## logic

It requires only a little processing power, but it's a giant leap for robotkind: engineers at the University of Southampton have developed a way of equipping spacecraft and satellites with human-like reasoning capabilities, which will enable them to make important decisions for themselves.

Many people like mathematics because it gives definite answers. Things are either true or false, and true things seem true in a very fundamental way. But it's not quite like that. You can actually build different versions of maths in which statements are true or false depending on your preference. So is maths just a game in which we choose the rules to suit our purpose? Or is there a "correct" set of rules to use? We find out with the mathematician Hugh Woodin.

**Phil Wilson**looks at

*constructivist mathematics*, which holds that some things are neither true, nor false, nor anything in between.

**Richard Elwes**explores how these questions brought triumph to one man and ruin to another, ventures to the limits of mathematics and finds that, with infinity, you're spoilt for choice.

**Richard Elwes**continues his investigation into Cantor and Cohen's work. He investigates the

*continuum hypothesis*, the question that caused Cantor so much grief.

**Runner up in the general public category**. Great minds spark controversy. This is something you'd expect to hear about a great philosopher or artist, but not about a mathematician. Get ready to bin your stereotypes as

**Rebecca Morris**describes some controversial ideas of the great mathematician David Hilbert.

*incompleteness theorem*in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. This put an end to the hope that all of maths could one day be unified in one elegant theory and had very real implications for computer science.

**John W Dawson**describes Gödel's brilliant work and troubled life.

**Yutaka Nishiyama**illuminates the connection between light bulbs, logic and binary arithmetic.

**Phil Wilson**, why should this be? Is mathematics a universal truth, and how would we tell?