W. T. Tutte

William Thomas Tutte (May 14 1917 – May 2 2002) was a British, later Canadian, codebreaker and mathematician. During World War II he broke a major German code system, which had a significant impact on the Allied invasion of Europe. He also had a number of significant mathematical accomplishments, including foundation work in the fields of combinatorics and graph theory.

Tutte was born in Newmarket in Suffolk, the son of a gardener. At age 18 he studied chemistry at Trinity College, Cambridge University. As a student he worked on the problem of squaring the square.

On the outbreak of World War II, his tutor suggested he join the Government Code and Cipher School, which he did in May 1941. Tutte worked at Bletchley Park as a codebreaker, and in a feat described as "one of the greatest intellectual featsof World War II" he was able to deduce the structure of the German Lorenz SZ 40/42 encryption machine (codenamed "Tunny"), used for high-level German Army communications, using only a number of intercepted encrypted messages. Using his breakthrough, the British constructed an entire organization (including the famed Colossus computer) to read the messages sent in this system.

In 1948, Tutte received a doctorate in mathematics from Cambridge under the supervision of Shaun Wylie, who had also worked at Bletchley Park on Tunny. From 1948-1962 he taught mathematics at the University of Toronto. A majority of his later work was done at the University of Waterloo in Waterloo, Canada, which he joined in 1962, and where he stayed until 1985. Tutte was instrumental in helping to found the [http://www.math.uwaterloo.ca/CandO_Dept/ Department of Combinatorics and Optimization] at the University of Waterloo.

His mathematical career concentrated on combinatorics, especially graph theory, which he is credited as having helped create in its modern form, and matroid theory, to which he made profound contributions; one colleague described him as "the leading mathematician in combinatorics for three decades". He was editor in chief of "The Journal of Combinatorial Theory" when it was started, and served on the editorial boards of several other mathematical research journals.

His work in graph theory includes the structure of cycle and cut spaces, size of maximum matchings and existence of "k"-factors in graphs, and Hamiltonian and non-Hamiltonian graphs. He disproved Tait's conjecture using the construction known as Tutte's fragment. The eventual proof of the four color theorem made use of his earlier work. The graph polynomial he called the "dichromate" has become famous and influential under the name "Tutte polynomial" and serves as the prototype of combinatorial invariants that are universal for all invariants that satisfy a specified reduction law.

In matroid theory he discovered the highly sophisticated homotopy theorem as well as founding the studies of chain groups and regular matroids, about which he proved deep results.

He was a Fellow of the Royal Society of London, and of the Royal Society of Canada. In October, 2001 he was inducted as an Officer of the Order of Canada.

See also

*Tutte theorem
*Tutte-Berge formula
*Tutte eight cage
*Systolic geometry

References

* Brooks, R. L.; Smith, C. A. B.; Stone, A. H.; and Tutte, W. T. "The Dissection of Rectangles into Squares." "Duke Math. J." 7, 312-340, 1940

External links

* [http://www.math.uwaterloo.ca/CandO_Dept/William_Tutte/tutte.shtml Professor William T. Tutte]
* [http://www.certicom.com/index.php?action=res,cc_1_1&article=2-tutte A Tribute to William Thomas Tutte: Mathematician and Cryptographer]
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*MathGenealogy |id=15096
*MacTutor Biography|id=Tutte
* [http://www.math.binghamton.edu/zaslav/Oldcourses/580.S04/tutte.html William Tutte, 84, Mathematician and Code-breaker, Dies] - Obituary from The New York Times
* [http://www.guardian.co.uk/obituaries/story/0,3604,712971,00.html William Tutte: Unsung mathematical mastermind] - Obituary from The Guardian
* [http://www.crm.umontreal.ca/prix/recipients.html#2001 CRM-Fields-PIMS Prize - 2001 - William T. Tutte]
* [http://frode.home.cern.ch/frode/crypto/tutte.html Tutte's paper on the Fish cipher]
* [http://www.math.niu.edu/%7Erusin/known-math/97/tutte Tutte's disproof of Tait's conjecture]