Supergeometry and more broadly supermathematics has been around for few decades. Since its introduction by physicists, there has been an some mathematical interest in them.

Although interesting in its own, a classical mathematician (say someone who is only interested in smooth manifolds, complex geometry, representation theory, or number theory etc...) can say that these new super-objects are merely formal analogues that are only of interest to physicists, but not much to them.

One way to motivate such a classical mathematician to be interested in super-mathematics is to exploit some applications of the super world in the non-super world, and here comes my question:

What are the known examples of advances*/accomplishments in non-super mathematics in which super-mathematics has been used in an essential way?

I am mostly interested in examples coming from Geometry (algebraic and differential), number theory (in the broad sense) and representation theory (e.g. Lie algebras or algebraic groups), but I am open to hear about other areas as well.

Here, "advances" is meant in the broadest sense. It can mean a new perspective on an existing result/field, a new proof of a known fact or a totally new discovery etc...

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