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Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

Rogue waves — enigmatic giants of the sea — were thought to be caused by two different mechanisms. But a new idea that borrows from the hinterlands of probability theory has the potential to predict them all.

There are many different ways to think about probability. Quantum mechanics embodies them all.

Equations, like numbers, cannot always be split into simpler elements.

Computer code serves as a useful analogy for what our genes do, but the complexity and messiness of life go well beyond simple analogies and mathematical models.

Can a set of simple instructions produce complex, three-dimensional living structures?

When our brains don’t have a good intuition for reasoning with numbers, explicit probabilistic thinking can lead to improved decision-making.

When faced with a difficult decision, should you go with your gut or carefully calculate the attendant risks?

When a German retiree proved a famous long-standing mathematical conjecture, the response was underwhelming.

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