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Skew-symmetric forms possess unique capabilities. The properties of closedexterior and dual forms, namely, invariance, covariance, conjugacy and duality,either explicitly or implicitly appear in all invariant mathematicalformalisms. This enables one to see an internal connection between variousbranches of mathematics. However, the theory of closed exterior forms cannot becompleted without an answer to a question of how the closed exterior formsemerge. In the present paper we discus essentially new skew-symmetric forms,which generate closed exterior forms. Such skew-symmetric forms, which areevolutionary ones, are derived from differential equations, and, in contrast toexterior forms, they are defined on nonintegrable manifolds.

Role of skew-symmetric differential forms in mathematics