He entered the École Normale Supérieure in 1857, and finished his studies there in 1860,[1] the same year in which he published the paper containing his theorem on constant-width curves.
He began teaching at a lycée in Nice, but it was not a success, and he soon moved to a position as an assistant astronomer at the Paris Observatory.
He left there in 1865, and in 1880 Joseph Louis François Bertrand found him in the Charenton asylum.
Bertrand arranged for Barbier's support and encouraged him to return to mathematical publication.
[5] He was given the Francoeur Prize for his mathematical research by the French Academy of Sciences in multiple years.