Reasoning, convincing and proving

This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.

What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.

This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians with significant food for thought.

Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.

We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.

Here are some examples of 'cons', and see if you can figure out where the trick is.

Yatir from Israel describes his method for summing a series of triangle numbers.

Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.