It's Christmas eve! On this very special day we thought we'd explore a very special theorem. Its initial proof, first announced in 1981, ran to over 10,000 pages, spread across 500 or so journal articles, by over 100 different authors from around the world, was without precedent. It must be counted...

Group theory is essentially the study of symmetry. It underpins much of modern mathematics and is also hugely relevant to other areas — from physics to computer science. And although the field is over two hundred years old, it's still a vibrant and dynamic area in which exciting things are...

Cheryl PraegerIn Yesterday's door of the Plus advent calendar, we found out what a magician can do with a card shuffle. But what might a mathematician do when shuffling cards? To find out we asked Cheryl Praeger, from the University of Western Australia. It was Praeger who first intrigued us in...

Rachel ThomasLiving through a pandemic we all know by now how important the reproduction ratio, R, is to understanding the progress of a disease. But what do you need to know to calculate it? How long does it take until one infection generates another? Knowing R, the average number of people...

How do you shuffle a pack of cards? Our shuffling is very unimpressive, we've even been known to resort to jumbling them around in a big pile on the table. But good news – here is how you shuffle like a professional! How to shuffle perfectly Take a pack of cards and split the pack into two...

Rachel ThomasHow long does it take a person infected with a virus to infect someone else? How long does it take one infection to generate another? Answering this question requires knowledge from all the levels on which a virus operates: inside our bodies, how it spreads from one person to another...

This article is about understanding abstracts objects called groups. If you don't know what they are, then you might want to read this brief explanation. Some things go round and round. An example are the hours of a clock. If you start at 12 and add one hour you get to 1, add another hour and you...

One way to start getting your head around groups, those slightly scary abstract structures that belong to the field of algebra, is to think of a 12-hour clock. You can add hours on this clock, for example 2 o'clock + 4 hours = 6 o'clock 8 o'clock + 5 hours = 1 o'clock 3 o'clock + 12 hours = 3...

When you are buying online you usually get the option to see the items you searched for ordered by price, average customer rating, or perhaps date. If you have ever tried to put a bunch of things (e.g. books on your shelf) in order, you'll know it takes time. This is why the world owes a huge...

This article about complex numbers is a little advanced. Take a look behind yesterday's door for a basic introduction to complex numbers. Many things in mathematics are named after Leonhard Euler, who probably was the most prolific mathematician of all time. In this article we explore a formula...

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