Articles about Mathematics

Keeping it Safe and Quiet

Stage: 2, 3, 4 and 5

Simon Singh describes PKC, its origins, and why the science of code making and breaking is such a secret occupation.

Sums of Powers - A Festive Story

Stage: 3 and 4

A story for students about adding powers of integers - with a festive twist.

The Best Card Trick?

Stage: 3 and 4 Challenge Level: Challenge Level:1

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Divisibility Tests

Stage: 3 and 4

This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.

All about Infinity

Stage: 3, 4 and 5

Infinity is not a number, and trying to treat it as one tends to be a pretty bad idea. At best you're likely to come away with a headache, at worse the firm belief that 1 = 0. This article discusses the different types of infinity.

Tournament Scheduling

Stage: 3, 4 and 5

Scheduling games is a little more challenging than one might desire. Here are some tournament formats that sport schedulers use.

The Random World

Stage: 3, 4 and 5

Think that a coin toss is 50-50 heads or tails? Read on to appreciate the ever-changing and random nature of the world in which we live.

Ding Dong Bell

Stage: 3, 4 and 5

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.


Stage: 4

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

Links and Knots

Stage: 4 and 5

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.

The Chinese Remainder Theorem

Stage: 4 and 5

In this article we shall consider how to solve problems such as "Find all integers that leave a remainder of 1 when divided by 2, 3, and 5."

Whole Number Dynamics I

Stage: 4 and 5

The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.

Some Circuits in Graph or Network Theory

Stage: 4 and 5

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

Where Do We Get Our Feet Wet?

Stage: 5

Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.

Mathematics in the Financial Markets

Stage: 5

Financial markets mean the business of trading risk. The article describes in simple terms what is involved in this trading, the work people do and the figures for starting salaries.

Euler's Formula

Stage: 5

Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.

Fractional Calculus I

Stage: 5

You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.

Infinite Continued Fractions

Stage: 5

In this article we are going to look at infinite continued fractions - continued fractions that do not terminate.

The Use of Mathematics in Computer Games

Stage: 5

An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.

Proofs with Pictures

Stage: 5

Some diagrammatic 'proofs' of algebraic identities and inequalities.

Conic Sections

Stage: 5

The interplay between the two and three dimensional Euclidean geometry of conic sections is explored in this article. Suitable for students from 16+, teachers and parents.

How Many Geometries Are There?

Stage: 5

An account of how axioms underpin geometry and how by changing one axiom we get an entirely different geometry.

Public Key Cryptography

Stage: 5

An introduction to the ideas of public key cryptography using small numbers to explain the process. In practice the numbers used are too large to factorise in a reasonable time.

The Why and How of Substitution

Stage: 5

Step back and reflect! This article reviews techniques such as substitution and change of coordinates which enable us to exploit underlying structures to crack problems.

Approximations, Euclid's Algorithm & Continued Fractions

Stage: 5

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

What Are Complex Numbers?

Stage: 5

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.