Invention of Rolle's Theorem (1691)

Michel Rolle proved a theorem on polynomial roots in 1691, which later became known as Rolle's theorem. Although he used the result in 1690, the formal proof appeared in his 1691 publication. This work is essential for basic proofs in calculus, despite Rolle's own criticism of infinitesimal methods.

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Background and detail

Background. Michel Rolle was a French mathematician known for his work in Diophantine analysis and algebra. His most important work, Traité d'algèbre, was published in 1690. While he is best known for Rolle's theorem in differential calculus, he was also a vocal early antagonist of calculus, arguing that infinitesimal methods led to errors.

Development. Rolle used the result in 1690 and proved it by the standards of the time in 1691. His 1691 proof covered only the case of polynomial functions. The theorem states that a real-valued differentiable function attaining equal values at two distinct points must have a stationary point between them. It is a special case of the mean value theorem.

Attribution. The theorem is named after Michel Rolle, though Barrow-Green remarks it might have been named for someone else had not a few copies of Rolle's 1691 publication survived. An early form of the theorem was stated by Bhāskara II in the 12th century, though without a modern formal proof. Rolle's contribution was the formal proof in the context of algebraic equations.

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