Ciro Santilli
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The beauty of mathematics | 🗖 nosplit | ↑ parent "Mathematics" | 243, 4, 520

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Ciro Santilli intends to move his beauty list here little by little: https://github.com/cirosantilli/mathematics/blob/master/beauty.md
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The most beautiful things in mathematics are results that are:
  • simple to state and understand (pre-high school, high-school, lower undergrad), but extremely hard to prove, e.g. Fermat's
  • surprising results: we had intuitive reasons to believe something as possible or not, but a theorem shatters that conviction and brings us on our knees.
    General surprise themes include:
  • applications: make life easier and/or modeling some phenomena well, e.g. in physics. See also: explain how to make money with the lesson
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Good lists of such problems Lists of mathematical problems.
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Specific examples:
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