In 1825, he traveled to Paris and learned mathematics at École Polytechnique, where he met Joseph Liouville (1833).

Though he was politically active and strongly left-wing, leading him to participate in the 1848 Revolution, he had an animated career and also sat in the France's Chamber of Deputies.

Later, in 1849, Catalan was visited at his home by the French Police, searching for illicit teaching material; however, none was found.

Before that, he had stated the famous Catalan's conjecture, which was published in 1844 and was eventually proved in 2002, by the Romanian mathematician Preda Mihăilescu.

He introduced the Catalan numbers to solve a combinatorial problem (although these were actually discovered a century earlier by the Chinese astronomer Minggatu).