Oskar Bolza

After eight years of study and many changes of direction, he completed his doctoral studies at the Georg-August-Universität Göttingen in 1886, where he wrote his thesis under the supervision of Felix Klein.[5]

In 1889 Bolza worked at Johns Hopkins University, where Simon Newcomb gave him a temporary short-term appointment "reader in mathematics", then he obtained a position as an associate professor at Clark University.[4] While at Clark, Bolza published the important paper On the theory of substitution groups and its application to algebraic equations in the American Journal of Mathematics. In 1892 Bolza joined the University of Chicago and worked there up to 1910, when he decided to return to Freiburg in Germany: he was appointed there as honorary professor,[6] while the University Chicago awarded him the title of "non-resident professor of mathematics" which he retained for the rest of his life.[7]

Bolza published The elliptic s-functions considered as a special case of the hyperelliptic s-functions in 1900 which related to work he had been studying for his doctorate under Klein. However, he worked on the calculus of variations from 1901. Papers which appeared in the Transactions of the American Mathematical Society over the next few years were: New proof of a theorem of Osgood's in the calculus of variations (1901); Proof of the sufficiency of Jacobi's condition for a permanent sign of the second variation in the so-called isoperimetric problems (1902); Weierstrass' theorem and Kneser's theorem on transversals for the most general case of an extremum of a simple definite integral (1906); and Existence proof for a field of extremals tangent to a given curve (1907). His text Lectures on the Calculus of Variations published by the University of Chicago Press in 1904,[8] became a classic in its field and was republished several times: the augmented German edition of the same work[9] was considered by his former student Gilbert Ames Bliss "a classic, indispensable to every scholar in the field, and much wider in its scope than his earlier book".[10]

Immediately after his return to Germany Bolza continued teaching and research, in particular on function theory, integral equations and the calculus of variations. Two papers of 1913 and 1914 are particularly important. The first Problem mit gemischten Bedingungen und variablen Endpunkten formulated a new type of variational problem now called "the Bolza problem of Bolza" after him and the second studied variations for an integral problem involving inequalities. This latter work was to become important in control theory. Bolza returned to Chicago for part of 1913 giving lecturers during the summer on function theory and integral equations.

Bolza joined the University of Chicago in 1892. Working eighteen years between 1892 and 1910. During this time the mathematics department was outstandingly successful with thirty-nine students graduating with doctorates (nine of them students of Bolza). 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.

In 1908 Bolza moved into Freiburg and managed to become a professor at the University of Freiburg and lectured there for years. However, his teachings were interrupted by World War I afterword he continued lecturing at Freiburg until 1926. After three years he returned to the University of Freiburg to continue lecturing he kept up his classes until 1933.