Warning

This work brings together, without substantial modification, most of the Historical Notes published up to the present in my Elements of Mathematics. They have merely been made independent in their reading of the chapters of the Elements to which these Notes are subsequent; they are therefore in principle accessible to any reader possessing a solid classical mathematical background, at the level of the first cycle of higher education.

Of course, the separate studies which make up this volume cannot in any way claim to sketch, even in a summary manner, a continuous and complete history of the development of Mathematics up to the present day. Entire parts of classical mathematics such as Differential Geometry, Algebraic Geometry, the Calculus of Variations, are mentioned in them only by allusions; others, such as the theory of analytic functions, that of differential equations or partial differential equations, are barely touched upon; a fortiori, these gaps become more numerous and more important when one reaches the modern period. It goes without saying that these are not intentional omissions; they are simply due to the fact that the corresponding chapters of the Elements have not yet been published.

Finally, the reader will find practically no biographical or anecdotal information in these Notes about the mathematicians in question; the main aim has been, for each theory, to make appear as clearly as possible what its guiding ideas have been, and how these ideas have developed and reacted upon one another.

The numbers in italic characters refer to the Bibliography placed at the end of the volume.