Strongly committed to left-wing politics, he took part in the 1848 revolution. This later hindered his efforts to secure a teaching position commensurate with his abilities. He therefore returned to Belgium and obtained a post at the University of Liège.
Catalan's research covered multiple integrals (we owe him the change-of-variables formula for double integrals using the Jacobian), differential equations, power series, algebraic geometry and number theory.
Catalan is known for the numbers bearing his name, but also for the following conjecture, which he stated in 1844: the equation *a m ‒ b n = 1, where m and n are given strictly positive integers and the unknowns a and b* are integers greater than or equal to 2, has only one solution, 32 ‒ 23 = 1.
This conjecture remained unproved for more than 150 years; it was proved in 2002 by the Romanian mathematician Preda Mihăilescu.
