The course of higher mathematics at technical universities is reduced annually due to the reduction of the time allotted for the development of its program. The use of more effective teaching methods can only partially compensate for these losses. Especially depressing is the loss of the opportunity to bring proofs of even the simplest statements and theorems in the course of mathematics. If, as R. Kronecker said, definitions are the soul of mathematics, then its beauty lies in the impeccable application of logic, and the driving forces and its very life are in the ideas of proofs.