Research in mathematics is a deeply imaginative and intuitive process. This might come as a surprise for those who are still recovering from high-school algebra. What does the world look like at the quantum scale? What shape would our universe take if we were as large as a galaxy? What would it be like to live in six or even 60 dimensions? These are the problems that mathematicians and physicists are grappling with every day. To find the answers, mathematicians like me try to find patterns that relate complicated mathematical objects by making conjectures (ideas about how those patterns might…
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