## logic

**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?

Suppose you walk past a barber's shop one day, and see a sign that says

"Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and noone else."

This seems fair enough, and fairly simple, until, a little later, the following question occurs to you - does the barber shave himself?

**John Conway**believes they are going to want to talk mathematics. He talks to

*Plus*about his

*Life*game, artificial life and what we will have in common with extraterrestrials.