determinant of any skew symmetric matrix is the square of a polynomial #pfaffian can be shown by writing the matrix as a block matrix, then using induction and examining the Schur complement, which is skew symmetric as well
This subject is alive because of computers

#Frobenius theorem can be restated more economically in modern language. Frobenius' original version of the theorem was stated in terms of #Pfaffian systems, which today can be translated into the language of differential forms.

#Frobenius theorem can be restated more economically in modern language. Frobenius' original version of the theorem was stated in terms of #Pfaffian systems, which today can be translated into the language of differential forms.