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‘Groups’ Underpin Modern Math. Here’s How They Work

What do the integers have in common with the symmetries of a triangle? In the 19th century, mathematicians invented groups as an answer to this question.

The term “group” in a mathematical context was coined in 1830 by Évariste Galois, a French prodigy, just 18 years old at the time. “It’s not like a bunch of mathematicians got together one day and said, ‘Let’s create an abstract structure just for a laugh,’” said Sarah Hart, a group theorist at Gresham College in London. In 1892, the mathematician Otto Hölder proposed that researchers assemble a complete list of all possible finite simple groups.

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