2016 Nobel Prize Physics is Mathematics (Topology) applied in Superconductor and Superfluid to explain the Phase Transitions and Phases of Matter.
Phases of Matter: Solid, Liquid, Gas
Phase Transitions: Solid -> Liquid -> Gas
Superconductor below Tc (critical temperature) : zero resistance.
Superfluid below Tc : zero viscosity.
Reason explained by Mathematics : Topological invariant (拓扑不变量) 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 (2 holes).