**Charles-François Sturm** is best remembered for the Sturm-Liouville problem, an eigenvalue problem in second order differential equations.

- Charles-François's parents gave him a good education and at school he showed great promise, particularly in Greek and Latin poetry for which he had a remarkable talent.
- He was taught mathematics at Geneva Academy by Simon Lhuilier in 1821 and immediately Lhuilier recognised the mathematical genius in Sturm.
- However, Lhuilier was over seventy years of age and close to retiring at this time so it was his successor Jean-Jacques Schaub who inspired Sturm.
- Schaub did more than teach Sturm mathematics for he supported him financially at the Academy.
- At the Academy Sturm's best friend was Daniel Colladon and the friendship would have a marked influence on Sturm's early research career.
- This was clearly an extremely fortunate opportunity for Sturm.
- The Paris Academy had set a prize topic on the compressibility of water and Sturm, with his friend Colladon, decided to begin experiments on Lake Geneva with the aim of putting in an entry for the prize.
- In December 1825 Sturm and Colladon went to Paris to take courses in mathematics and physics and also to collect further instruments to repeat their experiments.
- The Paris contacts that Sturm had made proved useful for he lived at Arago's house for a while as tutor to his son.
- The time was very fruitful for Sturm who attended lectures by Ampère, Gay-Lussac, Cauchy, and Lacroix.
- Fourier suggested projects for both Sturm and Colladon, recognising that Colladon was essentially a physicist while Sturm was a mathematician.
- By this time Sturm and Colladon were both working as assistants to Fourier.
- The value of the prize was enough to allow Sturm and Colladon to continue their research in Paris.
- Sturm's theoretical work in mathematical physics involved the study of caustic curves, and poles and polars of conic sections.
- One of Sturm's most famous papers Mémoire sur la résolution des équations numériques Ⓣ(Dissertation on solving numerical equations) was published in 1829.
- Sturm achieved fame with his paper which, using ideas of Fourier, gave a simple solution.
- The author describes how Tarski showed in 1940 that Sturm's method of proof could be used in mathematical logic to prove the completeness of elementary algebra and geometry.
- seeks to determine the mutual influence between A-L Cauchy's and Ch-F Sturm's research from 1829 to around 1840 on the roots of algebraic equations.
- Sturm became interested in obtaining results on specific differential equations which occurred in Poisson's theory of heat.
- Papers of 1836-1837 by Sturm and Liouville on differential equations involved expansions of functions in series and is today well-known as the Sturm-Liouville problem, an eigenvalue problem in second order differential equations.

Born 29 September 1803, Geneva, Switzerland. Died 18 December 1855, Paris, France.

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Algebra, Ancient Greek, Geometry, Origin Switzerland, Puzzles And Problems

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive