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Euler's Gem by David S. Richeson

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EPILOGUE: THE MILLION-DOLLAR QUESTION

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.—Bertrand Russell, “The Study of Mathematics”1

In the twentieth century topology rose to become one of the pillars of mathematics, sitting side by side with algebra and analysis. Many mathematicians who do not consider themselves topologists use topology on a daily basis. It is inescapable. Today, most first-year graduate students in mathematics are required take a full-year course in topology. ...

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