Lothar Collatz

{{Infobox scientist

|name = Lothar Collatz

|image = Lothar Collatz.jpg

|caption = Lothar Collatz (Photo courtesy MFO)

|birth_date = {{birth date |1910|07|06 |mf=yes}}

|birth_place = Arnsberg, Westphalia, German Empire

|death_date = {{death date and age |1990|09|26 |1910|07|06 |mf=yes}}

|death_place = Varna, Bulgaria

|nationality = German

|field = Mathematics

|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
{{ill|Heinz Unger (mathematician)|lt=Heinz Unger|de|Heinz Unger (Mathematiker)}}

}}

Lothar Collatz ({{IPA|de|ˈkɔlaʦ|lang}}; 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,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. who had been killed in the bombing of Darmstadt in World War II,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. 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.{{Cite web|url=https://www.math.uni-hamburg.de/home/collatz/|title=Homepage Lothar Collatz (ug)|last=Webmaster|first=Dept Mathematik|date=2019-08-22|website=www.math.uni-hamburg.de|language=de|access-date=2019-09-16}}

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.{{Cite web|last1=Meinardus|first1=Günter|last2=Nürnberger|first2=Günther|title=PII: 0021-9045(91)90108-M |url=https://www.math.technion.ac.il/hat/people/obits/collatz.pdf|access-date=15 October 2022 |website=math.techniion.ac.li}}

Selected works

File:Lothar Collatz 1984.jpg

Das Differenzenverfahren mit höherer Approximation für lineare Differentialgleichungen (= Schriften des mathematischen Seminars und des Instituts für angewandte Mathematik der Universität Berlin{{snd}} 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,{{cite journal|author=Milne, William Edmund|title=Review: Numerische Behandlung von Differentialgleichungen, by L. Collatz, 1951|journal=Bull. Amer. Math. Soc.|year=1953|volume=59|issue=1|pages=94–96|url=https://www.ams.org/journals/bull/1953-59-01/S0002-9904-1953-09668-9/|doi=10.1090/s0002-9904-1953-09668-9|doi-access=free}} 1955{{cite journal|author=Milne, William Edmund|title=Review: Numerische Behandlung von Differentialgleichungen, by L. Collatz, 1955|journal=Bull. Amer. Math. Soc.|year=1956|volume=62|issue=1|page=74|url=https://www.ams.org/journals/bull/1956-62-01/S0002-9904-1956-09990-2/|doi=10.1090/s0002-9904-1956-09990-2|doi-access=free}} (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

References

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
{{citation|first=Lothar |last= Collatz| author-link = Lothar Collatz|title=Einschließungssatz für die charakteristischen Zahlen von Matrizen

|journal= Mathematische Zeitschrift |year=1942|pages=221–226

|doi = 10.1007/BF01180013| volume = 48 | issue =1 |s2cid= 120958677}}