A recent study from Harvard reported that eating red meat is associated with a 13% increased risk of death. But what does this mean? Surely our risk of death is already 100%, and a risk of 113% does not seem very sensible? To really interpret this number we need to use some maths.

If you look at the pattern of rowers in a racing four or eight rowing boat then you expect to find them positioned in a symmetrical fashion, alternately right-left, right-left as you go from one end of the boat to the other. However, the regularity of the rower's positions hides a significant asymmetry that affects the way the boat will move through the water.

Some things are so familiar to us that they are simply expected, and we may forget to wonder why they should be that way in the first place. Sex ratios are a good example of this: the number of men and women in the world is roughly equal, but why should this be the case? A simple mathematical argument provides an answer.

The number 1 can be written as a sum of unit fractions, that is fractions with 1 in the numerator. But how long can we make such a sum?

Some of the things I overheard at Stephen Hawking's 70th birthday conference did make me wonder whether I hadn't got the wrong building and stumbled in on a sci-fi convention. "The state of the multiverse". "The Universe is simple but strange". "The future for intelligent life is potentially infinite". And — excuse me — "the Big Bang was just the decay of our parent vacuum"?!

This is the first part of the lecture given by Astronomer Royal Martin Rees at Stephen Hawking's birthday symposium.

This is the second part of the lecture given by Astronomer Royal Martin Rees at Stephen Hawking's birthday symposium.

A traditional view of science holds that every system — including ourselves — is no more than the sum of its parts. To understand it, all you have to do is take it apart and see what's happening to the smallest constituents. But the mathematician and cosmologist George Ellis disagrees. He believes that complexity can arise from simple components and physical effects can have non-physical causes, opening a door for our free will to make a difference in a physical world.

Most of us think that we have the capacity to act freely. Our sense of morality, our legal system, our whole culture is based on the idea that there is such a thing as free will. It's embarrassing then that classical physics seems to tell a different story. And what does quantum theory have to say about free will?

Many risks we take don't kill us straight away: think of all the lifestyle frailties we get warned about, such as smoking, drinking, eating badly, not exercising and so on. The microlife aims to make all these chronic risks comparable by showing how much life we lose on average when we're exposed to them.