The year is 1830, on the eve of the July Revolution, one of the most momentous episodes in the turbulent first half of the 19th century, during which Augustin Louis Cauchy lived.
Recognized as one of history’s most prolific mathematicians, Cauchy was both an exceptional researcher and a man deeply engaged with the upheavals of the society of his day. Complex analysis, geometry, group theory, differential equations, probability… One might readily imagine that a mathematician who made major contributions to all these fields would have little inclination—and still less time—to devote much attention to the noise and fury of contemporary unrest. Yet Cauchy’s life was also that of a man who threw himself without hesitation into debates and struggles for influence. He preferred exile to submission and was prepared to give up a post at the Bureau des longitudes rather than swear allegiance to a regime he considered illegitimate. His loyalty to his convictions, particularly his fervent Catholicism, was thus inseparable from his scientific career.
In touch with most of the leading mathematicians of his day, Cauchy also knew how to make the most of his position as a teacher at the young yet already prestigious École polytechnique. It is no coincidence that what we call Cauchy sequences, a fundamental concept for understanding the structure of the set of real numbers, were first introduced not in the context of research but in a textbook, Cours d’analyse. Initially criticized for what was seen as excessive abstraction, this seminal work would mark a decisive step in the history of mathematics by ushering the concept of a limit fully into the modern age. To those dismayed by the disembodied nature of the ε’s and δ’s that flooded analysis in the wake of Cauchy’s research, Armand Sylvestre replied at the end of the 19th century: "Truth, like Beauty, is always expressed through rhythm and symmetry, through a harmony of characters and lines. Whether they like it or not, Cauchy and Hermite are poets, just like Homer."
