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)

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