Olinde Rodrigues

Benjamin Olinde Rodrigues (1795–1851) is one of history's most delightful part-time mathematicians. A French banker and social reformer who did mathematics on the side, he published a formula in his doctoral thesis, then largely walked away from academic maths to campaign for radical social causes. Decades later, that "side project" turned out to describe every rotation in three-dimensional space.

A mark on the subject

If you want to spin an object by an angle \theta around some axis \mathbf{k}, the clean, compact recipe is the Rodrigues rotation formula:

\mathbf{v}_{\text{rot}} = \mathbf{v}\cos\theta + (\mathbf{k}\times\mathbf{v})\sin\theta + \mathbf{k}\,(\mathbf{k}\cdot\mathbf{v})(1-\cos\theta).

It's the formula every robot arm, flight simulator and 3D game engine uses to turn objects smoothly. His name also lives on in Rodrigues' formula for generating the Legendre polynomials — two quite different results, one busy banker.

Rodrigues was far more passionate about society than about spheres. He was a devoted follower of Henri de Saint-Simon and became a leading voice of Saint-Simonianism, an early socialist movement dreaming of a fairer, more industrial world. He wrote fiercely against the exploitation of workers and in favour of merit over inherited privilege. That his lasting fame came instead from a rotation formula he tossed off as a young man is one of mathematics' happier accidents.