Octacube (mathematics)
Encyclopedia
Galois theory
In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory...
of operator algebras.
It was designed by Adrian Ocneanu, a professor of pure mathematics at Penn State
Pennsylvania State University
The Pennsylvania State University, commonly referred to as Penn State or PSU, is a public research university with campuses and facilities throughout the state of Pennsylvania, United States. Founded in 1855, the university has a threefold mission of teaching, research, and public service...
, which commissioned the sculpture. Ocneanu was also an International Mathematical Olympiad
International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...
gold medalist in 1974 by recording a perfect score for his native country, Romania.
A feature article on the sculpture appeared in the March 2006 issue of the popular journal Playboy
Playboy
Playboy is an American men's magazine that features photographs of nude women as well as journalism and fiction. It was founded in Chicago in 1953 by Hugh Hefner and his associates, and funded in part by a $1,000 loan from Hefner's mother. The magazine has grown into Playboy Enterprises, Inc., with...
.
A more complete technical explanation of the sculpture, including how it came to be made, how its construction was funded and its role 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 physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, has been made available by Penn State.
In addition Ocneanu has provided his own detailed commentary. The octacube provides a physical means of visualising quantum symmetries
Topological quantum field theory
A topological quantum field theory is a quantum field theory which computes topological invariants....
associated with exceptional structures arising in the theory of subfactor
Subfactor
In the theory of von Neumann algebras, a subfactor of a factor M is a subalgebra that is a factor and contains 1. The theory of subfactors led to the discovery of theJones polynomial in knot theory.-Index of a subfactor:...
s, initiated by Vaughan Jones
Vaughan Jones
Sir Vaughan Frederick Randal Jones, KNZM, FRS, FRSNZ is a New Zealand mathematician, known for his work on von Neumann algebras, knot polynomials and conformal field theory. He was awarded a Fields Medal in 1990, and famously wore a New Zealand rugby jersey when he accepted the prize...
.