Initially a phenomenological guess to explain the periodic table. Later it was apparently proven properly with the spin-statistics theorem, physics.stackexchange.com/questions/360140/theoretical-proof-of-paulis-exclusion-principle.

And it was understood more and more that basically this is what prevents solids from collapsing into a single nucleus, not electrical repulsion: electron degeneracy pressure!

Bibliography:

- www.youtube.com/watch?v=EK_6OzZAh5k How Electron Spin Makes Matter Possible by PBS Space Time (2021)

The name actually comes from "any". Amazing.

All known anyons are quasiparticles.

On particle exchange:
so it is a generalization of bosons and fermions which have $θ=0$ and $θ=π$ respectively.

$ψ=e_{θi}ψ$

Key physical experiment: fractional quantum Hall effect.

Exotic and hard to find experimentally.

Video "The Biggest Ideas in the Universe | 17. Matter by Sean Carroll (2020)" at youtu.be/dQWn9NzvX4s?t=3707 says that no one has ever been able to come up with an intuitive reason for the proof.