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.

[3] In 1829, he discovered the theorem that bears his name, and concerns real-root isolation, that is the determination of the number and the localization of the real roots of a polynomial.

[4] Sturm benefited from the 1830 revolution, as his Protestant faith ceased to be an obstacle to employment in public high schools.

The same year, after the death of Poisson, Sturm was appointed as mechanics professor of the Faculté des sciences de Paris [fr].

In 1826, with his colleague Jean-Daniel Colladon, Sturm helped make the first experimental determination of the speed of sound in water.