> “Gauge theory” is a term which has connotations of being a fearsomely complicated part of mathematics – for instance, playing an important role in quantum field theory, general relativity, geometric PDE, and so forth. But the underlying concept is really quite simple:
Then goes on to write an incomprehensible novella length explanation.
I like Tao, but this is a problem in 'pure' maths. I feel the issue is exacerbated by the fact that if you can follow along with Terry then you likely will be unable to recognise the issue.
A good counter point is this series by Timothy Gowers developing a proof of "Pingala's Determinant".
When Gowers finds the proof he states:
> Since this clearly has determinant 1 and this clearly has determinant 1, so does their products, ie. Pascal's[sic] determinant is 1. Could have done that, but that would have been uh, well depends on what you find interesting, but that would have been really sort of rabbit out of the hat, look what a billiant clever mathematician I am. I can just sort of produce this fabulous identity out of nowhere and it's got a nice simple proof that also came out of nowhere. What I want to emphasize is these sort of proofs don't come out of nowhere.
Timestamped to quotation: https://youtu.be/m8R9rVb0M5o?t=886
The series is great and will show anyone outside the field of pure maths that even pure mathematicians use numerical reasoning while trying to reason about a subject.