Marianne Freiberger

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?

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?

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.

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.

This is the second article in our four-part series exploring quantum electrodynamics. After successfully applying quantum mechanics to the electromagnetic field, physicists faced a problem of boundless proportions: every calculation they made returned infinity as the answer.

You may have heard of quantum theory and you probably know what a field is. But what is quantum field theory? This article traces the development of quantum electrodynamics in the first half of the 20th century. Hair raising difficulties, heroic struggle and illustrious characters — this story has it all!

This is the third article in our four-part series exploring quantum electrodynamics. After struggling with a theory plagued by unwieldy infinities an ingenious trick put QED back on track.

This is the last article in a four-part series exploring quantum electrodynamics. After a breakthrough that tamed QED in theory, the stick-like drawings known as Feynman diagrams, policed by a young Freeman Dyson, made the theory useable.

Agreeing to pay £50,000 for something worth £2 wouldn't win you any haggling competitions. In mathematics, however, a similar result can bring you international acclaim. This is the case with recent progress towards the famous twin prime conjecture.

Space is the stage on which physics happens. It's unaffected by what happens in it and it would still be there if everything in it disappeared. This is how we learn to think about space at school. But the idea is as novel as it is out-dated.