Clifford Hugh Dowker
Encyclopedia
Clifford Hugh Dowker was a topologist known for his work in point-set topology and also for his contributions in category theory
, sheaf theory and knot theory
.
, Canada
. He excelled in mathematics
and was paid to teach his math teacher math at his secondary school. He was awarded a scholarship at Western Ontario University, where he got his B.S. in 1933. He wanted to pursue a career as a teacher, but he was persuaded to continue with his education because of his extraordinary mathematical talent. He earned his Ph.D.
from Princeton University
in 1938. After earning his doctorate, he became an instructor at the Western Ontario University for a year. The next year, he worked as an assistant back at Princeton under John von Neumann
. During World War II
, he worked for the U.S. Air Force, calculating the trajectories of projectiles. He married Yael Naim in 1944. After the war, he was appointed associate professor at the Tufts University
. Because of Senator Joseph McCarthy
's red scare
, he decided to take his family to England
shortly thereafter, where he was appointed Reader in applied mathematics at Birkbeck University in 1951. In 1962 he was granted a personal chair, until he retired in 1979. The last years of his life were marked by a long illness, yet he continued working, developing Dowker notation
in the weeks before his death. Although a mathematical genius, he remained modest, with a gentle humor, to the end of his days.
and Vietoris
homology
groups coincide, as do the Čech cohomology
and Alexander cohomology groups.
Dowker, along with Morwen Thistlethwaite
, developed Dowker notation
, a simple way of describing knots, suitable for computers.
Dowker conjectured that Dowker space
s could not exist, a conjecture ultimately proven false.
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
, sheaf theory and knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
.
Biography
Clifford Hugh Dowker was brought up on a small farm in Western OntarioOntario
Ontario is a province of Canada, located in east-central Canada. It is Canada's most populous province and second largest in total area. It is home to the nation's most populous city, Toronto, and the nation's capital, Ottawa....
, Canada
Canada
Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...
. He excelled in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and was paid to teach his math teacher math at his secondary school. He was awarded a scholarship at Western Ontario University, where he got his B.S. in 1933. He wanted to pursue a career as a teacher, but he was persuaded to continue with his education because of his extraordinary mathematical talent. He earned his Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
from Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
in 1938. After earning his doctorate, he became an instructor at the Western Ontario University for a year. The next year, he worked as an assistant back at Princeton under John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...
. During World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, he worked for the U.S. Air Force, calculating the trajectories of projectiles. He married Yael Naim in 1944. After the war, he was appointed associate professor at the Tufts University
Tufts University
Tufts University is a private research university located in Medford/Somerville, near Boston, Massachusetts. It is organized into ten schools, including two undergraduate programs and eight graduate divisions, on four campuses in Massachusetts and on the eastern border of France...
. Because of Senator Joseph McCarthy
Joseph McCarthy
Joseph Raymond "Joe" McCarthy was an American politician who served as a Republican U.S. Senator from the state of Wisconsin from 1947 until his death in 1957...
's red scare
Red Scare
Durrell Blackwell Durrell Blackwell The term Red Scare denotes two distinct periods of strong Anti-Communism in the United States: the First Red Scare, from 1919 to 1920, and the Second Red Scare, from 1947 to 1957. The First Red Scare was about worker revolution and...
, he decided to take his family to England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
shortly thereafter, where he was appointed Reader in applied mathematics at Birkbeck University in 1951. In 1962 he was granted a personal chair, until he retired in 1979. The last years of his life were marked by a long illness, yet he continued working, developing Dowker notation
Dowker notation
thumb|200px|A knot diagram with crossings labelled for a Dowker sequenceIn the mathematical field of knot theory, the Dowker notation, also called the Dowker–Thistlethwaite notation or code, for a knot is a sequence of even integers. The notation is named after Clifford Hugh Dowker and...
in the weeks before his death. Although a mathematical genius, he remained modest, with a gentle humor, to the end of his days.
Work
Dowker showed that ČechEduard Cech
Eduard Čech was a Czech mathematician born in Stračov, Bohemia . His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin...
and Vietoris
Vietoris
Vietoris may refer to*Christian Vietoris, a German racing driver*Leopold Vietoris, an Austrian mathematician...
homology
Homology theory
In mathematics, homology theory is the axiomatic study of the intuitive geometric idea of homology of cycles on topological spaces. It can be broadly defined as the study of homology theories on topological spaces.-The general idea:...
groups coincide, as do the Čech cohomology
Cech cohomology
In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech.-Motivation:...
and Alexander cohomology groups.
Dowker, along with Morwen Thistlethwaite
Morwen Thistlethwaite
Morwen B. Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to both knot theory, and Rubik's cube group theory.-Biography:...
, developed Dowker notation
Dowker notation
thumb|200px|A knot diagram with crossings labelled for a Dowker sequenceIn the mathematical field of knot theory, the Dowker notation, also called the Dowker–Thistlethwaite notation or code, for a knot is a sequence of even integers. The notation is named after Clifford Hugh Dowker and...
, a simple way of describing knots, suitable for computers.
Dowker conjectured that Dowker space
Dowker space
A Dowker space is a topological space that is T4 but not countably paracompact.-Equivalences:If X is a normal T1 space , then the following are equivalent:* X is a Dowker space...
s could not exist, a conjecture ultimately proven false.
See also
- Dowker notationDowker notationthumb|200px|A knot diagram with crossings labelled for a Dowker sequenceIn the mathematical field of knot theory, the Dowker notation, also called the Dowker–Thistlethwaite notation or code, for a knot is a sequence of even integers. The notation is named after Clifford Hugh Dowker and...
- Dowker spaceDowker spaceA Dowker space is a topological space that is T4 but not countably paracompact.-Equivalences:If X is a normal T1 space , then the following are equivalent:* X is a Dowker space...
- Čech cohomologyCech cohomologyIn mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech.-Motivation:...
- Morwen ThistlethwaiteMorwen ThistlethwaiteMorwen B. Thistlethwaite is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville. He has made important contributions to both knot theory, and Rubik's cube group theory.-Biography:...
- Sheaf theory