Michel Rolle

"Traité d'Algebre" by Michel Rolle (1690).

Michel Rolle (Ambert, April 21, 1652 - Paris, November 8, 1719) was a French mathematician. He devoted himself preferably to the theory of equations, a domain in which he found various results, among which stands out the recognized theorem that bears his name, formulated in 1691, in which he represents an application of the theory of functions to that of algebraic equations. He also invented the notation xn{displaystyle {sqrt}{n}{x}}}} to designate the saddle root x{displaystyle x} e made the first publication about the Gaussian elimination in Europe.

Biography

Rolle was born in Ambert, Basse-Auvergne. The son of a merchant, he only received a primary education. He married at a young age and supported his family financially with the low wages he received for making transcriptions for notaries and lawyers. Despite his economic situation and his minimal education, Rolle studied algebra and Diophantine analysis at his own expense. He moved from Ambert to Paris in 1675.

His life changed completely in 1682, when he published a solution to a difficult unresolved problem within Diophantine analysis. Public recognition for his achievement earned him a patronage from Minister Louvois, a job as a primary mathematics teacher, and even an administrative position at the Ministry of War for a short time.

In 1685 he joined the French Academy of Sciences in a low-ranking position for which he would not receive a salary until 1699. In that year, he was promoted to pensionnaire géometre, which was a position important since of 70 members that were in the Academy, only 20 received a remuneration. Rolle had also received a pension from Jean-Baptiste Colbert, after he solved a mathematical problem for Jacques Ozanam. Michell stayed there in Paris until he died of a stroke in 1719.

Although his forte was Diophantine analysis, his most important work was his book on algebraic equations called Traité d'algèbre, published in 1690. In it, Rolle established the notation of the nth root of a real number and proved a polynomial version of the theorem that today bears his name. (Rolle's Theorem was named after Giusto Bellavitis in 1846.)

Rolle was an early opponent of calculus, which is ironic because Rolle's Theorem is essential to basic proofs of calculus. He took pains to show that it gave wrong results and that it was based on faulty reasoning. He fought so hard on the subject that many times the Academy of Sciences was forced to intervene.

Among his many accomplishments, Rolle helped advance the currently accepted order of size for negative numbers. Descartes, for example, considered -2 to be less than -5. Michel preceded most of his contemporaries in adopting the current convention in 1691.

Work

Rolle was an early critic of calculus, arguing that it was inaccurate, but later changed his mind.

In 1690, Rolle published Traité d'algèbre. It contains the first published description in Europe of the Gaussian elimination algorithm, which he called the "substitution method". Some examples of the method had already appeared in algebra books, and Isaac Newton had already described it in his notes, but these were not published until 1707. The method proposed by Rolle does not seem to have received as much recognition, because in the lesson on Gaussian elimination that was taught in algebra textbooks in the 18th and 19th centuries recognized Newton's achievement.

Rolle is best known for Rolle's theorem in differential calculus. He raised it in 1690, and finished demonstrating it in 1691 (under the standards of the time). His theorem is necessary to prove the Mean Value Theorem and the existence of Taylor series. As the importance of the theorem increased, so did interest in identifying its origin and eventually Giusto Bellavitis named it Rolle's theorem in the XIX.