After one year studying mathematics at the Sorbonne, Bernstein decided that he would rather become an engineer and entered the École supérieure d'électricité.

However, he continued to be interested in mathematics and spent three terms at the University of Göttingen, beginning in the autumn of 1902, where his studies were supervised by David Hilbert.

In his doctoral dissertation, submitted in 1904 to the Sorbonne, Bernstein solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations.

[4] His later work was devoted to Dirichlet's boundary problem for non-linear equations of elliptic type, where, in particular, he introduced a priori estimates.

[9] His plenary address Sur les liaisons entre quantités aléatoires was read by Bohuslav Hostinsky.