He was born in 1906 in Warsaw to father Feliks Jaśkowski and mother Kazimiera (nee Dzierzbicka).

In 1924, he graduated from high school in Zakopane and enrolled at the University of Warsaw to study mathematics.

He was taught mathematical logic under Jan Łukasiewicz and participated in the Polish Mathematicians' Congresses in Lviv (1927) and Vilnius (1931).

In 1945, he continued his scientific career at the University of Toruń where he defended his habilitation and assumed the post of the head of the Faculty of Mathematical Logic.

Jaśkowski is considered to be one of the founders of natural deduction, which he discovered independently of Gerhard Gentzen in the 1930s.