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.
Mathematics started with numbers — clear, concrete, intuitive. Over the last two centuries, however, it has become a far more abstract enterprise. One of the first major steps down this road was taken in the late 18th and early 19th centuries. It involved a field called group theory, and it changed math — theoretical and applied — as we know it.
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