2016 Nobel Prize Physics is Mathematics (Topology) applied in SuperConductor and SuperFluid to explain the Phase Transitions and Phase matters.

Phase matters: Solid, Liquid, Gas

Phase Transition: Solid -> Liquid -> Gas

Superconductor below Tc (critical temperature) : zero resistance.

Superfluid below Tc : zero viscosity.

Reason explained by Mathematics : Topological invariance increased step-wise.

Eg. Disk (0 hole), Circle (1 hole), Donut (2 holes), Coffee Cup (2 holes)… XYZ (n holes). [**n increased by steps from 0, 1, 2, 3… **]

We say donut and coffee cup are **homeomorphic** (同胚) because they have the same** topological invariant 拓扑不变量**(2 holes).