Pincherle was born into a Jewish family in Trieste (then part of the Austrian Littoral) and spent his childhood in Marseille, France.

After completing his basic schooling in Marseille, he left in 1869 to study mathematics at the University of Pisa, where he was a student under both Enrico Betti and Ulisse Dini.

In 1901, collaborating with Ugo Amaldi, he published his main scientific book, Le Operazioni Distributive e loro Applicazioni all'Analisi.

Four years later, he became President of the Third International Congress and played a significant role in re-admitting German mathematicians after a ban imposed because of World War I.

In honor of the centenary of his birth, the Italian Mathematical Union edited a selection of 62 of his notes and treatises; they were published in 1954 in Rome.