Michel Rolle

Michel Rolle had little formal education being largely self-educated. He worked as assistant to several attorneys around Ambert, then in 1675 he went to Paris. In Paris he worked as a scribe, and arithmetical expert.

He was elected to the Académie Royale des Sciences in 1685, and became Pensionnaire Géometre of the Académie in 1699.

Rolle worked on Diophantine analysis, algebra (using methods of Bachet involving use of the Euclidean algorithm) and geometry. He published a work Traité d'algèbre on the theory of equations.

In 1682 he achieved a certain fame by solving a problem which had been publicly posed by Ozanam. Jean-Baptiste Colbert, controller general of finance and secretary of state for the navy under King Louis XIV of France, rewarded Rolle for this achievement. Colbert arranged a pension for Rolle and he also received a pension form the Académie in 1699, as mentioned above.

Rolle is best remembered, however, for 'Rolle's Theorem' which was published in an obscure book in 1691, using a method of Hudde in the proof.

If f(a) = f(b) = 0 then f '(x) = 0 for some x with a x b.

Rolle described the calculus as a collection of ingenious fallacies. He invented the notation ⁿx for the nth root of x. He also adopted the notion that if a > b then -b > -a in opposition to Descartes and others.