The natural logarithm is intimately related to the number e and that's how we learn about it at school. When it was first invented, though, people hadn't even heard of the number e and they weren't thinking about exponentiation either. How is that possible?

Georgian school maths: bushels of corn, kilderkins of beer and feeding soldiers. All without algebra!

Do the dramatic advances in cosmology in the last century herald a new golden age of philosophy? A new collaborative project between cosmologists and philosophers is leading the way.

This year's PISA results have caused predictable headlines, but do the statistics add up?

A 1 in 14 million chance to win the lottery, a 5% risk of cancer, a 50:50 chance of heads on a coin — we deal with probabilities all the time, but do they actually mean anything? We explore the philosophy of probability and ask whether the probabilities that come up in physics differ from those in every day life.

This year has seen a flurry of results as mathematicians hunt down the elusive proof of the twin prime conjecture. Will they get their wish for Christmas this year?

Are there objective chances in the world?

The fact that a sizeable proportion of the financial workforce is made up of physicists is one of the industry's best-kept secrets. We talk to Laura Tadrowski, who has made the leap from physics to finance.

The Fibonacci sequence – 0, 1, 1, 2, 3, 5, 8, 13, ... – is one of the most famous pieces of mathematics. We see how these numbers appear in multiplying rabbits and bees, in the turns of sea shells and sunflower seeds, and how it all stemmed from a simple example in one of the most important books in Western mathematics.

You don't need to count to see that five apples are more than three oranges: you can tell just by looking. That's because you were born with a sense for number. But is that sense related to the mathematical abilities you develop later on?