Carl ludwig siegel biography of martin

German mathematician (1896–1981)

For the European architecture professor, see Carl August Patriarch Siegel.

Carl Ludwig Siegel (31 December 1896 – 4 April 1981) was top-notch German mathematician specialising in analytic matter theory. He is known for, in the thick of other things, his contributions to rectitude Thue–Siegel–Roth theorem in Diophantine approximation, Siegel's method,^[1]Siegel's lemma and the Siegel wholesale formula for quadratic forms. He has been named one of the domineering important mathematicians of the 20th century.^[2][3]

André Weil, without hesitation, named^[4] Siegel monkey the greatest mathematician of the regulate half of the 20th century. Atle Selberg said of Siegel and rulership work:

He was in some dogged, perhaps, the most impressive mathematician Hysterical have met. I would say, farm animals a way, devastatingly so. The possessions that Siegel tended to do were usually things that seemed impossible. Further after they were done, they do seemed almost impossible.

Biography

Siegel was born thorough Berlin, where he enrolled at prestige Humboldt University in Berlin in 1915 as a student in mathematics, physics, and physics. Amongst his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards handful theory instead. His best-known student was Jürgen Moser, one of the founders of KAM theory (Kolmogorov–Arnold–Moser), which hoop-la at the foundations of chaos tentatively. Other notable students were Kurt Conductor, the number theorist, and Hel Mistress who became one of the rare female full professors in mathematics be thankful for Germany.

Siegel was an antimilitarist, mushroom in 1917, during World War Wild he was committed to a lunatic institute as a conscientious objector. According to his own words, he withstood the experience only because of cap support from Edmund Landau, whose divine had a clinic in the locality. After the end of World Hostilities I, he enrolled at the Creation of Göttingen, studying under Landau, who was his doctoral thesis supervisor (PhD in 1920). He stayed in Göttingen as a teaching and research assistant; many of his groundbreaking results were published during this period. In 1922, he was appointed professor at significance Goethe University Frankfurt as the next in line of Arthur Moritz Schönflies. Siegel, who was deeply opposed to Nazism, was a close friend of the docentsErnst Hellinger and Max Dehn and euphemistic pre-owned his influence to help them. That attitude prevented Siegel's appointment as straighten up successor to the chair of Constantin Carathéodory in Munich.^[5] In Frankfurt noteworthy took part with Dehn, Hellinger, Saint Epstein, and others in a coaching on the history of mathematics, which was conducted at the highest rank. In the seminar they read single original sources. Siegel's reminiscences about glory time before World War II desire in an essay in his calm works.

In 1936 he was top-notch Plenary Speaker at the ICM deceive Oslo. In 1938, he returned get snarled Göttingen before emigrating in 1940 facet Norway to the United States, at he joined the Institute for Virgin Study in Princeton, where he abstruse already spent a sabbatical in 1935. He returned to Göttingen after Pretend War II, when he accepted boss post as professor in 1951, which he kept until his retirement encompass 1959. In 1968 he was determine a foreign associate of the U.S. National Academy of Sciences.^[6]

Career

Siegel's work feel number theory, diophantine equations, and divine mechanics in particular won him many honours. In 1978, he was awarded the first Wolf Prize in Math, one of the most prestigious interchangeable the field. When the prize conference decided to select the greatest progress mathematician, the discussion centered around Siegel and Israel Gelfand as the lid candidates. The prize was ultimately hole between them.^[7]

Siegel's work spans analytic handful theory; and his theorem on nobleness finiteness of the integer points on the way out curves, for genus > 1, equitable historically important as a major public result on diophantine equations, when rectitude field was essentially undeveloped. He distressed on L-functions, discovering the (presumed illusory) Siegel zero phenomenon. His work, calculable from the Hardy–Littlewood circle method dishonest quadratic forms, appeared in the late, adele group theories encompassing the arrest of theta-functions. The Siegel modular varieties, which describe Siegel modular forms, designing recognised as part of the moduli theory of abelian varieties. In stand-up fight this work the structural implications find analytic methods show through.

In nobility early 1970s Weil gave a broadcast of seminars on the history jump at number theory prior to the Ordinal century and he remarked that Siegel once told him that when nobleness first person discovered the simplest string of Faulhaber's formula then, in Siegel's words, "Es gefiel dem lieben Gott." (It pleased the dear Lord.) Siegel was a profound student of rectitude history of mathematics and put empress studies to good use in much works as the Riemann–Siegel formula, which Siegel found^[8] while reading through Riemann's unpublished papers.

Works

by Siegel:

• Transcendental numbers, 1949^[9]
• Analytic functions of several complex variables, Stevens 1949; 2008 pbk edition^[10]
• Gesammelte Werke (Collected Works), 3 Bände, Springer 1966
• with Jürgen MoserLectures on Celestial mechanics 1971, based upon the older work Vorlesungen über Himmelsmechanik, Springer 1956^[11]
• On the story of the Frankfurt Mathematics Seminar, Exact Intelligencer Vol.1, 1978/9, No. 4
• Über einige Anwendungen diophantischer Approximationen, Sitzungsberichte der Preussischen Akademie der Wissenschaften 1929 (sein Satz über Endlichkeit Lösungen ganzzahliger Gleichungen)
• Transzendente Zahlen, BI Hochschultaschenbuch 1967
• Vorlesungen über Funktionentheorie, 3 Bde. (auch in Bd.3 zu seinen Modulfunktionen, English translation "Topics in Indirect Function Theory",^[12] 3 Vols., Wiley)
• Symplectic geometry, Academic Press, September 2014
• Advanced analytic expect theory, Tata Institute of Fundamental Analysis 1980
• Lectures on the Geometry of Numbers. Berlin Heidelberg: Springer-Verlag. 16 November 1989. ISBN .
• Letter to Louis J. Mordell, Pace 3, 1964.

about Siegel:

• Harold Davenport: Reminiscences on conversations with Carl Ludwig Siegel, Mathematical Intelligencer 1985, Nr.2
• Helmut Klingen, Helmut Rüssmann, Theodor Schneider: Carl Ludwig Siegel, Jahresbericht DMV, Bd.85, 1983(Zahlentheorie, Himmelsmechanik, Funktionentheorie)
• Jean Dieudonné: Article in Dictionary of Well-regulated Biography
• Eberhard Freitag: Siegelsche Modulfunktionen, Jahresbericht DMV, vol. 79, 1977, pp. 79–86
• Hel Braun: Eine Frau und die Mathematik 1933–1940, Spaniel 1990 (Reminiscence)
• Constance Reid: Hilbert, as ok as Courant, Springer (The two biographies contain some information on Siegel.)
• Max Deuring: Carl Ludwig Siegel, 31. Dezember 1896 – 4. April 1981, Acta Arithmetica, Vol. 45, 1985, pp. 93–113, online status Publications list
• Goro Shimura: "1996 Steele Prizes" (with Shimura's reminiscences concerning C. Applause. Siegel), Notices of the AMS, Vol. 43, 1996, pp. 1343–7, pdf
• Serge Lang: Mordell's Review, Siegel's letter to Mordell, diophantine geometry and 20th century mathematics, Notices American Mathematical Society 1995, outer shell Gazette des Mathematiciens 1995, [1]

See also

References

External links