## curvature

Can physics do for maths what maths has done for physics?

Since he Universe is all there is, there's nothing for it to expand into. So what does "expansion" mean?

Following on from our previous article about curvature of lines and surfaces, we now move up to curvature of their higher dimensional equivalent – manifolds.

That geometry should be relevant to physics is no surprise — after all, space is the arena in which physics happens. What is surprising, though, is the extent to which the geometry of space actually determines physics and just how exotic the geometric structure of our Universe appears to be. *Plus* met up with mathematician Shing-Tung Yau to find out more.

The famous mathematician Euclid is credited with being the first person to axiomatise the geometry of the world we live in - that is, to describe the geometric rules which govern it. Based on these axioms, he proved theorems - some of the earliest uses of proof in the history of mathematics.

**Janna Levin**tells us more.