proof
Proof is the essence of mathematics. But is the standard of proof in research maths really as high as mathematicians would like to believe?
The great thing about geometry is that you can sometimes prove things using pictures. Enjoy these three great visual proofs of Pythagoras' theorem!
If you can prove that a statement can't possibly be false, does this mean it's true?
What are mathematical proofs, why do we need them and what can they say about sheep?
Kurt Gödel, who would have celebrated his 100th birthday next year, showed in 1931 that the power of maths to explain the world is limited: his famous incompleteness theorem proves mathematically that maths cannot prove everything. 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.
Why do so many people say they hate mathematics, asks David Acheson? The truth, he says, is that most of them have never been anywhere near it, and that mathematicians could do more to change this perception - perhaps by emphasising the element of surprise that so often accompanies mathematics at its best.
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...