# Walter Feit

### Quick Info

Vienna, Austria

Branford, Connecticut, USA

**Walter Feit**was an Austrian mathematician who (with John Thompson) proved one of the most important theorems about finite simple groups.

### Biography

**Walter Feit**'s parents were Paul and Esther Feit. Esther had lived in Vienna from the age of one year, but Paul had only moved there when he married Esther. Paul was well educated and spoke several languages, but in Vienna he ran a shop selling soap, perfume and other such items. The shop was on Molkerei Strasse, and the family had an appartment above the shop.

In March 1938 German troops marched into Austria. Feit's family were Jewish and this turn of events proved disasterous for them. Feit wrote [4]:-

When the Germans came the business more or less evaporated. We were lucky on Krystalnacht as my father hadn't bothered to open that day.Krystalnacht was the night of 9 November 1938 when anti-Jewish violence, organised by the Nazis, broke out across the whole of Germany and Austria. Synagogues were destroyed, and businesses owned by Jews were severely damaged. After this all Jewish families understood the danger that they were in. However, there was no way that the whole Feit family could escape despite the fact that his father's sister Pauline Feit lived in the United States and tried to encourage them to come to live with her in Miami. The only option was the KinderTransport which allowed children between the ages of 5 and 17 to reach Britain as refugees. Feit wrote [4]:-

The children were to travel in sealed trains. The first transport left barely six weeks after the Kristallnacht, the last, just two days before war broke out, which put an end to the programme.Walter's parents had put him on that last train which left Vienna on one of the last days in August 1939. He was only eight years old and, on arriving in England, went to live with Frieda, a sister of his mother, who had come to London to work as a maid. Soon after he arrived the evacuation of children from London began. He then was moved to what was considered a safer area and there followed a number of moves before he finally was sent to a hostel in Oxford. Len Scott writes [2]:-

In 1943 he won a scholarship to an Oxford technical high school. His teachers were very encouraging and he recorded that it was at this time that he became "passionately interested in mathematics."Feit, speaking much later in his life, said:-

I have many vivid memories of Oxford since I spent the formative years of my life there.When the war ended, his father's sister Pauline who was married to Max and lived in Miami, Florida, in the United States made huge efforts to obtain a visa to allow Feit to come to live with them. His parents had died after being sent to a concentration camp by the Nazis. Eventually Pauline's efforts paid off and Feit was able to sail to the United States in December 1946. Leaving Southampton on 19th December, the ship docked in New York on the 29th . He wrote from New York to Aunt Frieda in London on 1st January 1947:-

Yesterday night was New Years Eve in the U.S.A. this is an important holiday so I went to the "Feit & Auster family society" banquet. There were over four hundred people present. It was a 35th Anniversary and a victory banquet given in honour of the ex-servicemen in the family. There was a relative from Canada there as well. On Monday I was outfitted for Miami; I now possess five new pairs of trousers, two new jackets plus new shoes and lots of new underwear. I have also a watch in my possession. ... I have been making inquiries about the educational system here and have been told that my maths is already past college entrance standard and that in other subjects I am good enough to enter college, except that I lack a foreign language. ... All this seems like a dream to me, what do you think about it? ...After graduating with a high school diploma in Miami he entered the University of Chicago in September 1947. Four years later, in June 1951, he was awarded both his bachelor's and master's degrees. He had developed a strong interest in group theory and was advised to go to the University of Michigan at Ann Arbor to study for his doctorate under Richard Brauer. Feit attended Brauer's seminar which was on the modular representations of finite groups and also took an informal reading course from Brauer on class field theory.

In 1951 Harvard University offered Brauer a chair and, in 1952, he took up the position in Harvard. Feit remained at the University of Michigan and Brauer continued to supervise his doctoral thesis. However, formally Feit had to have a supervisor on the Michigan faculty, so Robert Thrall took on that role. Feit graduated with a doctorate in 1955, awarded for the thesis

*Topics in the Theory of Group Characters*. Before this, however, he had accepted an instructorship at Cornell in 1953. He met Sidnie Dresher in 1954, when she was beginning her studies at Cornell. Feit was drafted into the army in 1955, and after he returned to Cornell he began to date Sidnie. They were married on his 27th birthday, the 26th October 1957. They had a son Paul, who became a professor of mathematics, and a daughter Alexandra who became an artist.

Rapid progress began to be made in the study of finite groups. John Thompson proved significant results in his thesis presented to the University of Chicago in 1959, and character theoretic results proved by Feit were seen to be relevant. Adrian Albert, chairmen of the Chicago Mathematics Department, decided to facilitate the ongoing work by organising a 'Finite Group Theory Year' in 1960-61. This brought together many leading group theorists, and in particular it provided the opportunity for Feit and Thompson to embark on the ambitious project of attempting to prove the conjecture that all groups of odd order are soluble. They achieved their aim and the result appeared in their joint 250 page paper

*Solvability of groups of odd order*published in the

*Pacific Journal of Mathematics*in 1963. Thompson writes [2]:-

I was lucky to team up with Walter. He had completed his Ph.D. with Brauer; I had studied Hall's work; we both benefited from Suzuki; and we both had the confidence to attack the odd order problem, which still looks to me like granite. I think there are only a few who understood the precision and subtlety with which Walter handled a variety of character-theoretic situations. Suzuki and, of course, Brauer appreciated Walter's strength. But only Walter and I knew just how intertwined our thinking was over a period of more than a year. There was a false dawn of a few days when we thought the thing was done. Walter then discovered that there was one case that our techniques did not cover, and he told me of this.Solomon, in [3], describes the odd order paper as:-

If Walter had not found the gap, I almost certainly would not have found it; we would have submitted a flawed manuscript, and eventually someone would have blown the whistle. If that had happened, it is doubtful that we could have generated a new head of steam to bust the difficulty, which in fact took us several additional months of thought and nail biting.

... a moment in the evolution of finiteIn [2] Solomon writes:-group theory analogous to the emergence of fish onto dry land.

It defined the monumental scale of the classification project for finite simple groups and threw down a gauntlet to other researchers in the field. It resolved a seemingly intractable case of the problem and offered entirely new and powerful ways of thinking about finite simple groups - ways of thinking that proved powerful enough to complete the entire project.In 1964 Feit moved to Yale University [1]:-

He served the Yale mathematics department in several administrative roles, acting as Director of Undergraduate Studies, Director of Graduate Studies, and Chairman. His standing in the mathematics community was marked by award of the American Mathematical Society Cole Prize in Algebra, election to the National Academy of Sciences and the American Academy of Arts and Sciences, editorship of various journals, and Vice-Presidency of the International Mathematical Union.We have said nothing of Feit's achievements so far, other than the odd order paper. Although he published around 100 other papers, his name will always be most closely associated with this one result, described by Zelmanov as "easily the best single theorem in group theory." However, his other contributions on finite group theory, character theory, and modular representation theory, are also impressive. Towards the end of his career he added an interest in Galois theory to this list of interests.

Let us record that Feit addressed the British Mathematical Colloquium as a plenary speaker in Swansea in 1967. I [EFR] heard him address the colloquium on

*p-adic and modular representations of finite groups*. In 1990 he again addressed the British Mathematical Colloquium, this time in East Anglia on

*The construction of Galois groups*. He addressed the International Congresses of Mathematicians in Nice in 1970 on

*The Current Situation in the Theory of Finite Simple Groups*.

In [4] it is recorded that Feit:-

... loved to travel and talk to mathematicians in far-away places. In mid-1976, Walter went to China with a delegation headed by Saunders Mac Lane. The delegation was supposed to evaluate the condition of China's mathematicians. At that time, the infamous "Gang of 4" was still in power. The Gang was deposed after Mao died in September. This allowed the delegation to write an honest report without endangering the welfare or lives of many Chinese mathematicians who had been dispersed to factories or sent to Outer Mongolia.In 1990 his 60th birthday was celebrated with an 'International Symposium on the Inverse Galois Problem' held in Oxford. His retirement from Yale in October 2003 was marked with the holding of a 'Conference on Groups, Representations and Galois Theory' in his honour. Feit died after a long illness at the Connecticut Hospice in Branford, Connecticut, USA. A memorial service was held on Sunday 10 October 2004 at the New Haven Lawn Club, New Haven, Connecticut.

Solomon writes in [2] of Feit's character:-

Walter loved conversation, and his judgments and opinions - whether mathematical, political, or culinary - were never hedged or falsely polite, but always were leavened with wit and delivered with a twinkle in his eye.Dan Mostow writes (see [2]):-

Anyone ... who ever discussed world affairs with Walter knows what a history buff he was. He knew, in detail, the history of every country, ancient or modern, as far as I could tell. So it is significant that he refrained from telling his own history to his children until begged by [his daughter] Alexandra ten years ago to relate his family history.

### References (show)

- J R Emanuel, In Memoriam: Mathematician Walter Feit, Pioneer in Finite Group Theory,
*Yale News*(30 August 2004). - L Scott, R Solomon, J Thompson, J Walter and E Zelmanov, Walter Feit (1930-2004),
*Notices Amer. Math. Soc.***52**(7) 728-735. - R Solomon, A brief history of the classification of the finite simple groups,
*Bull. Amer. Math. Soc. (N.S.)***38**(2001), 315-352. - The Walter Feit archive. (www.math.yale.edu/public_html/WalterFeit/WalterFeit.html)

### Additional Resources (show)

Other websites about Walter Feit:

### Honours (show)

Honours awarded to Walter Feit

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update July 2008

Last Update July 2008