Photos: From the abacus to the Enigma, this exhibition tells the story of mathematics

Designed by Zaha Hadid, Mathematics: The Winton Gallery at London's Science Museum demonstrates the importance of mathematics in the history of technology -- and the wider world.
By Danny Palmer, Senior Writer
1 of 19 Nicholas Guttridge, © NIck Guttridge

The Winton Gallery

From powering the code which helps modern-day computers run to aiding commerce, government, health, the military, and transport, mathematics forms the basis of much of the world today.

Though mathematics has shaped many innovations throughout human history, many still struggle to grasp the critical role it's played in society.

Designed by the late architect Dame Zaha Hadid, the brand new Mathematics exhibition at the Science Museum looks to change that by revealing the importance of mathematics with a display of historical artifacts and machines, including many key to the history and development of computing and computer science.

2 of 19 Jody Kingzett

The Gugnunc centrepiece

The centre of the gallery features a Handley Page 'Gugnunc' aeroplane. Built in 1929 for a competition to construct safe aircraft, it incorporated ground-breaking aerodynamic research. It demonstrates the overarching theme of the exhibition -- how mathematics in practice has helped solve real-world problems and, in this instance, paved the way for the safe passenger flights that we rely on today.

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The Abacus

Humans have been using tools such as the abacus to help with addition and subtraction for thousands of years. While many might see the tool as obsolete in the age of digital mathematics, abacuses are still used to teach arithmetic and were used by scientists, clerks, and others regularly well into the 20th century.

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Babbage analytical engine

Computing pioneer Charles Babbage (1791-1871) designed the first automatic computing machines, like the analytical engine. Babbage designed many parts of what was intended to be a high-powered mathematical calculator, but this was one of the few parts to be completed. His ideas inspired mathematician Ada Lovelace, who worked on analytical engines to take the ideas further. Her notes on it include what's generally regarded as the first algorithm to be carried out by a machine and as a result she's often viewed as the world's first computer programmer.

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Babbage Difference Engine No. 2

While Babbage didn't build a difference engine mechanical calculating machine during his lifetime, one was created over 100 years later when in 1985 the Science Museum followed his designs and manufactured the 4000 cast-iron, steel and bronze components in accordance to the engineering standards of when it was designed between 1847 and 1849.

The engine made its first error-free calculation in 1991, 200 years after Babbage was born, and his vision was made complete when a printing mechanism was added in 2002.

The machine completes a complex calculation with every fourth turn of its handle, and each result can be up to 31 digits long, appearing on the cogs.

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Scheutz difference engine

Babbage may have designed the difference engine, but it was Geog and Edvard Scheutz who first brought a version of the machine to market in an effort to reduce the errors made by people dealing with Victorian science, engineering, and commerce.

In 1864, the machine was bought by the British government to calculate figures for the English Life Table, a publication which amongst other things included life expectancies in different parts of the country. But it didn't make things easier overnight; William Farr, a government statistician, said the machine "required incessant attention" and "had to be watched with anxiety".

The results of the Life Table were used by insurance companies to price premiums -- 150 years later, insurers are still using calculations to help price insurance, but now they're using big data software

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Dog-racing tote machine

As time went on, machines moved away from applications purely for scientists and government officials. By 1933, this huge electromechanical dog-racing tote machine was actively in use at Wembley Greyhound Stadium, where it calculated the odds for each dog in real-time as gamblers placed their bets, displaying outputs on a giant display.

This form of betting was different from the track-side bookmakers who all set their own odds. This machine allowed punters to pay into a single pool where winnings were worked out using mathematical calculations placed on each dog and split accordingly. This machine was giving punters the best odds possible.

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Differential analyser, 1935

Built in 1935, the differential analyser was designed to help physicists at the University of Manchester solve problems in fields ranging from electrical power transmission to the production of bombs.

Like many other mathematical machines of the era, it was operated by women who often worked in shifts to ensure that computations were being made around the clock and as quickly as possible.

The machine was later put to use in the field of military research in World War II, including on a secret project which involved calculating the mathematics of uranium enrichment, a key element in the manufacturing of the atomic bomb.

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Calculating machine, circa 1939

Founded in 1937, the Scientific Computing Service (SCS) employed women mathematicians to use machines such as this calculating machine, which was built around 1939 to solve a wide range of practical mathematical problems.

In essence, SCS acted like a human version of modern computers, breaking down complicated problems into smaller calculations which were carried out by different employees, enabling solutions to be found more quickly. The Scientific Computing Service operated until 1965, when the foundations of computers as we know them today were being laid out.

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The Enigma

Arguably the most famous early example of an encryption system, Enigmas were originally designed for business use -- the unit on display at the Science Museum mathematics exhibition was built in 1934 -- but were used extensively by the German military during World War II in order to encrypt military communications from Nazi high-command.

It was a secret at the time, but working at Bletchley Park, Alan Turing and other codebreakers developed advanced techniques using early computing technology in order to break Hitler's supposedly "unbreakable" Enigma code. Breaking the code helped to shorten the war and thus likely saved millions of lives.

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Electrical Logic machine

The post-war period saw a mini-boom in research into machine intelligence as a tool for solving problems. One example of this was the Electrical Logic Machine, built by physicist Dietrich Prinz (a protégé of Alan Turing) and philosopher Wolfe Mays in 1949.

The machine is an electrical device for testing certain logical statements and helped researchers build what were at the time pioneering, human-like deduction and pattern recognition qualities into machines using mathematical calculations.

Almost 70 years later and pattern recognition is widespread in computing processes, used in everything from driverless cars and robotics to surveillance and cybersecurity.

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The Elliott 401

Installed at the Rothamsted Agricultural Institute in 1954, the Elliott 401 was used for tasks including analysis of crop trials, insect damage to plants, and work in the fields of mathematics and genetics.

A pioneering site for statistical research, Rothhamsted was where statistician and biologist Sir Ronald Fisher laid out the foundation for much of modern statistical theory, including the randomisation element which is crucial in clinical and agricultural trials today.

The machine was brought to Rothamsted by Frank Yates, a wartime operational researcher who established the site as a statistical computing centre and encouraged the use of statistical analysis in government research. The size of a room, the Elliot 401 was used for 11 years, performing its final calculations in 1965.

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Ferranti Atlas console

Upon its release in 1962, the Ferranti Atlas was the most powerful computer in the world, but that power came at a price -- this console was just part of the University of London's machine, which occupied two rooms.

One problem the Ferranti Atlas was used to solve was calculating the best routes for British Petroleum oil tankers. Finding the shortest routes involved great complexity as a tanker could take millions of potential routes on a journey which only involved docking a handful of ports, but mathematical techniques simplified the problem and enabled the tanker to take the most efficient route.

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The PDP-8 mini computer

While the first computers were huge, often filling an entire room, their size made them impractical. By the arrival of the PDP-8 in 1965, computers were small enough to fit into offices and laboratories.

The software inside allowed users to test and model large sets of numbers, leading to the PDP-8 becoming widely used in the fields of engineering, science, and medicine, enabling researchers to do far more than would ever be possible with just a calculator.

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London Hospital Survival predictor

Hospital staff and health professionals need to make difficult decisions everyday in deciding what sort of condition a patient has and if they can recover from it.

This Survival Predictor was deployed around 1972 and used by medics at the London Hospital in Whitechapel to decide the likelihood of recovery in coma patients. The machine took brain measurements from the comatose patient and compared them to information about previous patients stored in its memory.

Using this information, the needle would point somewhere between the letter 'S' (standing for survive) and 'IBD' (meaning 'irreversible brain death' with no chance of survival). Of course, the machine didn't make the final decisions about treatment, which were left to the doctors and consultants.

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Wisard Pattern recognition machine

Built in 1981, the Wisard Pattern recognition machine was the first neural network ever constructed. Built to mimic how a human brain works, the machine was designed to look for patterns of data and derive meaning from the information presented.

Neural networks have since become used in a variety of environments as humans strive to use cognitive computing and artificial intelligence to solve some of the world's great problems.

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Lotus Notes

By the 1980s, personal computers were becoming a fixture in homes and offices across the Western World. Applications like this 1983 version of Lotus 1-2-3 software provided office workers with the ability to make calculations which just thirty years before may have required a computer the size of a room.

Along with other popular spreadsheet programs such as Microsoft Excel, Lotus 1-2-3 fundamentally altered how workers such as financial traders conducted business. Before desktop computers became common, traders had to send pricing models to be calculated for processing overnight. But now, using a spreadsheet, they could personally do this in mere minutes.

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Mathmatical software - part of everyday life

Today, people who need mathematics in their line of work have access to powerful computing technology and software which can calculate and model outcomes based on even the most abstract data.

No longer do these programmes require specialist users and overnight calculations, but people in all walks of life have access to vast mathematical power at their fingers -- sometimes literally if they're using a smartphone or tablet. Mathematics has ultimately fundamentally changed the world and how we operate within it.

19 of 19 Nicholas Guttridge, © NIck Guttridge

Here to stay...

The Science Museum's free Winton mathematics gallery features insight into the history of science, technology, engineering, and of course, mathematics. It's open now and represents the only public museum exhibition designed by Zaha Hadid anywhere in the world.

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