Before 1840, Liouville had pursued some clear paths to secure his own career; during the following twenty years, the promotion and development of other mathematicians' ideas became the central issue.
Bago mag-1840, Liouville had pursued ilang malinaw na mga landas na ligtas na sa kanyang sariling karera; habang ang mga sumusunod na dalawampung taon, ang pagsulong at pag-unlad ng iba pang mga mathematicians' ideya ay naging ang central issue.