Out of the minds of babies -- Elvis: the Welsh corgi who knows calculus -- What is mathematics? -- Where am I and where am I going? -- Nature's architects: the creatures that can do math of construction -- Natural artists: the animals (and plants) that create beautiful patterns -- It's just a step to the right: the math of motion -- The eyes have it: the hidden math of vision -- Animals in the math class -- Razor sharp: the mathematical tricks of street traders and supermarket shoppers -- All numbers great and small -- The trouble with meaningless math -- Tapping into our math instinct.