His father, also named Traian, was originally from Cornea, Caraș-Severin and worked as a superintendent at the Creditul Agricol Bank.

His dissertation, Sur les équations de Volterra, was written under the direction of Émile Picard.

[4] A year later, he was appointed full-time professor of analytical geometry, succeeding Spiru Haret; he lectured at the School (which would later become the Polytechnic University of Bucharest) until his death.

Also that year, he was appointed tenured professor of algebra and number theory at the University of Bucharest, a position he held until his death.

[1][2] In the fall of 1927, he caught a double pneumonia; in 1928, he went for a vacation in Nice and for treatment in Paris, but he succumbed to the disease the next year, at age 46.