Comment by lanstin

Having QFT formalized rigorously means a ton of mathematical apparatus can now be applied to it. Where that might lead to is difficult to say, but this gap was a problem in claiming we understand how the universe works, in detail.

Having a sub exponential but super polynomial limit to complexity isn’t that much different than having an exponential limit - in analysis you have excruciatingly fine degrees of asymptotic growth all of which are kind of morally equivalent but not mathematically equivalent.

I am not sure about the harmonic analysis stuff - I was actually working on constructing sets of positive Fourier dimension a few years ago but never really got a big picture feel for it.