Jacques Charles François Sturm (29 September 1803 – 15 December 1855) was a French
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
, who made a significant addition to equation theory with his work,
Sturm's theorem
In mathematics, the Sturm sequence of a univariate polynomial is a sequence of polynomials associated with and its derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real number, real R ...
.
Early life
Sturm was born in
Geneva
Geneva ( , ; ) ; ; . is the List of cities in Switzerland, second-most populous city in Switzerland and the most populous in French-speaking Romandy. Situated in the southwest of the country, where the Rhône exits Lake Geneva, it is the ca ...
,
France
France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...
in 1803. The family of his father, Jean-Henri Sturm, had emigrated from
Strasbourg
Strasbourg ( , ; ; ) is the Prefectures in France, prefecture and largest city of the Grand Est Regions of France, region of Geography of France, eastern France, in the historic region of Alsace. It is the prefecture of the Bas-Rhin Departmen ...
around 1760—about 50 years before Charles-François's birth. His mother's name was Jeanne-Louise-Henriette Gremay.
In 1818, he started to follow the lectures of the
academy of Geneva. The death of his father forced Sturm to give lessons to children of the rich in order to support his own family the following year. In 1823, he became tutor to the son of
Madame de Staël.
At the end of that year, Sturm stayed in
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
for a short time following the family of his student. He resolved, with his school-fellow
Jean-Daniel Colladon, to try his fortune in Paris, and obtained employment on the ''Bulletin universel''.
Discovery
In 1829, he discovered the
theorem
In mathematics and formal logic, a theorem is a statement (logic), statement that has been Mathematical proof, proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to esta ...
that bears his name, and concerns
real-root isolation, that is the determination of the number and the localization of the real
roots
A root is the part of a plant, generally underground, that anchors the plant body, and absorbs and stores water and nutrients.
Root or roots may also refer to:
Art, entertainment, and media
* ''The Root'' (magazine), an online magazine focusin ...
of a
polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...
.
Work
Sturm benefited from the 1830 revolution, as his Protestant faith ceased to be an obstacle to employment in public high schools. At the end of 1830, he was thus appointed as a professor of Mathématiques Spéciales at the
collège Rollin.
He was chosen a member of the
Académie des Sciences in 1836, filling the seat of
André-Marie Ampère
André-Marie Ampère (, ; ; 20 January 177510 June 1836) was a French physicist and mathematician who was one of the founders of the science of classical electromagnetism, which he referred to as ''electrodynamics''. He is also the inventor of ...
. Sturm became ''répétiteur'' in 1838, and in 1840 professor in the
École Polytechnique
(, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris.
The school was founded in 1794 by mat ...
. The same year, after the death of
Poisson, Sturm was appointed as
mechanics
Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...
professor of the . His works, ''Cours d'analyse de l'école polytechnique'' (1857–1863) and ''Cours de mécanique de l'école polytechnique'' (1861), were published after his death in Paris,
and were regularly republished.
He was the co-
eponym
An eponym is a noun after which or for which someone or something is, or is believed to be, named. Adjectives derived from the word ''eponym'' include ''eponymous'' and ''eponymic''.
Eponyms are commonly used for time periods, places, innovati ...
of the
Sturm–Liouville theory
In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form
\frac \left (x) \frac\right+ q(x)y = -\lambda w(x) y
for given functions p(x), q(x) and w(x), together with some ...
with
Joseph Liouville
Joseph Liouville ( ; ; 24 March 1809 – 8 September 1882) was a French mathematician and engineer.
Life and work
He was born in Saint-Omer in France on 24 March 1809. His parents were Claude-Joseph Liouville (an army officer) and Thérès ...
.
In 1826, with his colleague
Jean-Daniel Colladon, Sturm helped make the first experimental determination of the
speed of sound
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elasticity (solid mechanics), elastic medium. More simply, the speed of sound is how fast vibrations travel. At , the speed of sound in a ...
in water.
Death
In 1851 his health began to fail. He was able to return to teaching for a while during his long illness, but died in 1855.
The asteroid
31043 Sturm is named for him.
Sturm's name is one of
the 72 names engraved at the
Eiffel Tower
The Eiffel Tower ( ; ) is a wrought-iron lattice tower on the Champ de Mars in Paris, France. It is named after the engineer Gustave Eiffel, whose company designed and built the tower from 1887 to 1889.
Locally nicknamed "''La dame de fe ...
.
Distinctions
* Grand prix de Mathématiques (4 December 1834)
* Member of the academy of Berlin (1835)
* Member of the academy of Saint-Petersburg (1836)
* Officier de la
Légion d'Honneur
The National Order of the Legion of Honour ( ), formerly the Imperial Order of the Legion of Honour (), is the highest and most prestigious French national order of merit, both military and Civil society, civil. Currently consisting of five cl ...
(1837)
*
Copley Medal
The Copley Medal is the most prestigious award of the Royal Society of the United Kingdom, conferred "for sustained, outstanding achievements in any field of science". The award alternates between the physical sciences or mathematics and the bio ...
of the
Royal Society of London
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...
(1840)
* Member of the
Royal Society of London (1840)
Selected writing
*
*
Cours d'analyse de l'Ecole polytechnique. Tome premier(Gauthier-Villars, 1877)
Cours d'analyse de l'Ecole polytechnique. Tome second(Gauthier-Villars, 1877)
Cours de mécanique de l'Ecole polytechnique(Gauthier-Villars, 1883)
See also
*
Control theory
Control theory is a field of control engineering and applied mathematics that deals with the control system, control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the applic ...
*
Oscillation theory
*
Spectral theory of ordinary differential equations
*
Submarine signals
References
External links
*
*
{{DEFAULTSORT:Sturm, Jacques Charles Francois
1803 births
1855 deaths
Members of the French Academy of Sciences
Officers of the Legion of Honour
Recipients of the Copley Medal
19th-century French mathematicians
Scientists from Geneva