FACES OF MATHEMATICS

Shahn Majid

Professor Shahn Majid

Queen Mary, London

Shahn Majid's research explores the world of quantum geometry, on the frontier between pure mathematics and the foundations of theoretical physics. He uses mathematical structures from algebra and category theory to develop ideas concerning the structure of space and time. His research philosophy drives a search for the right mathematical language for a unified expression for the ideas of quantum physics, founded on the notion of non-commutative geometry.

"What it boils down to is that in mathematics you have the notion of a structure and a representation of it, and the representation is an equally good mathematical structure. In fact, there is a pairing between them, and you could say that the set of representations was the reality, the abstract structure, and that the original object was the dual of the dual, the representations of the set of representations... So this is the kind of engine that drives the evolution of physics. Physics is the quest for reality, the construction of representations of those bits of reality, the realisation that those representations themselves are reality, and then unification to a new object. Then repeat the cycle.

"It is really to do with awareness -- or self-awareness if you like -- that reality is a consequence of the assumptions you have forgotten about. So reality is really the flipside of certain assumptions that you have taken on, and mathematicians are very aware of this kind of duality between the arbitrariness of the axioms that you choose to take on, and the reality that they open up.

"Our system of knowledge is organised in a hierarchy, where we have more and more assumptions that we take on. And with those assumptions, to the extent that we are aware of them, we are behaving like mathematicians and we are exploring their consequences, and to the extent that we are not aware of them, we are behaving like physicists and are living in that world."

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