# Who is Cohl Furey?

Table of Contents

## Who is Cohl Furey?

Dr Cohl Furey is a Walter Grant Scott Fellow in the Department of Applied Mathematics and Theoretical Physics, and a member of Trinity Hall. Here, she tells us about the elegance of mathematical physics, which ‘gets better and better the further you go. ‘

## What are octonions?

In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface O or blackboard bold. .

## Who discovered octonions?

John Graves

John Graves, a lawyer friend of Hamilton’s, subsequently showed that pairs of quaternions make octonions: numbers that define coordinates in an abstract 8-D space. John Graves, the Irish lawyer and mathematician who discovered the octonions in 1843.

## Are octonions necessary to the standard model?

The emergence of SU(3), SU(2) and U(1) groups in octonion-based structures is suggestive of the symmetries of the Standard Model, but octonions themselves are an unsatisfactory model for physical application because they are antiassociative and consequently not a group.

## Are quaternions complex numbers?

The quaternions are structured like the complex numbers, but with additional square roots of –1, which Hamilton called j and k. Every quaternion has the form a + bi + cj +dk, where a, b, c and d are real numbers, and i^2=j^2=k^2=-1.

## How are physics and math related?

Math and physics are two closely connected fields. For physicists, math is a tool used to answer questions. For mathematicians, physics can be a source of inspiration, with theoretical concepts such as general relativity and quantum theory providing an impetus for mathematicians to develop new tools.

## What are the 9 spatial dimensions?

The most studied are the regular polytopes, of which there are only three in nine dimensions: the 9-simplex, 9-cube, and 9-orthoplex. A broader family are the uniform 9-polytopes, constructed from fundamental symmetry domains of reflection, each domain defined by a Coxeter group.

## Are the quaternions a field?

The quaternions almost form a field. They have the basic operations of addition and multiplication, and these operations satisfy the associative laws, (p + q) + r = p + (q + r), (pq)r = p(qr). The only thing missing is the commutative law for the multiplication.

## Are complex numbers real?

Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra. Because either part could be 0, technically any real number or imaginary number can be considered a complex number.

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