Grassman variables are a neat and handy way to talk about exterior algebras and the geometric objects built on them, like forms and spinors. The physics notation in particular gets a lot of mileage out of Grassman calculations that look formally like Gaussian integrals and behave remarkably like them. The best intro to that, and the bet purely mathematical application I know, is Matthai and Quillen's paper where they get an explicit representation of the Thom form that is quite powerful. They can be a little intimidating because physicists speak about them in language grating to mathematicians and tend to use them in the vicinity of highly nonrigorous thinking, but they themselves can be worked with mathematically without difficulty.

Grassman variables are a neat and handy way to talk about exterior algebras and the geometric objects built on them, like forms and spinors. The physics notation in particular gets a lot of mileage out of Grassman calculations that look formally like Gaussian integrals and behave remarkably like them. The best intro to that, and the bet purely mathematical application I know, is Mathai and Quillen's paper where they get an explicit representation of the Thom form that is quite powerful. They can be a little intimidating because physicists speak about them in language grating to mathematicians and tend to use them in the vicinity of highly nonrigorous thinking, but they themselves can be worked with mathematically without difficulty.