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Case Against Cases

Gödel's Lost Letter and P=NP

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Theon of Alexandria was history’s main editor of Euclid’s Elements.

Today I want to talk about case analysis proofs.

The connection is that Euclid is sometimes credited with inventing case analysis proofs. He can also be credited as the first to evince a desire to avoid them. Euclid made a habit of giving just one case and leaving the reader to imitate his proof for others. One example is the theorem that given a triangle $latex {ABC}&fg=000000$ with apex $latex {C}&fg=000000$, every other point $latex {D}&fg=000000$ on the same side of the base $latex {AB}&fg=000000$ as $latex {C}&fg=000000$ makes either $latex {|AD| neq |AC|}&fg=000000$ or $latex {|BD| neq |BC|}&fg=000000$. Euclid gives a proof only for the case where $latex {D}&fg=000000$ is outside the triangle. In other cases $latex {D}&fg=000000$ could be inside the triangle or incident to one of its edges.

Theon lived from 335 to 405 CE in…

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