defined as elements of Grassmann algebra (an algebra with anticom-
muting generators). The derivatives of these elements with respect to
anticommuting generators were defined according to algebraic laws, and
nothing like Newton's analysis arose when Martin's approach was used.
Later, during the next twenty years, the algebraic apparatus de- veloped
by Martin was used in all mathematical works. We must point out here the
considerable contribution made by F. A. Berezin, G 1. Kac, D. A. Leites,
B. Kostant. In their works, they constructed a new division of
mathematics which can naturally be called an algebraic superanalysis.
Following the example of physicists, researchers called the
investigations carried out with the use of commuting and anticom- muting
coordinates supermathematics; all mathematical objects that appeared in
supermathematics were called superobjects, although, of course, there is
nothing "super" in supermathematics. However, despite the great
achievements in algebraic superanaly- sis, this formalism could not be
regarded as a generalization to the case of commuting and anticommuting
variables from the ordinary Newton analysis. What is more, Schwinger's
formalism was still used in practically all physical works, on an
intuitive level, and physicists regarded functions of anticommuting
variables as "real functions" == maps of sets and not as elements of
Grassmann algebras. In 1974, Salam and Strathdee proposed a very apt
name for a set of super- points. They called this set a superspace.
