Daniel Bernoulli

Daniel Bernoulli belonged to the most extraordinary family in the history of mathematics — uncle, father, brothers, and cousins all produced first-rank work in calculus and mechanics. He trained as a physician but spent his career as a mathematician in Basel, Saint Petersburg, and again in Basel.

His 1738 Hydrodynamica introduced the principle that bears his name, relating the pressure, velocity, and height of a fluid along a streamline. It laid the foundation of fluid dynamics and anticipated the kinetic theory of gases by more than a century. His work on oscillating bodies, compound pendulums, and the vibrating string led him, around 1750, to propose that the general motion of a finite string is a superposition of sinusoidal modes — a fundamental and its harmonics — each with its own amplitude and phase.

His friend and rival Euler refused to believe it. Only an "arbitrary" function, Euler argued, could represent a plucked string, and he did not see how a sum of sines could. The dispute remained unresolved in their lifetimes; Fourier settled it in their favour sixty years later, by proving that any reasonable function can be decomposed into sinusoids.