My model now gives Brazil odds of >1/3 that they will win the World Cup.

## Complex Reflection Groups

After a spring clean I came across a talk I gave on the classification of complex reflection groups back in March 2011.

## 1 = 2

Many people have seen “proofs” that 1 = 2. However most of them have an obvious fallacy – a division by 0.

## Recurring Decimals – Something on the Repetend

I have no practical application for what I am going to post about today (although that doesn’t mean there aren’t any), but I “discovered” (okay so I know loads of people will have done it before, but it was a personal discovery) a nice little fact about recurring decimals.

## GAP: A System for Computational Discrete Algebra

GAP (Groups, Algorithms, Programming) is a program for computational discrete algebra, which is particularly useful for computational group theory. It is a text based computer system which includes a large number of functions that implement various algebraic algorithms. A vast number of these are with regards to groups, using the program you can find the

## God’s Number is 20

The Rubik Cube was invented by one Erno Rubik in 1974 and has gone one to be one of the most popular puzzles in the world, having sold over 350 million units worldwide, even though many people can not solve one! Although perhaps that isn’t overly surprising given the vast number of possible positions that

## Hilbert’s Hotel

David Hilbert was a greatly influential mathematician born in 1862. He worked in a variety of areas including infinite sets and it is in this area that he presented his ‘Hotel’, or his ‘paradox of the Grand Hotel’. Which makes the reader consider the infinite. So lets give it a go:

## Probability of Sharing a Birthday

Yesterday was my wife, Katie’s, birthday and it reminded me about the so called ‘Birthday Problem’. Or, in a group what is the likelihood of two people sharing a birthday? The result is really quite surprising!

## WhatEverTrevor – Free £25,000 Football bet

For all the people who can’t be bothered to read this whole post I’ll sum it up really quickly. Go to WhatEverTrevor, predict the order in which the Premier League will finish, for free, and if you’re right you’ll get £25,000!