He was born in Bad Bergzabern, Palatinate, then a district of Bavaria, known for his research in the calculus of variations, particularly influenced by Karl Weierstrass' 1879 lectures on the subject.

His first interest was in linguistics, then he studied physics with Gustav Kirchhoff and Hermann von Helmholtz, but experimental work did not attract him, so he decided on mathematics in 1878.

The years 1878–1881 were spent studying under Elwin Christoffel and Theodor Reye at Strasbourg, Hermann Schwarz at Göttingen, and particularly Karl Weierstrass in Berlin.

[4] In 1892 Bolza joined the University of Chicago and worked there up to 1910 when, after becoming unhappy in the United States as a consequence of the death of his friend Heinrich Maschke in 1908, he and his wife returned to Freiburg in Germany.

[10] Immediately after his return to Germany Bolza continued teaching and research, in particular on function theory, integral equations and the calculus of variations.

These included Leonard Dickson, who was the first to be awarded a Ph.D. in mathematics by the University of Chicago, Gilbert Bliss, Oswald Veblen, Robert Lee Moore, George D. Birkhoff, and Theophil Henry Hildebrandt.