Oskar Bolza
Encyclopedia
Oskar Bolza was a German
mathematician
, and student of Felix Klein
. He was born in Bad Bergzabern
, Rhenish Palatinate, and his parents were Luise Koenig and Moritz Bolza.
He completed his doctoral studies, after eight years of study and many changes of direction, in 1886, from the Georg-August-Universität Göttingen. His thesis was Über die Reduction hyperelliptischer Integrale erster Ordnung und erster Gattung auf elliptische, insbesondere über die Reduction durch eine Transformation vierten Grades (translated as On reduction of hyperelliptic integrals of first order and first kind to elliptic integrals, especially on reduction by transformation of fourth degree)
under the supervision of Felix Klein
.
In 1889 Bolza worked at Johns Hopkins University
, where Simon Newcomb
gave him a temporary short-term appointment, then he obtained a position at Clark University
. 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
.
Bolza joined the University of Chicago
in 1892. Between 1892 and 1910 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 T. H. Hildebrandt.
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, became a classic in its field and was republished in 1961 and 2005. After the death of his friend Maschke in 1908, Bolza became unhappy in the United States
and, in 1910, he and his wife returned to Freiburg
in Germany where he was appointed as an honorary professor. Chicago gave him the title of 'non-resident professor of mathematics' which he retained for the rest of his life.
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 problem of Bolza' 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.
World War I
greatly affected Bolza and, after 1914, he undertook no further research in mathematics. He became interested in religious psychology, languages (particularly Sanskrit
), and Indian religions. He published Glaubenlose Religion (religion without belief) in 1930 under the pseudonym F. H. Marneck. He returned to mathematics, however, lecturing at University of Freiburg
from 1929 to 1933, when he retired.
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, and student of Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
. He was born in Bad Bergzabern
Bad Bergzabern
Bad Bergzabern is a municipality in the Südliche Weinstraße district, on the German Wine Route in Rhineland-Palatinate, Germany. It is situated near the border with France, on the south-eastern edge of the Palatinate forest, approximately southwest of Landau....
, Rhenish Palatinate, and his parents were Luise Koenig and Moritz Bolza.
He completed his doctoral studies, after eight years of study and many changes of direction, in 1886, from the Georg-August-Universität Göttingen. His thesis was Über die Reduction hyperelliptischer Integrale erster Ordnung und erster Gattung auf elliptische, insbesondere über die Reduction durch eine Transformation vierten Grades (translated as On reduction of hyperelliptic integrals of first order and first kind to elliptic integrals, especially on reduction by transformation of fourth degree)
under the supervision of Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
.
In 1889 Bolza worked at Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
, where Simon Newcomb
Simon Newcomb
Simon Newcomb was a Canadian-American astronomer and mathematician. Though he had little conventional schooling, he made important contributions to timekeeping as well as writing on economics and statistics and authoring a science fiction novel.-Early life:Simon Newcomb was born in the town of...
gave him a temporary short-term appointment, then he obtained a position at Clark University
Clark University
Clark University is a private research university and liberal arts college in Worcester, Massachusetts.Founded in 1887, it is the oldest educational institution founded as an all-graduate university. Clark now also educates undergraduates...
. 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
American Journal of Mathematics
The American Journal of Mathematics is a bimonthly mathematics journal published by the Johns Hopkins University Press.- History :The American Journal of Mathematics is the oldest continuously-published mathematical journal in the United States, established in 1878 at the Johns Hopkins University...
.
Bolza joined the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
in 1892. Between 1892 and 1910 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.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
in mathematics by the University of Chicago, Gilbert Bliss, Oswald Veblen
Oswald Veblen
Oswald Veblen was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905.-Life:...
, Robert Lee Moore
Robert Lee Moore
Robert Lee Moore was an American mathematician, known for his work in general topology and the Moore method of teaching university mathematics.-Life:...
, George D. Birkhoff, and T. H. Hildebrandt.
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
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society is a monthly mathematics journal published by the American Mathematical Society. It started in 1900...
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
University of Chicago Press
The University of Chicago Press is the largest university press in the United States. It is operated by the University of Chicago and publishes a wide variety of academic titles, including The Chicago Manual of Style, dozens of academic journals, including Critical Inquiry, and a wide array of...
in 1904, became a classic in its field and was republished in 1961 and 2005. After the death of his friend Maschke in 1908, Bolza became unhappy in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
and, in 1910, he and his wife returned to Freiburg
Freiburg
Freiburg im Breisgau is a city in Baden-Württemberg, Germany. In the extreme south-west of the country, it straddles the Dreisam river, at the foot of the Schlossberg. Historically, the city has acted as the hub of the Breisgau region on the western edge of the Black Forest in the Upper Rhine Plain...
in Germany where he was appointed as an honorary professor. Chicago gave him the title of 'non-resident professor of mathematics' which he retained for the rest of his life.
Immediately after his return to Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
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 problem of Bolza' 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.
World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
greatly affected Bolza and, after 1914, he undertook no further research in mathematics. He became interested in religious psychology, languages (particularly Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
), and Indian religions. He published Glaubenlose Religion (religion without belief) in 1930 under the pseudonym F. H. Marneck. He returned to mathematics, however, lecturing at University of Freiburg
University of Freiburg
The University of Freiburg , sometimes referred to in English as the Albert Ludwig University of Freiburg, is a public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany.The university was founded in 1457 by the Habsburg dynasty as the...
from 1929 to 1933, when he retired.