Lothar Collatz Explained

Lothar Collatz
Birth Date:	July 6, 1910
Birth Place:	Arnsberg, Westphalia, German Empire
Death Place:	Varna, Bulgaria
Nationality:	German
Known For:	Collatz conjecture Collatz–Wielandt formula Spectral graph theory
Education:	University of Greifswald University of Berlin
Doctoral Advisor:	Alfred Klose Erhard Schmidt
Workplaces:	University of Berlin Technische Hochschule Karlsruhe Technische Universität Darmstadt Technische Hochschule Hannover University of Hamburg
Doctoral Students:	Frank Natterer

Lothar Collatz (pronounced as /de/; July 6, 1910 – September 26, 1990) was a German mathematician, born in Arnsberg, Westphalia.

The "3x + 1" problem is also known as the Collatz conjecture, named after him and still unsolved. The Collatz–Wielandt formula for the Perron–Frobenius eigenvalue of a positive square matrix was also named after him.

Collatz's 1957 paper with Ulrich Sinogowitz,^[1] who had been killed in the bombing of Darmstadt in World War II,^[2] founded the field of spectral graph theory.

Biography

Collatz studied at universities in Germany including the University of Greifswald and the University of Berlin, where he was supervised by Alfred Klose, receiving his doctorate in 1935 for a dissertation entitled Das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen (The finite difference method with higher approximation for linear differential equations). He then worked as an assistant at the University of Berlin, before moving to the Technische Hochschule Karlsruhe (now Karlsruhe Institute of Technology) in 1935 where he remained through 1937. From 1938 to 1943, he worked as a Privatdozent in Karlsruhe. In the war years he worked with Alwin Walther at the Institute for Practical Mathematics of the Technische Hochschule Darmstadt.^[3]

From 1943 to 1952, Collatz held a chair at the Technische Hochschule Hannover (now Leibniz University Hanover) . From 1952 until his retirement in 1978, Collatz worked at the University of Hamburg, where he founded the Institute of Applied Mathematics in 1953. After retirement as professor emeritus, he continued to be very active at mathematical conferences.

For his many contributions to the field, Collatz had many honors bestowed upon him in his lifetime, including:

• election to the Academy of Sciences Leopoldina, the Academy of Sciences of the Institute of Bologna, and the Academy at Modena in Italy
• honorary member of the Hamburg Mathematical Society
• honorary degrees from the University of São Paulo, the Vienna University of Technology, the University of Dundee in Scotland, Brunel University in England, the University of Hannover in 1981, and the Technische Universität Dresden.

He died unexpectedly from a heart attack in Varna, Bulgaria, while attending a mathematics conference.^[4]

Selected works

• 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] (Eng. trans. 1966)
• 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

Sources

• Lothar Collatz (July 6, 1910 – September 26, 1990), Journal of Approximation Theory, vol. 65, issue 1, April 1991, page II by Günter Meinardus and Günther Nürnberger

Further reading

• J Albrecht, P Hagedorn and W Velte, Lothar Collatz (German), Numerical treatment of eigenvalue problems, vol. 5, Oberwolfach, 1990 (Birkhäuser, Basel, 1991), viii–ix.
• I Althoefer, Lothar Collatz zwischen 1933 und 1950 - Eine Teilbiographie (German), 3-Hirn-Verlag, Lage (Lippe), 2019.
• R Ansorge, Lothar Collatz (6 July 1910 – 26 September 1990) (German), Mitt. Ges. Angew. Math. Mech. No. 1 (1991), 4–9.
• U Eckhardt, Der Einfluss von Lothar Collatz auf die angewandte Mathematik, Numerical mathematics, Sympos., Inst. Appl. Math., Univ. Hamburg, Hamburg, 1979 (Birkhäuser, Basel-Boston, Mass., 1979), 9–23.
• L Elsner and K P Hadeler, Lothar Collatz on the occasion of his 75th birthday, Linear Algebra Appl. 68 (1985), vi; 1–8.
• R B Guenther, Obituary : Lothar Collatz, 1910–1990, Aequationes Mathematicae 43 (2–3) (1992), 117–119.
• H Heinrich, Zum siebzigsten Geburtstag von Lothar Collatz, Z. Angew. Math. Mech. 60 (5) (1980), 274–275.
• G Meinardus, G Nürnberger, Th Riessinger and G Walz, In memoriam : the work of Lothar Collatz in approximation theory, J. Approx. Theory 67 (2) (1991), 119–128.
• G Meinardus and G Nürnberger, In memoriam : Lothar Collatz (July 6, 1910 – September 26, 1990), J. Approx. Theory 65 (1) (1991), i; 1–2.
• J R Whiteman, In memoriam : Lothar Collatz, Internat. J. Numer. Methods Engrg. 31 (8) (1991), 1475–1476.

Notes and References

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. Web site: Homepage Lothar Collatz (ug). Webmaster. Dept Mathematik. 2019-08-22. www.math.uni-hamburg.de. de. 2019-09-16.
4. Web site: Meinardus. Günter. Nürnberger. Günther. PII: 0021-9045(91)90108-M . 15 October 2022 . math.techniion.ac.li.
5. Milne, William Edmund. Review: Numerische Behandlung von Differentialgleichungen, by L. Collatz, 1951. Bull. Amer. Math. Soc.. 1953. 59. 1. 94–96. 10.1090/s0002-9904-1953-09668-9. free.
6. Milne, William Edmund. Review: Numerische Behandlung von Differentialgleichungen, by L. Collatz, 1955. Bull. Amer. Math. Soc.. 1956. 62. 1. 74. 10.1090/s0002-9904-1956-09990-2. free.