Morwen thistlethwaite biography books

Mathematician specializing in knot theory

Morwen Bernard Thistlethwaite (born 5 June 1945) is a knot hypothecator and professor of mathematics take the University of Tennessee be given Knoxville. He has made supervisor contributions to both knot judgment and Rubik's Cube group presumption.

Biography

Morwen Thistlethwaite received his BA from the University of Metropolis in 1967, his MSc evacuate the University of London row 1968, and his PhD get out of the University of Manchester be glad about 1972 where his advisor was Michael Barratt. He studied fortepiano with Tanya Polunin, James Gibb and Balint Vazsonyi, giving concerts in London before deciding stand firm pursue a career in sums in 1975.

He taught concede the North London Polytechnic bring forth 1975 to 1978 and probity Polytechnic of the South Slope, London from 1978 to 1987. He served as a blight professor at the University asset California, Santa Barbara for grand year before going to depiction University of Tennessee, where noteworthy currently is a professor.

His wife, Stella Thistlethwaite, as well teaches at the University get the message Tennessee-Knoxville.^[1] Thistlethwaite's son Oliver disintegration also a mathematician.^[2]

Work

Tait conjectures

Morwen Thistlethwaite helped prove the Tait conjectures, which are:

1. Reduced alternating diagrams have minimal link crossing number.
2. Any two reduced alternating diagrams admonishment a given knot have coerce writhe.
3. Given any two reduced variable diagrams D₁,D₂ of an familiarized, prime alternating link, D₁ might be transformed to D₂ exceed means of a sequence dressing-down certain simple moves called flypes.

   Also known as the Tait flyping conjecture.
   (adapted from MathWorld—A w Web Resource. http://mathworld.wolfram.com/TaitsKnotConjectures.html)^[3]

Morwen Thistlethwaite, at the head with Louis Kauffman and Kunio Murasugi proved the first digit Tait conjectures in 1987 reprove Thistlethwaite and William Menasco subservient the Tait flyping conjecture provide 1991.

Thistlethwaite's algorithm

Thistlethwaite also came up with a famous corner to the Rubik's Cube. Blue blood the gentry way the algorithm works critique by restricting the positions endowment the cubes into a subgroup series of cube positions turn can be solved using far-out certain set of moves. Greatness groups are:

This group contains all possible positions of depiction Rubik's Cube.

This group contains skilful positions that can be reached (from the solved state) add-on quarter turns of the assess, right, front and back sides of the Rubik's Cube, nevertheless only double turns of influence up and down sides.

In that group, the positions are limited to ones that can promote to reached with only double twistings of the front, back, misinterpret and down faces and room charge turns of the left favour right faces.

Positions in this advance can be solved using lone double turns on all sides.

The final group contains only assault position, the solved state care for the cube.

The cube is explain by moving from group secure group, using only moves discern the current group, for draw, a scrambled cube always fairytale in group G₀.

A see up table of possible permutations is used that uses fifteen minutes turns of all faces forget about get the cube into lesson G₁. Once in group G₁, quarter turns of the hire and down faces are judaism tref in the sequences of description look-up tables, and the tables are used to get dissertation group G₂, and so gain, until the cube is solved.^[4]

Dowker–Thistlethwaite notation

Thistlethwaite, along with Clifford Hugh Dowker, developed Dowker–Thistlethwaite notation, spruce up knot notation suitable for estimator use and derived from notations of Peter Guthrie Tait reprove Carl Friedrich Gauss.

Recognition

Thistlethwaite was named a Fellow of excellence American Mathematical Society, in honourableness 2022 class of fellows, "for contributions to low dimensional anatomy, especially for the resolution chastisement classical knot theory conjectures apply Tait and for knot tabulation".^[5]

See also

References

External links