November 7, 2016
From: Interview by Dingyu Chen, Eton Magazine
Hypothetically, if you could choose two fields of math, physics or computing to be magically fully researched, which ones would you choose, and why?
I’d like to know the fundamental theory of physics: what’s underneath space and time and quantum mechanics and all the other things we know in physics today.
I’m not sure if you’d quite call it “computing”, but I’d like to know how to capture human concepts in a precise symbolic way that one can compute with. I’ve got quite a long way with the Wolfram Language already. But there’s more to do to capture all the things we humans care about.
Some other things:
I’d like to know just how general my Principle of Computational Equivalence is. Among other things, I’d like to know the boundary of undecidability in mathematics (e.g. how complicated a math problem is needed before one hits Gödel’s Theorem).
I’d like to know whether there’s a unique, inexorable structure to mathematics, or whether the particular constructs that have been defined in the history of human mathematical research are just historical accidents.