Lothar Collatz

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Lothar Collatz
Lothar Collatz (Photo courtesy MFO)
Born(1910-07-06)July 6, 1910
DiedSeptember 26, 1990(1990-09-26) (aged 80)
Scientific career
Doctoral advisorAlfred Klose
Erhard Schmidt
Doctoral studentsFrank Natterer
Heinz Unger [de]

Lothar Collatz (German: [ˈkɔlaʦ]; 6 July, 1910 – 26 September 1990) was a German mathematician. He was born in Arnsberg, Westphalia. The "3x + 1" problem also known as the Collatz conjecture was named after him, and is still not solved. The Collatz–Wielandt formula for the Perron–Frobenius theorem was also named after him. His 1957 paper with Ulrich Sinogowitz,[1] who was killed in the bombing of Darmstadt in World War II,[2] started the field of spectral graph theory.

Biography[change | change source]

Collatz studied at universities in Germany, including the University of Berlin under Alfred Klose. He received his doctorate in 1935 for writing a paper about linear differential equations. He worked as an assistant for the university. Then, he worked at the Technical University of Karlsruhe in 1935. He habilitated (achieved the highest university degree in European countries) in 1937. He worked as a Privatdozent (sign of position given to special students in Europe) from 1938 to 1943. He worked with Alwin Walther at the Institute for Practical Mathematics. Collatz worked at the University of Hamburg from 1952 until 1978. There, he created the Institute of Applied Mathematics. After leaving his job, he continued to be active.[3]

Honors[change | change source]

For his work in mathematics, Collatz earned honors, such as:

Death[change | change source]

He died without knowledge from a heart attack in Varna, Bulgaria, while in a mathematics conference.[4]

Works[change | change source]

  • Das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen (= Schriften des mathematischen Seminars und des Instituts für angewandte Mathematik der Universität Berlin – Band 3/Heft 1), Leipzig 1935
  • Eigenwertprobleme und ihre numerische Behandlung. Leipzig 1945
  • Eigenwertaufgaben mit technischen Anwendungen. Leipzig 1949, 1963
  • Numerische Behandlung von Differentialgleichungen. Berlin 1951,[5] 1955[6]
  • Differentialgleichungen für Ingenieure. Stuttgart 1960
  • with Wolfgang Wetterling: Optimierungsaufgaben Berlin 1966, 1971 (Eng. trans. 1975)
  • Funktionalanalysis und Numerische Mathematik. Berlin 1964
  • Differentialgleichungen. Eine Einführung unter besonderer Berücksichtigung der Anwendungen. Stuttgart, Teubner Verlag, 1966, 7th edn. 1990
  • with Julius Albrecht: Aufgaben aus der angewandten Mathematik I. Gleichungen in einer und mehreren Variablen. Approximationen. Berlin 1972
  • ''Numerische Methoden der Approximationstheorie. vol. 2. Vortragsauszüge der Tagung über Numerische Methoden der Approximationstheorie vom 3.-9. Juni 1973 im Mathematischen Forschungsinstitut Oberwolfach, Stuttgart 1975
  • Approximationstheorie: Tschebyscheffsche Approximation und Anwendungen. Teubner 1973

References[change | change source]

  1. Von Collatz, L. and Sinogowitz, U., 1957, December. Spektren endlicher Grafen. In Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg (vol. 21, no. 1, pp. 63–77). Springer-Verlag.
  2. Mallion, R.B., 2005. An autobiographical account of chemical graph theory in the years surrounding the launch of MATCH: An Oxford participant's highly personal and parochial reminiscence about the period 1969–1976. Match-Communications In Mathematical And In Computer Chemistry, 53(1), pp. 15–52.
  3. Webmaster, Dept Mathematik (2019-08-22). "Homepage Lothar Collatz (ug)". www.math.uni-hamburg.de (in German). Retrieved 2019-09-16.
  4. Meinardus, Günter; Nürnberger, Günther. "PII: 0021-9045(91)90108-M" (PDF). math.techniion.ac.li. Archived from the original (PDF) on 3 November 2021. Retrieved 15 October 2022.
  5. Milne, William Edmund (1953). "Review: Numerische Behandlung von Differentialgleichungen, by L. Collatz, 1951". Bull. Amer. Math. Soc. 59 (1): 94–96. doi:10.1090/s0002-9904-1953-09668-9.
  6. Milne, William Edmund (1956). "Review: Numerische Behandlung von Differentialgleichungen, by L. Collatz, 1955". Bull. Amer. Math. Soc. 62 (1): 74. doi:10.1090/s0002-9904-1956-09990-2.