We're looking for inspiring images that illustrate your favourite mathematical ideas. Illustrations, photographs, computer simulations or even clever doodles — anything that's colourful and inspirational. The best fifty images will be used as part of a book fifty to be published by Oxford University Press to coincide with the fiftieth anniversary of the Institute of Mathematics and its Applications (IMA).

Here's a well-known conundrum: suppose I need to buy a book from a shop that costs £7. I haven't got any money, so I borrow £5 from my brother and £5 from my sister. I buy the book and get £3 change. I give £1 back to each my brother and sister and I keep the remaining £1. I now owe each of them £4 and I have £1, giving £9 in total. But I borrowed £10. Where's the missing pound?

What a lovely coincidence! Pi day (the 14th of March, written 3/14 in the US) is also Albert Einstein's birthday. How are you going to celebrate? .

We've been dabbling a lot in the mysterious world of quantum physics lately, so to get back down to Earth we thought we'd bring you reminder of good old classical physics.

Mathematics of Planet Earth 2013 is a year-­long international effort highlighting the contributions made by mathematics in the study of global planetary problems: migrations, climate change, sustainability, natural disasters, pandemics... and in the search for solutions.

Solving equations often involves taking square roots of numbers and if you're not careful you might accidentally take a square root of something that's negative. That isn't allowed of course, but if you hold your breath and just carry on, then you might eventually square the illegal entity again and end up with a negative number that's a perfectly valid solution to your equation.

Science advisors to government are an embattled lot. Remember the l'Alquila earthquake debacle or David Nutt's stance on drugs which cost him his job. Bridging the gap between politics and science isn't easy. Politicians like clear messages but science, and the reality it tries to describe, is rarely clear-cut.

Modelling the spread of disease is a difficult business. Epidemiologists use incredibly complex models involving huge amounts of transport, social contact and disease data to predict the spread of diseases. But is there a way to hide all this complexity and draw a simpler picture of how diseases spread, even in today's complex world?