Before scientists can develop medicines or engineers can advance technology, they throw numbers onto whiteboards using concepts laid out by mathematicians sometimes centuries earlier.
Generations of school children will disagree, but no other field of study has played a bigger role in changing the course of history as mathematics.
Unfortunately, mathematicians often get little recognition for their contributions to history.
We're changing that right now.
We've identified the 20 mathematicians responsible for the modern world.
William Playfair, inventor of charts
William Playfair, a Scottish engineer, was the founder of graphical statistics. Besides that signature accomplishment, he was at various times in his life a banker, an accountant, a journalist, an economist, and one of the men to storm the Bastille.
It's difficult to overstate his importance. He was the inventor of the line graph, bar chart, and the pie chart. He also pioneered the use of timelines. You're probably familiar with his work.
James Maxwell, the first color photographer
Maxwell was a Scottish mathematician who formed the classical electromagnetic theory. This combined centuries of research in magnetism, electricity, and optics into a single theoretical framework. He was the first to demonstrate that electricity traveled through space at the speed of light.
How crucial was he? Einstein kept a framed photo of Maxwell on his desk beside pictures of Michael Faraday and Issac Newton. He was the first to develop a color photograph. Connecting light with electromagnetism is considered one of the greatest accomplishments of modern physics. He's in many ways the founder of his field.
Alan Turing, World War II codebreaker
Alan Turing is a British mathematician who is hailed as the father of computer science. His work laid the groundwork for the PC you're presumably reading this on.
Turing is especially unique on this list for his efforts during the Second World War. Working at the famous Bletchley Park, Turing is credited as one of most important people in devising the techniques for breaking the German Enigma cipher.
He developed the method by which the Bombe – a massive electromechanical machine built by the Allies – could crack the Enigma on an industrial scale, allowing them to read nearly all German communication. In that regard, he is one of the founders of modern cryptanalysis, and by all rights played one of the most crucial parts in winning the Battle of the Atlantic for the Allies.
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