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Christiaan Huygens was the greatest mathematician in the generation before Newton and Leibniz. He spent his prime years in Paris, where he was a key member of the Academy of Sciences. Here he is with his buddies. The young Leibniz wanted nothing more than to join these esteemed gentlemen. He admired the great Huygens and followed his example in wigs and mathematics alike.

But times change. French politics soured and foreigners were chased out of the country. Leibniz had to return to Germany. Huygens withdrew to his family mansion in the Netherlands. The Academy descended into reactionary mediocrity.

But Huygens did not retire to feed the ducks in his estate gardens. Though old and frail at this point, he kept up with the latest mathematics. This meant learning the new calculus developed by his former protégé Leibniz. The student had become the master, as the saying goes. But perhaps more interestingly, the master had become the student.

What a treat of history this is. Reading the correspondence between Huygens and Leibniz during these years, we get to see learning in action. We get to see how the calculus is taught by its inventor, and how a sage mathematician of the highest credentials goes about learning it. We get to see the former director of scientific research at the Academy of Sciences take a seat in the front row of Calculus I, pencils sharpened and notebook in hand. It’s a naked view of calculus genesis, unique in history.

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