"We hope that these results mark the beginning of a transition in which quantum field theory, the most important framework in modern theoretical physics, becomes a mathematically rigorous field. "
except that quantum field theory is, when done properly, already very rigorous, as you would well know! For other people:
https://ncatlab.org/nlab/show/Quantum+Gauge+Theories+--+A+True+Ghost+Story
or
https://ncatlab.org/nlab/show/Perturbative+Algebraic+Quantum+Field+Theory
It's just that most physicists either don't know this (my QFT lecturer was gleeful that mathematicians were concerned about lack of rigour, but I later found out the material was actually done properly) or don't care. Obviously *non-perturbative* QFT is a mystery, but then it's not like physicists know how to do that anyway.