Edmund Landau

Edmund Landau (before 1930)

Edmund Georg Hermann Landau (born February 14, 1877 in Berlin ; † February 19, 1938 there ) was a German mathematician who made a name for himself in analytical number theory .

Life

Edmund Landau came from an upper-class, assimilated German-Jewish family. His father Leopold Landau was a gynecologist and saw himself as both a German patriot and a Zionist . He passed these views on to his son. Landau attended the French grammar school in Berlin . Even when he was at school, his extraordinary mathematical talent was noticeable. He studied at the Friedrich-Wilhelms-Universität zu Berlin , where he received his doctorate on a number theory topic under Ferdinand Georg Frobenius in 1899 . In 1901 he completed his habilitation under Frobenius and taught as a private lecturer at Berlin University until 1908. In 1905 he married Marianne Ehrlich, the daughter of the later Nobel Prize winner Paul Ehrlich .

In 1909 he accepted a call to Göttingen to succeed Hermann Minkowski . There he worked on an equal footing with his high-ranking colleagues David Hilbert and Felix Klein . In 1912 he gave a plenary lecture at the International Congress of Mathematicians in Cambridge ( Solved and unsolved problems from the theory of prime number distribution and the Riemann zeta function ). Since 1914 he was a full member (and from 1933 a foreign member) of the Göttingen Academy of Sciences .

Landau practiced his Jewish faith (he later added his first name Yechezkel, after a well-known Prague rabbi among his ancestors) and learned Hebrew for his speech at the opening of the Hebrew University in Jerusalem in 1925. He was visiting professor in Jerusalem for one year in 1927/28. Landau was very committed to founding and equipping the Hebrew University and bequeathed his extensive library to it in his estate. He was also very wealthy - when someone asked him how to get to his house in Gottingen, he replied that you couldn't miss it, that it was the most beautiful house in town.

In 1921 he was chairman of the German Mathematicians Association ; in the same year he was also elected a member of the Leopoldina . In 1924 he became an honorary member of the London Mathematical Society and a corresponding member of the Prussian Academy of Sciences . Since 1924 he was also a corresponding and since 1932 honorary member of the then Soviet Academy of Sciences .

For a long time Landau did not take the threat posed by the National Socialists seriously. When his friend Fritz Rathenau, a cousin of Walther Rathenau , told him about plans for concentration camps for Jews in 1923, he said that in this case he would secure a room with a balcony and a view to the south. In 1933 he was boycotted by National Socialist students (led by Oswald Teichmüller ) and in 1934 he was given early retirement as a result of the law to restore the civil service . Until his death he only taught sporadically in Brussels and Cambridge .

Landau's students included Harald Bohr , Dunham Jackson , Paul Bernays , Detlef Cauer , Werner Schmeidler , Adolf Hammerstein , Alexander Ostrowski , Carl Ludwig Siegel , Gustav Doetsch , Erich Kamke , Werner Rogosinski , Arnold Walfisz and Hans Heilbronn .

Personality and scientific work

Landau was considered a very committed and good teacher. He was known for making the highest demands on himself and his students. His books were written in a dry, laconic style (“Landau style”), which, however, was not devoid of humor. Landau was the personification of a “pure” mathematician who sniffed at all applied mathematics . Even geometry was considered too applied to him, so he excluded it from his work area. His main area of ​​work was analytical number theory . Among other things, he succeeded in simplifying the existing proofs of the prime number theorem and generalizing it to algebraic number fields. Landau's lectures and publications were works of art of mathematically concise and exact argumentation (in the manner of “sentence:… proof:…, sentence:… proof:…”), which left out any form of explanation and explanation of motivation. This was especially true of his foundations of analysis . However, this did not make it easy for its listeners and readers to understand. When Hilbert found out about Landau's death in 1938, he is said to have said with regard to this rigor and precision : "He was the most dutiful of us all".

His books on number theory, especially the theory of the distribution of prime numbers (1909), were considered standard works.

As a representative of the "pure mathematics" Landau, however, was increasingly isolated in Göttingen's faculty, after his colleagues (in particular Hilbert, Courant , Born increasingly for mathematical problems in) theoretical physics , particularly in quantum physics and relativity became interested .

Landau was not considered a simple personality. His considerable self-confidence was often perceived by others as arrogance. After receiving doctoral theses from the institute of Ludwig Prandtl , at least a world-famous fluid mechanic and aerodynamicist , from then on he referred to such work, which dealt with questions of application, only ironically and disrespectfully as "lubricating oil" and the associated Science as "lubricating oil mathematics".

On the doctoral thesis of Maria-Pia Geppert , which appeared in the Mathematische Zeitschrift in 1932 , he wrote a critical article the following year, which consists of more than twenty comments on her work. On the other hand, Landau praised non-strict proof attempts by other mathematicians and developed them further, for example the work of Ernst Pfeiffer and Adolf Piltz .

Landau problems

In his lecture given at the 1912 International Congress of Mathematicians in Cambridge, Landau listed four conjectures from the theory of prime numbers, formulated as "questions with precise wording", which in his view were not open to attack given the then state of mathematical science and which are still unsolved, known today as the Landau problems:

(1) "Does the function for integer numbers represent infinitely many prime numbers?" ${\displaystyle u^{2}+1}$ ${\displaystyle u}$

(2) "Does the equation have a solution in the prime numbers for each ?" ( Goldbach's conjecture ) ${\displaystyle m=p+p'}$ ${\displaystyle m>2}$

(3) "Does the equation have infinitely many solutions in prime numbers?" ( Prime number twin conjecture ) ${\displaystyle 2=p-p'}$

(4) "Is there at least one prime number between and for all positive integers ?" ( Legendre's conjecture ) ${\displaystyle n^{2}}$ ${\displaystyle (n+1)^{2}}$ ${\displaystyle n}$

See also

• Landau symbols
• Landau's constant

Fonts

• Collected Works. 9 volumes. Thales, Essen from 1979 (editor L. Mirsky et al.)
• New proof of the equation ${\displaystyle \textstyle \sum \limits _{k=1}^{\infty }{\frac {\mu (k)}{k}}\,=\,0}$ , Berlin 1899 (inaugural dissertation; is the Möbius function ; with a Latin curriculum vitae until 1899; at the GDZ ; in the Internet archive ). ${\displaystyle \mu }$
• Handbook of the doctrine of the distribution of prime numbers. 2 volumes. Teubner, Leipzig 1909 (with historical overview; at the University of Michigan: Volumes 1 , 2 ; in the Internet archive: Volumes 1 , 2 , 2 ), reprint New York, Chelsea Publ. 1974.
• Presentation and justification of some recent results of the function theory. Springer, Berlin 1916 ( in the internet archive ).
• Introduction to the elementary and analytical theory of algebraic numbers and ideals. Teubner, Leipzig 1918 ( in the internet archive ).
• Lectures on number theory. 3 volumes. Hirzel, Leipzig 1927 ( English review ), Reprint New York, Chelsea Publ. 1955.
• Basics of Analysis. (Calculating with whole, rational, irrational, complex numbers). Akademische Verlagsgesellschaft, Leipzig 1930 ( with Scribd ), reprint New York, Chelsea Publ. 1965 and Wissenschaftliche Buchgesellschaft, Darmstadt 1963.
• Introduction to differential and integral calculus. Noordhoff 1934 (English translation: Differential and Integral Calculus , Oxford University Press 2001).
• About some recent advances in additive number theory. Cambridge University Press, London 1937 ( English review ).
• Diophantine equations with a finite number of solutions (= university books for mathematics . Vol. 44). German Science Publishers, Berlin 1959.
• Selected treatises on grid point theory. German Science Publishers, Berlin 1962.

literature

• GH Hardy , H. Heilbronn : Edmund Landau , Journal of the London Mathematical Society 13, October 1938, pp. 302–310 (English; obituary)
• Konrad Knopp : Edmund Landau , annual report of DMV 54, 1951, pp. 55–62 (obituary)
• Helmut Rechenberg :  Landau. Edmund. In: New German Biography (NDB). Volume 13, Duncker & Humblot, Berlin 1982, ISBN 3-428-00194-X , p. 479 f. ( Digitized version ).
• Norbert Schappacher : The Mathematical Institute of the University of Göttingen 1929–1950 ( PDF file, 4.4 MB) in Heinrich Becker, Hans-Joachim Dahms, Cornelia Wegeler (eds.): The University of Göttingen under National Socialism (2nd, expanded edition ), KG Saur, Munich 1998, ISBN 3-598-10853-2 , pp. 523-551
• Edmund Landau: The master rigorist ( Memento from January 18, 2013 in the Internet Archive ) ( PDF file, 273 kB) in Eli Maor : Trigonometric delights , Princeton University Press, 1998, ISBN 0-691-05754-0 , p. 192 –197 (English)
• Edmund Landau in Sanford L. Segal: Mathematicians under the Nazis , Princeton University Press, 2003, ISBN 0-691-00451-X , pp. 454–455 (English)
• Reinhard Siegmund-Schultze : Landau and Schur - documents of a friendship until death in inhuman times , communications DMV 19, 2011, pp. 164-173

Web links

Commons : Edmund Landau  - Collection of pictures, videos and audio files

Wikiquote: Edmund Landau  - Quotes

• Literature by and about Edmund Landau in the catalog of the German National Library
• John J. O'Connor, Edmund F. Robertson :  Edmund Landau. In: MacTutor History of Mathematics archive .
• Edmund Landau in the Mathematics Genealogy Project (English)
• Historical personalities of Göttingen in mathematics. Edmund Landau - Short biography at the Georg-August-Universität Göttingen
• The Edmund Landau Minerva Center for Research in Mathematical Analysis and Related Areas - biographical information at the Hebrew University of Jerusalem, with Edmund Landau (1877–1938) and Edmund Landau and the Hebrew University , 2004 (English; with pictures)
• Spektrum .de: Edmund Landau (1877–1938) April 1, 2017

Individual evidence

1. ^ E. Landau: New proof of the equation ${\displaystyle \textstyle \sum \limits _{k=1}^{\infty }{\frac {\mu (k)}{k}}\,=\,0}$ , Inaugural dissertation Berlin, July 15, 1899
2. ↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 144.
3. ^ Sanford Segal Mathematicians under the Nazis , p. 454
4. ^ Foreign members of the Russian Academy of Sciences. Edmund Georg Hermann Landau. Russian Academy of Sciences, accessed September 28, 2015 . 
5. ^ Sanford Segal Mathematicians under the Nazis , p. 454
6. ↑ Constance Reid : Richard Courant 1888–1972. The mathematician as a contemporary . Springer-Verlag, Berlin 1979, ISBN 0-387-09177-7 , p. 33
7. ↑ Maria-Pia Geppert : Approximate representations of analytical functions given by Dirichlet series (April 1, 1931), Mathematische Zeitschrift 35, 1932, pp. 190–211
8. ↑ Edmund Landau: Comments on the M.-P. Geppert's treatise “Approximate Representations of Analytical Functions Given by Dirichlet Series” in Volume 35 of this journal, pp. 190–211 (January 13, 1933), Mathematische Zeitschrift 37, 1933, pp. 314–320
9. ↑ Cf. Eric W. Weisstein: Landau's Problems. On Mathworld - A Wolfram Web Resource.
10. ↑ Edmund Landau: Solved and unsolved problems from the theory of the prime number distribution and the Riemann zeta function. In: Annual report of the German Mathematicians Association 21 (1912), pp. 208–228, here p. 224.