The issue is quantum field theory (QFT):
“This is [a] very embarrassing thing that we don’t have a single quantum field theory we can describe in four dimensions, nonperturbatively,” said Rejzner. “It’s a hard problem, and apparently it needs more than one or two generations of mathematicians and physicists to solve it.”
But that doesn’t stop mathematicians and physicists from eyeing it greedily. For mathematicians, QFT is as rich a type of object as they could hope for. 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.
If mathematicians can understand QFT, there’s no telling what mathematical discoveries await in its unlocking. Mathematicians defined the characteristic properties of other objects, like manifolds and groups, long ago, and those objects now permeate virtually every corner of mathematics. When they were first defined, it would have been impossible to anticipate all their mathematical ramifications. QFT holds at least as much promise for math.Kevin Hartnett, “The Mystery at the Heart of Physics That Only Math Can Solve” at Quanta
Be warned: The quantum world is tricky and nothing is what it seems. 😉
See also: In quantum physics, “reality” really is what we choose to observe. Physicist Bruce Gordon argues that idealist philosophy is the best way to make sense of the puzzling world of quantum physics.
Can a materialist consciousness theory survive quantum mechanics? Quantum mechanics requires that the observer be part of the measurement; thus quantum measurements must include consciousness.