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After 2000 years of searching we only know of 51 perfect numbers and they're all even. What else do and don't we know about these rare and precious jewels of maths?
If there's a multiverse, then how many of its component universes are like our own?
Here's an easy game that leads you straight to an unsolved question in maths.
Have you ever been in an aeroplane on a smooth flight when suddenly the plane bumps up and down for a short time as it goes through turbulent air? The study of turbulence is used to understand a range of phenomena from the simple squirting of a jet of water to the activity of the sun.
Daniel Bernoulli (1700-1782) discovered the relationship between the density of a fluid in a pipe, the speed it is travelling in the pipe and the pressure exerted by the fluid against the walls of the pipe. This is the story of what happened.
Find out how an early interest in Mathematics and Physics led Dr Helen Mason to a career in solar studies.
Mark Langley, a student at Hills Road Sixth Form College in Cambridge, tells us about his experiences doing A-level Mathematics.