In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb O . There are only four such algebras, the other three being the real numbers R, the complex numbers C, and the quaternions H. The octonions are the largest such algebra, with eight dimensions, double the number of the quaternions from which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity, power associativity.

Octonions are not as well known as the quaternions and complex numbers, which are much more widely studied and used. Despite this they have some interesting properties and are related to a number of exceptional structures in mathematics, among them the exceptional Lie groups. Additionally, octonions have applications in fields such as string theory, special relativity, and quantum logic.

Tevian Dray (born March 17, 1956) is an American mathematician who has worked in general relativity, mathematical physics, Geometry, science and mathematical education.

He has primarily worked in the area of classical general relativity. His research results include confirmation of the existence of solutions of Einstein's equation containing gravitational radiation, the use of computer algebra to classify exact solutions of Einstein's equation, an analysis of a class of gravitational shock waves (including one of the few known exact 2-body solutions in general relativity), and the study of signature change, a possible model for the Big Bang. More recently, his work has focused on applications of the octonions to the theory of fundamental particles.

He was a graduate student under Rainer Sachs at Berkeley, where he received his Ph.D. in 1981, although much of his dissertation research was done in collaboration with Abhay Ashtekar. The context of his dissertation, titled The Asymptotic Structure of a Family of Einstein-Maxwell Solutions was mostly focused on the families of space-time. Specifically, the ones which describe accelerating black holes contain gravitational radiation. This demonstrated the existence of exact radiating solutions to the Einstein field equations
. He is currently a professor of mathematics at Oregon State University. In addition to his ongoing work in mathematical physics, he has made significant contributions in science education, where he directs the Vector Calculus Bridge Project , an attempt to teach vector calculus the way it is used by scientists and engineers, and is part of the development team of the Paradigms Project , a complete restructuring of the undergraduate physics major around several core "paradigms".