Articles

How to add up quicklyThe number pi can be expressed beautifully in terms of infinite sums. For practical purposes though, these sums are rather disappointing: they converge slowly, so you need to sum a large number of terms to get accurate estimates of pi. Here's a clever way to make them converge faster.

Maths in a minute: Newton's laws of motionWe'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.

Playing games in many worlds - Part IWould you stake your fortune on a 100 to 1 outsider? Probably not. But what if, somewhere in a parallel universe, the straggling nag does come in first? Would the pleasure you feel in that universe outweigh the pain you feel in the one in which you've lost? Questions not dissimilar to this one occupy physicists and for entirely respectable reasons.

Are there parallel universes?Are there parallel universes? Universes in which, rather than reading this article, you are still asleep; in which you are happier, unhappier, richer, poorer, or even dead? The answer is "possibly". It's a controversial claim but one that has won more and more followers over the last few decades.

The many lives of Hugh Everett IIIHugh Everett III is the father of the many-worlds interpretation of quantum mechanics. He published the idea in his PhD thesis but died before it gained the recognition it deserves. This article gives an insight into Everett's difficult life.

Playing games in many worlds - Part IIIn the previous article we explored how a clever argument involving gambling makes the idea that there are parallel universes more credible. But does it really?

Is the Universe simple or complex?On the face of it the Universe is a fairly complex place. But could mathematics ultimately lead to a simple description of it? In fact, should simplicity be a defining feature of a "theory of everything"? We ponder the answers.

Is the Universe simple or complex? Part IIIn this, the second part of this series, we look at a mathematical notion of complexity and wonder whether the Universe is just too complex for our tiny little minds to understand.

The Tower of Hanoi: Where maths meets psychology

Mathematicians and psychologists don't cross paths that often and when they do you wouldn't expect it to involve an (apparently) unassuming puzzle like the Tower of Hanoi. Yet, the puzzle holds fascination in both fields.

Beneath the wavesOcean waves are not moving walls of water. Instead, it's some kind of energy that moves along. But then, what happens to the water itself? This isn't just an idle question to ponder while watching the ocean — its answer may help protect us from it too. And it requires some sophisticated maths.

Triples and quadruples: from Pythagoras to FermatIf there's one bit of maths you remember from school it's probably Pythagoras' theorem. But what's a Pythagorean triple? How many triples are there and how do you find them? And what about quadruples, quintuples, sextuples....

Understanding uncertainty: ESP and BayesIn the previous article we looked at a psychological study which claims to provide evidence that certain types of extra-sensory perception exist, using a statistical method called significance testing. But do the results of the study really justify this conclusion?