Are there mathematical propositions for which there is a considerable amount of computational evidence, evidence that is so persuasive that a physici… - Gregory Chaitin

Mathematicians are coming up with s that they use in their actual mathematical research. And these, like , I think is the name of one of them ... these are actually like s that have been engineered in a way that they can actually be used by working mathematicians to check the work they're doing.

I'm interested in the computer as a new idea, a new and fundamental philosophical concept that changes mathematics, that solves old problems better and suggests new problems, that changes our way of thinking and helps us to understand things better, that gives us radically new insights...

Why do I think that Turing's paper "On computable numbers" is so important? Well, in my opinion it's a paper on epistemology, because we only understand something if we can program it, as I will explain in more detail later. And it's a paper on physics, because what we can actually compute depends on the laws of physics in our particular universe and distinguishes it from other possible universes. And it's a paper on ontology, because it shows that some real numbers are uncomputable, which I shall argue calls into question their very existence, their mathematical and physical existence.