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In some sense, all of maths should come under the label "logic", and in this collection of articles we try to explain why.

When it comes to doing maths, a picture can be worth a thousand equations.

Why do mathematicians always want proof and what do they mean by it?

Don't like trigonometry? Don't worry, here are three beautiful proofs of a well-known result that make do without it.

Proof is the essence of mathematics. But is the standard of proof in research maths really as high as mathematicians would like to believe?

Will sophisticated algorithms one day replace mathematicians?

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?

Will computers ever replace human mathematicians?

What are mathematical proofs, why do we need them and what can they say about sheep?

Human versus machine: who's better at proving theorems?

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.