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Gustav Conrad Bauer (18 November 1820, Augsburg – 3 April 1906, Munich) was a German mathematician, known for the Bauer-Muir transformation and Bauer's conic sections. He earned a footnote in the history of science as the doctoral advisor (''Doktorvater'') of Heinrich Burkhardt, who became one of the two referees of Albert Einstein's doctoral dissertation.


Education and family

Gustav Bauer passed in 1837 his ''
Abitur ''Abitur'' (), often shortened colloquially to ''Abi'', is a qualification granted at the end of secondary education in Germany. It is conferred on students who pass their final exams at the end of ISCED 3, usually after twelve or thirteen year ...
'' at Augsburg's Gymnasium bei St. Anna. He continued his studies of mathematics at the Polytechnischen Schule Augsburg and also the universities of Erlangen, Vienna and Berlin. At Humboldt University in Berlin, Bauer received in 1842 his Promotierung under Peter Gustav Lejeune Dirichlet. From 1842 Gustav Bauer continued his studies in Paris under Joseph Liouville, as well as other mathematicians. In 1862 Gustav Bauer married Amalie, daughter of the ''Archivrat'' and Professor Honorarius Nathanael von Schlichtegroll. The marriage produced two daughters and a son Gustav junior, who became a well-known engineer.


Professional career

At the beginning of his professional employment, Bauer applied for a civil service position as a schoolteacher but became a private tutor from 1845 to 1853 in the royal house of Prince Mihail Sturdza and his successor Prince Grigore Alexandru Ghica in what is now Rumania. In 1857 Bauer spent three months in England and upon his return to Germany became a
Privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...
for the Mathematics Faculty of the
Ludwig Maximilian University of Munich The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operatio ...
. There he received his
Habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...
and became in 1865 professor extraordinarius, in 1869 professor ordinarius, and in 1900 professor emeritus. Bauer's mathematical research dealt with algebra, geometric problems, spherical harmonics, the
gamma function In mathematics, the gamma function (represented by , the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except ...
, and generalized continued fractions. In 1871 Bauer was elected a full member of the
Bayerische Akademie der Wissenschaften The Bavarian Academy of Sciences and Humanities (german: Bayerische Akademie der Wissenschaften) is an independent public institution, located in Munich. It appoints scholars whose research has contributed considerably to the increase of knowledg ...
. In 1884 he was elected a member of the Academy of Sciences Leopoldina. His doctoral students include Heinrich Burkhardt, Eduard Ritter von Weber, and Christian August Vogler.


Footnotes in the history of mathematics

In Ramanujan's first letter to G. H. Hardy, one of the theorems that impressed Hardy was: : 1 - 5\left(\frac12\right)^3 + 9\left(\frac\right)^3 - 13\left(\frac\right)^3 + \cdots = \frac However, Bauer proved the theorem in 1859. Using a result of Bauer on generalized continued fractions,
Oskar Perron Oskar Perron (7 May 1880 – 22 February 1975) was a German mathematician. He was a professor at the University of Heidelberg from 1914 to 1922 and at the University of Munich from 1922 to 1951. He made numerous contributions to differential ...
published in 1952 the first proof of another formula of Ramanujan.


Selected publications

* ''Von den Integralen gewisser Differential-Gleichungen, welche in der Theorie der Anziehung vorkommen,'' Wild, München, 1857
''Von einigen Summen-und Differenzenformeln und den Bernouillschen Zahlen''
Journal für die reine und angewandte Mathematik, vol. 58, pp. 292–300, 1861
"Ueber Kegelschnitte."
Journal für die reine und angewandte Mathematik, vol. 69, pp. 293–318, 1868
"Von der Zerlegung der Discriminante der cubischen Gleichung, welche die Hauptaxen einer Fläche zweiter Ordnung bestimmen, in eine Summe von Quadraten."
Journal für die reine und angewandte Mathematik vol. 71, pp. 40–45, 1869
''Über das Pascal'sche Theorem,''
in: ''Band 16 von Abhandlungen der Bayerischen Akademie der Wissenschaften, Mathematisch-Physikalische Klasse, Abhandlungen der Bayerischen Akademie der Wissenschaften, Mathematisch-Physikalische Klasse,'' Verlag der Akademie, München, 1873
''Gedächtnissrede auf Otto Hesse: gehalten in der öffentlichen Sitzung der k. b. Akademie der Wissenschaften zu München zur Feier ihres einhundert und dreiundzwanzigsten Stiftungstages am 28. März 1882
'' Verlag der Akademie, München, 1882 (See also Otto Hesse.)
''Von der Hesse'schen Determinante der Hesse'schen Fläche, einer Fläche dritter Ordnung,''
Verlag der Akademie, München, 1883 * ''Ueber die darstellung binärer formen als potenzsummen und insbesondere einer form vom grade 2 n̲ als eine summe von n̲ + 1 potenzen,'' Druck der Akademischen buchdruckerei von F. Straub, München, 1892 * ''Erinnerungen aus meinen Studienjahren, insbesondere mit Rücksicht auf die Entwickelung der Mathematik in jener Zeit : Fest -Vortrag zum XVI. Stiftungs-Feste am 7. Juli 1893,'' Buchdh. H. Wolf & S., München, 1893
''Vorlesungen über Algebra,''
B.G. Teubner, Leipzig, 1903


Sources

* Laetitia Boehm, Johannes Spörl, Universität München: ''Die Ludwig-Maximilians-Universität in ihren Fakultäten, Band 1,'' Duncker & Humblot, Berlin, 1972, , page 396. * Michael-Markus Toepell: ''Mathematiker und Mathematik an der Universität München : 500 Jahre Lehre und Forschung,'' Institut für Geschichte der Naturwissenschaften, München, 1996, page 193. * Walther Killy and Rudolf Vierhaus (eds.): '' Deutsche Biographische Enzyklopädie''. volume 1, K.G. Saur Verlag GmbH & Co. KG, Munich1996, , page 325.


References


External links

* {{DEFAULTSORT:Bauer, Gustav Conrad 1820 births 1906 deaths 19th-century German mathematicians Humboldt University of Berlin alumni Academic staff of the Ludwig Maximilian University of Munich