The title is more aimed at being clickbait than attempting to be informative.
The only thing in the underlying article is that specific neural networks are good and efficient at producing approximate solutions to large sparse systems of linear equations. Nothing else.
Such big systems of equations result when you try to solve partial differential equations on a finite-element mesh by substituting a lot of base functions.
There are broadly 2 ways of solving such systems: direct (e.g. using the sweep method) or iteratieve. The neural networks are just a way of implementing the iterative method.
The only thing interesting is that the specific neural networks proposed to do this can be calculated efficiently (also energy-efficiently) on specific hardware optimised specifically for that flacour of neural network.
The OP post tries to link 'math' and 'AI' here because, well, partial diffferential equations count as 'math', and neural networks are a form of 'AI', right? And that's how the OP 'justifies' its title.
Sorry folks, but his is a highly technical development which in no way merits the hoo-hah the OP throws at it.