Enigma machines were designed to create complex coded messages that were almost impossible to crack.
Throughout the Second World War Germany and its allies were using Enigma machines on the battlefield, at sea, in the sky and within its secret services, to send military messages.
The Germans considered the Enigma code to be unbreakable, but mathematicians in Poland, France and the UK developed advanced techniques that broke the Enigma code, helping to shorten the war.
Today mathematics is at the heart of all computer security—as well as attempts to break it.
Take this further: why not use an online enigma machine simulator to learn more about how this machine works?
KS2/3: Maths—Patterns and sequences, Probability
KS2/3: Computing Science—Computational thinking, Programming, Safety and ethics
KS3: History—Britain 1745–1901
A catalytic converter is a large metal box that sits underneath your car. Its job is to convert harmful, toxic fumes produced by your car’s engine into less harmful emissions.
In the 1970s, there was growing concern over the health risks caused by these fumes. By calculating the statistical risk to our health, mathematicians were able to work out the probability of these fumes causing us harm.
Catalytic converters were the answer as they help reduce the chances of us getting ill by reducing the emission of toxic fumes.
KS2/3: Maths—Probability, Statistics
KS3: Science—Gas exchange systems, The particulate nature of matter, Chemical reactions
KS4: Science—Fractional distillation, Rate and extent of chemical change, Earth and atmospheric science
A sextant is used by sailors to work out the location of their ship whilst at sea. To calculate the location of a ship you need to know latitude and longitude.
In the 18th century, sailors could calculate a ship’s latitude from the position of the Sun, but to calculate longitude a sailor needed to know the local time on board the ship, a sextant and nautical almanac.
The sextant is used to measure the height of the Moon and a star, or the Sun, above the horizon and the angles between them—this is called the lunar distance. A nautical almanac would tell you the time in Greenwich, London, based on the lunar distance calculated. To find the ship’s longitude you would then work out the difference between the time on board the ship and the time in Greenwich.
Today satellite navigation tools, such as GPS, are the most common form of navigation for people at sea. However, navigation techniques using time, mathematics, the Moon and stars are still useful skills to know.
KS2: Geography—Locational knowledge
KS3: History—Britain 1745–1901
Ishiguro storm model
Shizuo Ishiguro, an electrical engineer and mathematician, developed this machine storm model to simulate the North Sea and increase our ability to predict the impact of storm surges on our coastline.
It simulates a body of water using flows of electricity, which pass over an electrical grid and demonstrates how specific weather conditions affect the sea.
There was a huge increase in funding for this mathematical research after a severe storm with winds of up to 126mph caused a surge from the North Sea on the 31st January 1953. It hit the UK and parts of northern Europe, flooding 24,000 homes and killing more than 2500 people.
Research continues today with oceanographers using a range of engineering and mathematical techniques to collect and analyse vast quantities of data about the weather and the oceans. This research is helping us to predict and detect the effects of global climate change.
KS3: Science—Earth and atmosphere, Waves
KS3/KS4: Maths—Algebra, statistics and probability
KS4: Maths—Earth and atmospheric science