> Most unfortunately, it’s the truth value and the understanding which drive applications of mathematics, not the proof work itself. If the AI revolution decapitates the institution of mathematics which produces the understanding, and is unable to replace it, then the applications will cease as well.
In a world with no AI, it is vital for humans to understand math, in order to derive practical applications. But in a world where AI is able to both produce math theorems, and figure out practical applications for them, human understanding has minimal practical value to society.
But in a world where AI is able to both produce math theorems, and figure out practical applications for them, human understanding has minimal practical value to society.
We have examples of AI producing theorems but there is no evidence that AI will be able to find all of the practical applications of mathematics, at least not any time soon.
As I understand it, most of the theorem proving work done by AI today consists entirely of “glue code” style work: combining a bunch of different known results to prove a new result. This is great for those who desire completeness in the mathematical project but it’s often outside the areas of interest for mathematicians who are pursuing “big idea” problems whose solutions likely require development of entire new branches of mathematics. One famous example of such was Fermat’s Last Theorem.