The Horgan Surface and the Death of Proof
This is also well studied in Philosophy.<p>Even not that hard math proofs call on intuition pretty quickly, and I think it’s a legit question to ask when does it basically become empirical proof.<p>To my understanding maths has a common basis in set theory but set theory itself is just a common basis for maths (ie as opposed to “the truth”), but even so proofs are typically not given via set theory especially if the theorem is complicated.<p>The idea is that mechanising proof and making it more algorithmic will make it more like what the layman thought proof is , but it at the same time raises the question, what is this all for? Ie maths is what mathematicians do. I think it admits to no clearer a definition. So it’d probably make sense for mathematicians to decide, what precisely is the role of proof?<p>The author talks about this in addressing computer aided maths and the general recruitment of applied mathematicians to solve problems whilst caring less to advance “the science” whilst doing it. Chomsky spoke a lot about this in criticising the use of probabilistic models in science as ultimately scarcely contributing to causal understanding, which in itself is separate from being able to predict phenomena well. Ie you can do practical things without ever knowing what’s going on under the hood, but science wants to know what’s going on under the hood and so prefers different approaches to its advancement.