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.

Who knew that Robinson Crusoe contained a lost chapter about maths? Help us find the hidden mathematical references and win a prize!

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.

Are there objective chances in the world?

Saul Schleimer and Henry Segerman show off some of their beautiful 3D printed mathematical structures.

Why does time only ever move in one direction? We talk to philosophers of physics Jeremy Butterfield and David Wallace, as well as the eminent Roger Penrose about the puzzle time poses to physicists and what it has to do with the Big Bang and the second law of thermodynamics.

Is the Universe finite or infinite? Is there infinity inside a black hole? Is space infinitely divisible or is there a shortest length? We talk to philosophers and physicists to find out.

A commonly held belief about medieval Europe is that academic pursuits had fallen into a dark age. The majority of scholars were churchmen, and their enquiry often related to some principle of church practice. But is there a value to respecting the tenacity of historic mathematicians?