# Max August Zorn

**Max August Zorn** (German: [tsɔʁn]; June 6, 1906 – March 9, 1993) was a German mathematician. He was an algebraist, group theorist, and numerical analyst. He is best known for Zorn's lemma, a method used in set theory that is applicable to a wide range of mathematical constructs such as vector spaces, ordered sets and the like. Zorn's lemma was first postulated by Kazimierz Kuratowski in 1922, and then independently by Zorn in 1935.

Max August Zorn | |
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Max August Zorn, Jena, 1930 | |

Born | |

Died | March 9, 1993 86) | (aged

Nationality | German |

Alma mater | University of Hamburg |

Known for | Zorn's lemma Split-octonions |

Scientific career | |

Fields | Mathematics |

Institutions | Indiana University University of California, Los Angeles |

Doctoral advisor | Emil Artin |

Doctoral students | Israel Nathan Herstein |

## Life and career

Zorn was born in Krefeld, Germany. He attended the University of Hamburg. He received his Ph.D. in April 1930 for a thesis on alternative algebras. He published his findings in *Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg*.[1][2] Zorn showed that split-octonions could be represented by a mixed-style of matrices called Zorn's vector-matrix algebra.

Max Zorn was appointed as an assistant at the University of Halle. However, he did not have the opportunity to work there for long since he was forced to leave Germany in 1933 because of the Nazi policies. According to grandson Eric, "[Max] spoke with a raspy, airy voice most of his life. Few people knew why, because he only told the story after significant prodding, but he talked that way because pro-Hitler thugs who objected to his politics, had battered his throat in a 1933 street fight."[3]

Zorn emigrated to the U.S. and was appointed a Sterling Fellow at Yale University. While at Yale, Zorn wrote his paper "A Remark on Method in Transfinite Algebra"[4] that stated his Maximum Principle, later called Zorn's lemma. It requires a set that contains the union of any chain of subsets to have one chain not contained in any other, called the maximal element. He illustrated the principle with applications in ring theory and field extensions. Zorn’s lemma is an alternative expression of the axiom of choice, and thus a subject of interest in axiomatic set theory.

In 1936 he moved to UCLA and remained until 1946. While at UCLA Zorn revisited his study of alternative rings and proved the existence of the nilradical of certain alternative rings.[5] According to Angus E. Taylor, Max was his most stimulating colleague at UCLA.[6]

In 1946 Zorn became a professor at Indiana University where he taught until retiring in 1971. He was thesis advisor for Israel Nathan Herstein.

Zorn died in Bloomington, Indiana, United States, in March 1993, of congestive heart failure, according to his obituary in *The New York Times*.[7]

## Family

Max Zorn married Alice Schlottau and they had one son, Jens, and one daughter, Liz. Jens (born June 19, 1931) is an emeritus professor of physics at the University of Michigan and an accomplished sculptor. Max Zorn's grandson Eric Zorn is a columnist for the *Chicago Tribune*.

## See also

## References

- M. Zorn (1930) "Theorie der alternativen Ringen",
*Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg*8(2): 123–47 - M. Zorn (1931) "Alternativekörper und quadratische Systeme",
*Abhandlungen aus dem mathematischen Seminar der Universität Hamburg*9(3/4): 395–402 - Eric Zorn (1993) A Math Wizard, Hero to His Family from Chicago Tribune
- Zorn, Max (1935). "A remark on method in transfinite algebra".
*Bulletin of the American Mathematical Society*.**41**(10): 667–670. doi:10.1090/S0002-9904-1935-06166-X. - M. Zorn (1941) Alternative rings and related questions I: existence of the radical, Annals of Mathematics 42: 676–86 MR0005098
- Angus E. Taylor (1984) A Life in Mathematics Remembered, American Mathematical Monthly 91(10):613.
- Saxon, Wolfgang (11 March 1993). "Max A. Zorn, 86; Developed a Theory That Changed Math".
*NY Times*.

- Steve Carlson (2009) Max Zorn: World Renowned Mathematician and Member Indiana MAA Section, from Mathematics Association of America .
- Darrell Haile (1993) On Max Zorn's Contributions to Mathematics (includes John Ewing, "Zorn's Lemma"), from Memorial Conference at Indiana University, June 1993.