Lothar Collatz (; July 6, 1910 – September 26, 1990) was a German
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
, born in
Arnsberg
Arnsberg (; wep, Arensperg) is a town in the Hochsauerland county, in the German state of North Rhine-Westphalia. It is the location of the Regierungsbezirk Arnsberg administration and one of the three local administration offices of the Hochs ...
,
Westphalia
Westphalia (; german: Westfalen ; nds, Westfalen ) is a region of northwestern Germany and one of the three historic parts of the state of North Rhine-Westphalia. It has an area of and 7.9 million inhabitants.
The territory of the regio ...
.
The "3''x'' + 1" problem is also known as the
Collatz conjecture
The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integ ...
, 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, who had been killed in the
bombing of Darmstadt in World War II
Darmstadt was bombed a number of times during World War II. The most devastating air raid on Darmstadt occurred on the night of 11/12 September 1944 when No. 5 Group of the Royal Air Force (RAF) bombed the city. 66,000 of the 110,000 inhabitants ...
, founded the field of
spectral graph theory.
Biography
Collatz studied at universities in Germany including
University of Greifswald
The University of Greifswald (; german: Universität Greifswald), formerly also known as “Ernst-Moritz-Arndt University of Greifswald“, is a public research university located in Greifswald, Germany, in the state of Mecklenburg-Western Pom ...
and the
University of Berlin
Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...
, where he was supervised by
Alfred Klose
Wilhelm Rudolf Alfred Klose (September 19, 1895 in Görlitz – February 21, 1953 in Potsdam) was a German applied mathematician and astronomer.
Education and career
Klose studied at University of Breslau and University of Göttingen from 1916 ...
, 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
Technical University of Karlsruhe
The Karlsruhe Institute of Technology (KIT; german: Karlsruher Institut für Technologie) is a public research university in Karlsruhe, Germany. The institute is a national research center of the Helmholtz Association.
KIT was created in 2009 w ...
in 1935. There he also habilitated in 1937. From 1938 to 1943 he worked as a
Privatdozent
''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualific ...
in Karlsruhe. In the war years he worked with
Alwin Walther
Alwin Oswald Walther (born 6 May 1898 in Reick; died 4 January 1967 in Darmstadt) was a German mathematician, engineer and professor. He is one of the pioneers of mechanical computing technology in Germany.
Life
Alwin Walther was born in May ...
at the Institute for Practical Mathematics of the
Technische Hochschule Darmstadt.
From 1943 to 1952, Collatz held a chair at the
Technical University of Hannover. From 1952 until his retirement in 1978 Collatz worked at the
University of Hamburg
The University of Hamburg (german: link=no, Universität Hamburg, also referred to as UHH) is a public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('' Allgemeines Vor ...
, where he founded the Institute of Applied Mathematics in 1953. After retirement as professor
emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
he continued to be very active on 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 German National Academy of Sciences Leopoldina (german: Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften), short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded ...
, the
Academy of Sciences of the Institute of Bologna
The Academy of Sciences of the Institute of Bologna (''Accademia delle Scienze dell'Istituto di Bologna'') is an academic society in Bologna, Italy, that was founded in 1690 and prospered in the Age of Enlightenment. Today it is closely associated ...
and the Academy at Modena in Italy.
* honorary member of the
Hamburg Mathematical Society The Hamburg Mathematical Society (german: Mathematische Gesellschaft in Hamburg) is a learned society concerned with mathematics and located in the German city of Hamburg.
It was founded in 1690 by Heinrich Meissner as the "Kunstrechnungsübende S ...
* honorary degrees by the
University of São Paulo
The University of São Paulo ( pt, Universidade de São Paulo, USP) is a public university in the Brazilian state of São Paulo. It is the largest Brazilian public university and the country's most prestigious educational institution, the best ...
, the
Technical University of Vienna
TU Wien (TUW; german: Technische Universität Wien; still known in English as the Vienna University of Technology from 1975–2014) is one of the major universities in Vienna, Austria. The university finds high international and domestic recogn ...
, the
University of Dundee
The University of Dundee; . Abbreviated as ''Dund.'' for post-nominals. is a public university, public research university based in Dundee, Scotland. It was founded as a University college#United Kingdom, university college in 1881 with a donation ...
in
Scotland
Scotland (, ) is a country that is part of the United Kingdom. Covering the northern third of the island of Great Britain, mainland Scotland has a border with England to the southeast and is otherwise surrounded by the Atlantic Ocean to the ...
,
Brunel University
Brunel University London is a public research university located in the Uxbridge area of London, England. It was founded in 1966 and named after the Victorian engineer and pioneer of the Industrial Revolution, Isambard Kingdom Brunel. In June 1 ...
in England, the
Leibniz University Hannover in 1981, and the
Technical University of Dresden
TU Dresden (for german: Technische Universität Dresden, abbreviated as TUD and often wrongly translated as "Dresden University of Technology") is a public research university, the largest institute of higher education in the city of Dresden, th ...
.
He died unexpectedly from a heart attack in
Varna
Varna may refer to:
Places Europe
*Varna, Bulgaria, a city in Bulgaria
**Varna Province
**Varna Municipality
** Gulf of Varna
**Lake Varna
**Varna Necropolis
*Vahrn, or Varna, a municipality in Italy
*Varniai, a city in Lithuania
* Varna (Šaba ...
,
Bulgaria
Bulgaria (; bg, България, Bǎlgariya), officially the Republic of Bulgaria,, ) is a country in Southeast Europe. It is situated on the eastern flank of the Balkans, and is bordered by Romania to the north, Serbia and North Macedon ...
, while attending a mathematics conference.
Selected works
![Lothar Collatz 1984](https://upload.wikimedia.org/wikipedia/commons/e/e5/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 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, 1955
(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
*
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
''Aequationes Mathematicae'' is a mathematical journal. It is primarily devoted to functional equations, but also publishes papers in dynamical systems, combinatorics, and geometry. As well as publishing regular journal submissions on these topic ...
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.
External links
*
*
{{DEFAULTSORT:Collatz, Lothar
1910 births
1990 deaths
20th-century German mathematicians
People from Arnsberg
People from the Province of Westphalia
Academic staff of Technische Universität Darmstadt
Academic staff of the University of Hamburg
Academic staff of the Karlsruhe Institute of Technology
Humboldt University of Berlin alumni
Academic staff of the University of Hanover
University of Greifswald alumni
German mathematicians
Graph theorists