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graph theory

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Bridges of Königsberg

The bridges of Königsberg

Can you find a path through on this city map that crosses every bridge exactly once? Euler's answer to this problem started off the filed of graph theory.

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Counting the trees of life

How many possible genetic relationships are there between a collection of different species? The answer is mind-bogglingly large.
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The art gallery problem

Sometimes a piece of maths can be so neat and elegant, it makes you want to shout "eureka!" even if you haven't produced it yourself. One of our favourite examples is the art gallery problem.

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Friends and strangers

Can we always find order in systems that are disordered? If so, just how large does a system have to be to contain a certain amount of order?
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From bridges to networks

How a cute 18th century puzzle laid the foundations for one of the most modern areas of maths: network theory.
News story

Happy birthday, London Underground!

The London Underground turns 150 today! It's probably the most famous rail network in the world and much of that fame is due to the iconic London Underground map. But what makes this map so special?
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The Tower of Hanoi: Where maths meets psychology

Mathematicians and psychologists don't cross paths that often and when they do you wouldn't expect it to involve an (apparently) unassuming puzzle like the Tower of Hanoi. Yet, the puzzle holds fascination in both fields.

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Picking holes in mathematics

In the 1930s the logician Kurt Gödel showed that if you set out proper rules for mathematics, you lose the ability to decide whether certain statements are true or false. This is rather shocking and you may wonder why Gödel's result hasn't wiped out mathematics once and for all. The answer is that, initially at least, the unprovable statements logicians came up with were quite contrived. But are they about to enter mainstream mathematics?