## philosophy of mathematics

**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.

**Gregory Chaitin**explains why he thinks that Gödel's incompleteness theorem is only the tip of the iceberg, and why mathematics is far too complex ever to be described by a single theory.

"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?

**Robert Hunt**concludes our Origins of Proof series by asking what a proof really

*is*, and how we know that we've actually found one. One for the philosophers to ponder...

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