# Mathematics

Platonic solids are regular bodies in three dimensions, such as the cube and icosahedron, and have been known for millennia. They feature prominently in the natural world wherever geometry and symmetry are important, for instance in lattices and quasi-crystals, as well as fullerenes and viruses

Platonic solids have counterparts in four dimensions. Swiss mathematician Ludwig Schlaefli and Alicia Boole Stott showed that there are six of them, five of which have very strange symmetries. Stott, the third daughter of mathematician George Boole, is best known for establishing the term "polytope" for a convex solid in four dimensions, had a unique intuition into the geometry of four dimensions, which she visualised via three-dimensional cross-sections.

Exciting, right? Obviously this can be misused and the fact that its potential problems (if they can forecast it, they can manipulate it) are so obvious is why policymakers will address that. The brilliance will be what this sort of capability can do for science.

The Jacobi iterative method, a 169-year-old math strategy, may soon get a new lease on life.

On one occasion - I remember it as it was yesterday - my uncle picked me up and while he kept me with his arms he asked me "Ok, let's see this. Tommaso, what is the square root of 5968?". Mind you, I do not remember the exact number; I only recall it was between 5000 and 7000. I watched up into the void for two seconds, and I replied "77.3". Uncle Ciccio put me down and ran for the pocket calculator - he did have one, although they were a real novelty those years.

Cell migration, which is involved in wound healing, cancer and tumor growth, and embryonic growth and development, has been a topic of interest to mathematicians and biologists for decades.

It's often said that if we do make contact with Extra Terrestrials (ETs), e.g. detect a radio transmission from a distant galaxy through SETI, that maths would be one of the few things we would have in common with them. But - how similar would their maths actually be to ours?

Modern maths- with its many sizes of infinity and logical paradoxes, has lead to much debate and puzzlement over the last century or so. Would this be the same for ETs? And would it lead to many different ideas about maths and the philosophy of maths, as we have here, or would they find some other solution none of us have thought of?

What do you get when you mix theorists in computer science with evolutionary biologists? You get an algorithm to explain sex.

A fascinating mystery of evolution is how sexual recombination and natural selection produced the teeming diversity of life that exists today. The answer could lie in the game that genes play during sexual recombination, so computer scientists at the University of California, Berkeley, created an algorithm to describe the strategy used by these genes in this game.

“Wow, there’s a lot of plaques of fat. I need to stop eating French fries.”

Nine years later, the “cardiac tissue engineer,” is trying to re-create the human heart on a chip.

I'd like to share some of the amazing range of rhythms you can find, linking music and maths, some discovered only in the last few years. These include: fibonacci gamelan patterns - highly structured yet the pattern of beats never repeats; the rhythm you get if two musicians each with perfectly steady rhythm play as out of time as possible; the rhythm of the famous "Cantor's set"; and the fairly recent discovery that many rhythms of music throughout the world are "Euclidean rhythms" - uneven beat patterns pleasing to the ear made with a surprisingly simple construction.