you could construct theorems by multiplying equivalent numbers that represent theorems but I am sure you are well aware of it.
My argument is that it all happens through the application of operators and abstractions i.e. other numbers going through Gödel's approach.
In the same vein, we "should" in theory produce something similar. In RL, we have agents that learn to 'imagine' goals and then achieve them. Given the correct representation of such 'dreams' the models 'could' in theory learn to achieve such auxiliary theorems.
Another problem is that a lot of proofs starts by exploration. For example, certain bounds for functions or convergence rates are proved without knowing what will be the end result.
Of all the problems that ML could be applied to, I find mathematical proofs one of the least promising. One, I don't see enough similarity between proofs that would allow any algorithm to learn useful patterns; and two, I don't think most mathematicians would trust a proof that cannot be understood (even if the output is a set of steps for a formal system, I imagine translating that to human language could be quite difficult).