Morwen Bernard Thistlethwaite is a knot theorist and professor of mathematics for the

University of Tennessee The University of Tennessee (officially The University of Tennessee, Knoxville; or UT Knoxville; UTK; or UT) is a public land-grant research university in Knoxville, Tennessee. Founded in 1794, two years before Tennessee became the 16th state, ...

Knoxville Knoxville is a city in and the county seat of Knox County in the U.S. state of Tennessee. As of the 2020 United States census, Knoxville's population was 190,740, making it the largest city in the East Tennessee Grand Division and the state's ...

. He has made important contributions to both

knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

and

Rubik's Cube group The Rubik's Cube group is a Group (mathematics), group (G, \cdot ) that represents the Mathematical structure, structure of the Rubik's Cube mechanical puzzle. Each element of the Set (mathematics), set G corresponds to a cube move, which is the ...

theory.

Biography

Morwen Thistlethwaite received his BA from the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

in 1967, his MSc from the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degree ...

in 1968, and his PhD from the

University of Manchester , mottoeng = Knowledge, Wisdom, Humanity , established = 2004 – University of Manchester Predecessor institutions: 1956 – UMIST (as university college; university 1994) 1904 – Victoria University of Manchester 1880 – Victoria Univer ...

in 1972 where his advisor was Michael Barratt. He studied

piano The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...

with Tanya Polunin, James Gibb and

Balint Vazsonyi Balint Vázsonyi (7 March 193617 January 2003) was a Hungarian-born naturalized American pianist, educator, international recitalist/soloist with leading orchestras, and political activist and journalist. He made performance history in playing c ...

, giving concerts in London before deciding to pursue a career in mathematics in 1975. He taught at the

North London Polytechnic The University of North London (UNL) was a university in London, England, formed from the Polytechnic of North London (PNL) in 1992 when that institution was granted university status. PNL, in turn, had been formed by the amalgamation of the No ...

from 1975 to 1978 and the Polytechnic of the South Bank, London from 1978 to 1987. He served as a visiting professor at the

University of California, Santa Barbara The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, Santa Barbara, California with 23,196 undergraduate ...

for a year before going to the

, where he currently is a professor. His wife, Stella Thistlethwaite, also teaches at the University of Tennessee-Knoxville. Thistlethwaite's son Oliver is also a mathematician.

Work

Tait conjectures

Morwen Thistlethwaite helped prove the

Tait conjectures The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots.. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conje ...

, which are: #Reduced alternating diagrams have minimal link crossing number. #Any two reduced alternating diagrams of a given

knot A knot is an intentional complication in cordage which may be practical or decorative, or both. Practical knots are classified by function, including hitches, bends, loop knots, and splices: a ''hitch'' fastens a rope to another object; a ' ...

have equal

writhe In knot theory, there are several competing notions of the quantity writhe, or \operatorname. In one sense, it is purely a property of an oriented link diagram and assumes integer values. In another sense, it is a quantity that describes the amou ...

. #Given any two reduced alternating diagrams D₁,D₂ of an oriented, prime alternating link, D₁ may be transformed to D₂ by means of a sequence of certain simple moves called ''

flype In the mathematical theory of knots, a flype is a kind of manipulation of knot and link diagrams used in the Tait flyping conjecture. It consists of twisting a part of a knot, a tangle T, by 180 degrees. Flype comes from a Scots word meaning '' ...

s''. Also known as the

Tait flyping conjecture The Tait conjectures are three conjectures made by 19th-century mathematician Peter Guthrie Tait in his study of knots.. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the Tait conje ...

.
(adapted from MathWorld—A Wolfram Web Resource. http://mathworld.wolfram.com/TaitsKnotConjectures.html) Morwen Thistlethwaite, along with

Louis Kauffman Louis Hirsch Kauffman (born February 3, 1945) is an American mathematician, topologist, and professor of mathematics in the Department of Mathematics, Statistics, and Computer science at the University of Illinois at Chicago. He is known for the ...

and

Kunio Murasugi Kunio (written: 邦夫, 邦男, 邦雄, 邦生, 國男, 國士, 国男, 国夫, 州男 or 久仁生) is a masculine Japanese given name. Notable people with the name include: *, Japanese businessman *, Japanese businessman *, Japanese judge *, Jap ...

proved the first two Tait conjectures in 1987 and Thistlethwaite and

William Menasco William W. Menasco is a topologist and a professor at the University at Buffalo. He is best known for his work in knot theory. Biography Menasco received his B.A. from the University of California, Los Angeles in 1975, and his Ph.D. from the Unive ...

proved the

in 1991.

Thistlethwaite's algorithm

Thistlethwaite also came up with a famous solution to the

Rubik's Cube The Rubik's Cube is a Three-dimensional space, 3-D combination puzzle originally invented in 1974 by Hungarians, Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik t ...

. The way the algorithm works is by restricting the positions of the cubes into

groups A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic iden ...

of cube positions that can be solved using a certain set of moves. The groups are: *

G_0=\langle L,R,F,B,U,D\rangle

:This group contains all possible positions of the Rubik's Cube. *

G_1=\langle L,R,F,B,U^2,D^2\rangle

:This group contains all positions that can be reached (from the solved state) with quarter turns of the left, right, front and back sides of the Rubik's Cube, but only double turns of the up and down sides. *

G_2=\langle L,R,F^2,B^2,U^2,D^2\rangle

:In this group, the positions are restricted to ones that can be reached with only double turns of the front, back, up and down faces and quarter turns of the left and right faces. *

G_3=\langle L^2,R^2,F^2,B^2,U^2,D^2\rangle

:Positions in this group can be solved using only double turns on all sides. *

G_4=\

:The final group contains only one position, the solved state of the cube. The cube is solved by moving from group to group, using only moves in the current group, for example, a scrambled cube always lies in group G₀. A look up table of possible permutations is used that uses quarter turns of all faces to get the cube into group G₁. Once in group G₁, quarter turns of the up and down faces are disallowed in the sequences of the look-up tables, and the tables are used to get to group G₂, and so on, until the cube is solved.

Dowker notation

Thistlethwaite, along with

Clifford Hugh Dowker Clifford Hugh Dowker (; March 2, 1912 – October 14, 1982) was a topologist known for his work in point-set topology and also for his contributions in category theory, sheaf theory and knot theory. Biography Clifford Hugh Dowker grew up on a sm ...

, developed

Dowker notation Dowker is a surname. Notable people with the surname include: * Clifford Hugh Dowker (1912–1982), Canadian mathematician * Fay Dowker (born 1965), British physicist *Felicity Dowker, Australian fantasy writer * Hasted Dowker (1900–1986), Canadi ...

, a

notation suitable for computer use and derived from notations of

Peter Guthrie Tait Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook '' Treatise on Natural Philosophy'', which he co-wrote wi ...

and

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

Recognition

Thistlethwaite was named a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, in the 2022 class of fellows, "for contributions to low dimensional topology, especially for the resolution of classical knot theory conjectures of Tait and for knot tabulation".

References

External links

* http://www.math.utk.edu/~morwen/ - Morwen Thistlethwaite's home page. * {{DEFAULTSORT:Thistlethwaite, Morwen Year of birth missing (living people) Living people Topologists Academics of London South Bank University University of Tennessee faculty Alumni of the University of Cambridge Alumni of the University of London Alumni of the University of Manchester 20th-century British mathematicians 21st-century British mathematicians Rubik's Cube Fellows of the American Mathematical Society