Lothar Collatz

**Lothar Collatz** (; 6 July, 1910 – 26 September 1990) was a German mathematician. He was born in Arnsberg, Westphalia. The "3_x_ + 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, who was killed in the bombing of Darmstadt in World War II, started the field of spectral graph theory.

## Biography

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.

### Honors

For his work in mathematics, Collatz earned honors, such as:
- being elected to the Academy of Sciences Leopoldina, the Academy of Sciences of the Institute of Bologna and the Academy of Modena in Italy.
- becoming an honorary member of the Hamburg Mathematical Society
- getting honorary degrees from the University of São Paulo, the Technical University of Vienna, the University of Dundee in Scotland, Brunel University in England, the Leibniz University Hannover in 1981, and the Technical University of Dresden.

### Death

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

## 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, 1955
- _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

## Infobox (scientist)

- **name**: Lothar Collatz
- **image**: Lothar Collatz.jpg
- **caption**: Lothar Collatz (Photo courtesy MFO)
- **birth place**: Arnsberg, Province of Westphalia, Westphalia, German Empire
- **death place**: Varna, Bulgaria, Varna, People's Republic of Bulgaria, Bulgaria
- **nationality**: German
- **field**: Mathematics
- **doctoral advisor**: Alfred Klose (mathematician), Alfred Klose
Erhard Schmidt
- **doctoral students**: Frank Natterer