During the 17-th century, analytical methods were formed in the works of European scientists, replacing geometric and synthetic ones, where for each problem their own unique specific method was created, which did not allow generalization to a wide class of problems.Based on the generalization of analytical methods, I. Newton and G.W. Leibniz created their theories. Their presentation was difficult to master. Neither Newton nor Leibniz had direct students. In England, С. Maclaurin, E. Halley, A. de Moivre and D. Stirling took on thepropaganda of Newton’s doctrine. In Europe, the Bernoulli brothers took up the dissemination of Leibniz’s doctrine. The period under consideration is a transitional period from the era of classical geometric methods to universal analytical ones. Jacob and Johann Bernoulli were the best teachers of mathematics in Europe; no university gave such a volume of knowledge. Both in Basel and in Paris, they had many students and followers. Thanks to their teaching activities, the Basel mathematical school, the strongest in Europe, was formed. Groups of scientists who studied or consulted with Jacob Bernoulli and Johann Bernoulli, both personally and in correspondence, both regularly and occasionally, are identified, and their scientific activities are characterized. This generation, in turn, created the potential for the next generation and the further development of analytical methods, thanks to the generalization and classification of problems of analysis and analytical mechanics, by the middle of the 18-th century the architecture of mathematics had changed and its areas had expanded.