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Some shorter proofs are available in the book "Proofs without Words." But then again, that book begins with a description that visual arguments aren't truly pr

• Tloewald 11y ago
  As one of my favorite math professors once pointed out, a proof is merely an argument that convinces people, so whatever works works.
  • eru 11y ago
    Before the advent of computers we had two notions of proof in mathematics, the French school and the Russian school. The Russian school is basically `something that convinces humans'. The French school is all about formality. Since computer became a thing, the field has blossomed. Look at zero knowledge proofs and various forms of interactive proof systems as examples.
    • Tloewald 11y ago
      But the formality is, at bottom, just a set of rules for convincing somebody.
      • eru 11y ago
        Some people would say that the formal proof stands on its own. No need for anyone to appreciate it.