Michel Rolle
Encyclopedia
Michel Rolle was a French
mathematician
. He is best known for Rolle's theorem
(1691), and he deserves to be known as the co-inventor in Europe of Gaussian elimination
(1690).
, Basse-Auvergne. He moved from Ambert to Paris
in 1675, and he was admitted to the Académie Royale des Sciences
in 1685. Rolle was promoted to a salaried position in the Academy, a pensionnaire géometre, in 1699. This was a distinguished post because of the 70 members of the Academy, only 20 were paid. He had then already been given a pension
by Jean-Baptiste Colbert
after he solved one of Jacques Ozanam
's problems. Rolle died in Paris. No portrait of him is known.
, arguing that it was inaccurate, based upon unsound reasoning, and was a collection of ingenious fallacies, but later changed his opinion.
In 1690, Rolle published Traité d'Algebre. It contains the first published description in Europe of the Gaussian elimination
algorithm, which Rolle called the method of substitution. Some examples of the method had previously appeared in algebra books, and Isaac Newton had previously described the method in his lecture notes, but Newton's lesson was not published until 1707. Rolle's statement of the method seems not to have been noticed in so far as the lesson for Gaussian elimination that was taught in 18 and 19th century algebra textbooks owes more to Newton than to Rolle.
Rolle is best known for Rolle's theorem
in differential calculus. Rolle had used the result in 1690, and he proved it (by the standards of the time) in 1691. Given his animosity to infinitesimals it is fitting that the result was couched in terms of algebra rather than analysis. Only in the 18th century was the theorem interpreted as a fundamental result in differential calculus. Indeed, it is needed to prove both the mean value theorem and the existence of Taylor series. As the importance of the theorem grew, so did the interest in identifying the origin, and it was finally named Rolle's theorem in the 19th century. Barrow-Green remarks that the theorem might well have been named for someone else had not a few copies of Rolle's 1691 publication survived.
that predated George Berkeley
's, Rolle presented a series of papers at the French academy, alleging that the use of the methods of infinitesimal calculus leads to errors. Specifically, he presented an explicit algebraic curve, and alleged that some of its local minima are missed when one applies the methods of infinitesimal calculus. Pierre Varignon
responded by pointing out that Rolle had misrepresented the curve, and that the alleged local minima are in fact singular points with a vertical tangent.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is best known for Rolle's theorem
Rolle's theorem
In calculus, Rolle's theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative is zero.-Standard version of the theorem:If a real-valued function ƒ is continuous on a closed...
(1691), and he deserves to be known as the co-inventor in Europe of Gaussian elimination
Gaussian elimination
In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix...
(1690).
Life
Rolle was born in AmbertAmbert
-Places of interest:Ambert is famous for its fourme-d'Ambert cheese, its paper mills and its circular town hall ....
, Basse-Auvergne. He moved from Ambert to Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
in 1675, and he was admitted to the Académie Royale des Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
in 1685. Rolle was promoted to a salaried position in the Academy, a pensionnaire géometre, in 1699. This was a distinguished post because of the 70 members of the Academy, only 20 were paid. He had then already been given a pension
Pension
In general, a pension is an arrangement to provide people with an income when they are no longer earning a regular income from employment. Pensions should not be confused with severance pay; the former is paid in regular installments, while the latter is paid in one lump sum.The terms retirement...
by Jean-Baptiste Colbert
Jean-Baptiste Colbert
Jean-Baptiste Colbert was a French politician who served as the Minister of Finances of France from 1665 to 1683 under the rule of King Louis XIV. His relentless hard work and thrift made him an esteemed minister. He achieved a reputation for his work of improving the state of French manufacturing...
after he solved one of Jacques Ozanam
Jacques Ozanam
Jacques Ozanam was a French mathematician.-Biography:Jacques Ozanam was born in Sainte-Olive, Ain, France....
's problems. Rolle died in Paris. No portrait of him is known.
Work
Rolle was an early critic of infinitesimal calculusInfinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
, arguing that it was inaccurate, based upon unsound reasoning, and was a collection of ingenious fallacies, but later changed his opinion.
In 1690, Rolle published Traité d'Algebre. It contains the first published description in Europe of the Gaussian elimination
Gaussian elimination
In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix...
algorithm, which Rolle called the method of substitution. Some examples of the method had previously appeared in algebra books, and Isaac Newton had previously described the method in his lecture notes, but Newton's lesson was not published until 1707. Rolle's statement of the method seems not to have been noticed in so far as the lesson for Gaussian elimination that was taught in 18 and 19th century algebra textbooks owes more to Newton than to Rolle.
Rolle is best known for Rolle's theorem
Rolle's theorem
In calculus, Rolle's theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative is zero.-Standard version of the theorem:If a real-valued function ƒ is continuous on a closed...
in differential calculus. Rolle had used the result in 1690, and he proved it (by the standards of the time) in 1691. Given his animosity to infinitesimals it is fitting that the result was couched in terms of algebra rather than analysis. Only in the 18th century was the theorem interpreted as a fundamental result in differential calculus. Indeed, it is needed to prove both the mean value theorem and the existence of Taylor series. As the importance of the theorem grew, so did the interest in identifying the origin, and it was finally named Rolle's theorem in the 19th century. Barrow-Green remarks that the theorem might well have been named for someone else had not a few copies of Rolle's 1691 publication survived.
Critique of infinitesimal calculus
In a criticism of infinitesimal calculusInfinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
that predated George Berkeley
George Berkeley
George Berkeley , also known as Bishop Berkeley , was an Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism"...
's, Rolle presented a series of papers at the French academy, alleging that the use of the methods of infinitesimal calculus leads to errors. Specifically, he presented an explicit algebraic curve, and alleged that some of its local minima are missed when one applies the methods of infinitesimal calculus. Pierre Varignon
Pierre Varignon
Pierre Varignon was a French mathematician. He was educated at the Jesuit College and the University in Caen, where he received his M.A. in 1682. He took Holy Orders the following year....
responded by pointing out that Rolle had misrepresented the curve, and that the alleged local minima are in fact singular points with a vertical tangent.