Oskar Bolza
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Oskar Bolza (12 May 1857 – 5 July 1942) was a German
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
, and student of
Felix Klein Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and grou ...
. He was born in Bad Bergzabern, Palatinate, then a district of
Bavaria Bavaria ( ; ), officially the Free State of Bavaria (german: Freistaat Bayern, link=no ), is a state in the south-east of Germany. With an area of , Bavaria is the largest German state by land area, comprising roughly a fifth of the total lan ...
, known for his research in the calculus of variations, particularly influenced by
Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...
' 1879 lectures on the subject.


Life

Bolza entered the University of Berlin in 1875. His first interest was in
linguistics Linguistics is the science, scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure ...
, then he studied physics with Kirchhoff and 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 Karl Theodor Reye (born 20 June 1838 in Ritzebüttel, Germany and died 2 July 1919 in Würzburg, Germany) was a German mathematician. He contributed to geometry, particularly projective geometry and synthetic geometry. He is best known for his ...
at Strasbourg,
Hermann Schwarz Karl Hermann Amandus Schwarz (; 25 January 1843 – 30 November 1921) was a German mathematician, known for his work in complex analysis. Life Schwarz was born in Hermsdorf, Silesia (now Jerzmanowa, Poland). In 1868 he married Marie Kummer, ...
at Göttingen, and particularly
Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis". Despite leaving university without a degree, he studied mathematics ...
in Berlin. In the spring of 1888 he landed in Hoboken, NJ, searching for a job in the United States: he succeeded in finding a position in 1889 at
Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...
and then at the then newly founded
Clark University Clark University is a private research university in Worcester, Massachusetts. Founded in 1887 with a large endowment from its namesake Jonas Gilman Clark, a prominent businessman, Clark was one of the first modern research universities in the ...
.According to . In 1892 Bolza joined the
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
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 Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as o ...
in Germany. The events of
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
greatly affected Bolza and, after 1914, he stopped his research in mathematics. He became interested in religious psychology, languages (particularly
Sanskrit Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...
), and Indian religions. He published the book ''Glaubenlose Religion'' (religion without belief) in 1930 under the pseudonym F. H. Marneck. However, later in his life, he returned to do research in mathematics, lecturing at
University of Freiburg The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public research university located in Freiburg im Breisgau, Baden-Württemb ...
from 1929 up to his retirement in 1933.


Academic career

He completed his doctoral studies, after eight years of study and many changes of direction, in 1886, from the Georg-August-Universität Göttingen. He wrote his thesis, titled ''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 Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and grou ...
. In 1889 Bolza worked at
Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hemisphere. It consi ...
, where
Simon Newcomb Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadian–American astronomer, applied mathematician, and autodidactic polymath. He served as Professor of Mathematics in the United States Navy and at Johns Hopkins University. Born in N ...
gave him a temporary short-term appointment " reader in mathematics", then he obtained a position as an associate professor at
Clark University Clark University is a private research university in Worcester, Massachusetts. Founded in 1887 with a large endowment from its namesake Jonas Gilman Clark, a prominent businessman, Clark was one of the first modern research universities in the ...
. 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 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 S ...
. In 1892 Bolza joined the
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
and worked there up to 1910, when he decided to return to
Freiburg Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as o ...
in Germany: he was appointed there as honorary professor, while the University Chicago awarded him the title of "''non-resident professor of mathematics''" which he retained for the rest of his life.


Work


Research activity

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 The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...
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 The University of Chicago Press is the largest and one of the oldest university presses 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'', ...
in 1904, became a classic in its field and was republished several times: the augmented German edition of the same work was considered by his former student
Gilbert Ames Bliss Gilbert Ames Bliss, (9 May 1876 – 8 May 1951), was an American mathematician, known for his work on the calculus of variations. Life Bliss grew up in a Chicago family that eventually became affluent; in 1907, his father became president of the ...
"''a classic, indispensable to every scholar in the field, and much wider in its scope than his earlier book''". 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.


Teaching activity

Bolza joined the
University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private university, private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park, Chicago, Hyde Park neighborhood. The University of Chic ...
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 Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also reme ...
, who was the first to be awarded a
Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...
in mathematics by the University of Chicago, Gilbert Bliss,
Oswald Veblen Oswald Veblen (June 24, 1880 – August 10, 1960) 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; while this was lon ...
,
Robert Lee Moore Robert Lee Moore (November 14, 1882 – October 4, 1974) was an American mathematician who taught for many years at the University of Texas. He is known for his work in general topology, for the Moore method of teaching university mathematics, ...
, George D. Birkhoff, and T. H. Hildebrandt. In 1908 Bolza moved into
Freiburg Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as o ...
and managed to become a professor at the
University of Freiburg The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public research university located in Freiburg im Breisgau, Baden-Württemb ...
and lectured there for years. However, his teachings were interrupted by
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
afterword he continued lecturing at
Freiburg Freiburg im Breisgau (; abbreviated as Freiburg i. Br. or Freiburg i. B.; Low Alemannic: ''Friburg im Brisgau''), commonly referred to as Freiburg, is an independent city in Baden-Württemberg, Germany. With a population of about 230,000 (as o ...
until 1926. After three years he returned to the
University of Freiburg The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public research university located in Freiburg im Breisgau, Baden-Württemb ...
to continue lecturing he kept up his classes until 1933.


Selected publications

*. *: a corrected and improved edition was published in 1960 as , while unabridged unaltered reprints of the first edition appeared in 1961 as , and in 2005 as , available from University of Michigan Digital Mathematics Library. *. The "revised and notably augmented German edition""''...umgearbeitete und stark vermehrte deutsche Ausgabe''" as the title page reads. of the classical work .


See also

*
Bolza surface In mathematics, the Bolza surface, alternatively, complex algebraic Bolza curve (introduced by ), is a compact Riemann surface of genus 2 with the highest possible order of the conformal automorphism group in this genus, namely GL_2(3) of order 48 ...


Notes


Biographical references

*. *, available from
Project Euclid Project Euclid is a collaborative partnership between Cornell University Library and Duke University Press which seeks to advance scholarly communication in theoretical and applied mathematics and statistics through partnerships with independent an ...
. *, available from GDZ or from the DigiZeitschriften Document Server. *.


References

* *


External links


Bolza's geometry.net profile
* {{DEFAULTSORT:Bolza, Oskar Clark University faculty 1857 births 1942 deaths People from Bad Bergzabern 19th-century German mathematicians 20th-century German mathematicians Geometers University of Chicago faculty People from the Palatinate (region) Variational analysts