The Mystery at the Heart of Physics That Only Math Can Solve,  by  Kevin Hartnett

https://www.quantamagazine.org/the-mystery-at-the-heart-of-physics-that-only-math-can-solve-20210610/

Defining the characteristic properties shared by all quantum field theories will almost certainly require merging two of the pillars of mathematics: analysis, which explains how to control infinities, and geometry, which provides a language for talking about symmetry.

“It’s a fascinating problem just in math itself, because it combines two great ideas,” said Dijkgraaf.

研究由偏微分方程定义的几何对象（如双曲空间（复双曲空间）以及其中的极小曲面、其上的杨-米尔斯场）对应基本量如何通过重整化得到具有对称性的有限作用量。