Geometric form 12, inspired by Lambert's W function.
Toshimasa Kikuchi, 2014.
Until the dawn of the 19th century, no precise definition of the continuity of a function, a fortiori of its differentiability, had been stated explicitly. These concepts were used without reference to the underlying properties, which seemed to follow from intuition. Even the definitions of a function proposed by Leibniz and Euler were very vague.
The theory of Fourier series, developed by Napoleon's celebrated prefect, changed everything. Mathematicians suddenly realized that the sum of a series of continuous, even differentiable, functions need not be continuous.
When Abel challenges Cauchy
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