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.
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.
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.
Ocean 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.
If 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....