Fascinating discussion by @viktorblasjo of the letters between Huygens & Leibniz, when the student (Leibniz) became the teacher, and his old teacher (Huygens) tried to learn the new calculus. Lessons here for students & teachers today.http://intellectualmathematics.com/blog/learn-calculus-like-huygens/ …
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Replying to @stevenstrogatz @viktorblasjo
Huygens was surely a great mathematician, but I can't agree with the principle suggested here that mathematics is best studied only in virtue of its applications. Or that one should apologize for amusing mathematical play.
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Leibniz says to Huygens, “You are right, Sir, to not approve if one amuses oneself researching curves invented for pleasure.” I find this totally wrong. Mathematical play is the key to so many insights; it is to be strongly encouraged, not condemned as sin.
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I would love all my students to invent curves for their mathematical pleasure and then investigate them! Let's all invent mathematical curiosities for pleasure. Perhaps it will turn out that some of them have applications (but that does not concern me).
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Large cardinal valued modular forms.
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