Category Archives: mathematical aphorisms

Mathematical Aphorisms. Part 5.

Perhaps the best example1 of a sound and complete proof system for a general audience are the three Reidemeister moves. 1 Calling Reidemeister moves a ‘proof system’ goes back at least to Avi Wigderson’s 2006  ICM contribution. Advertisements

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Mathematical aphorisms. Part 4.

Bicategories are useful because they allow to constructively compare comparisons.

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Mathematical Aphorisms. Part 3.

With the discovery of higher dimensional algebra, the standard technical term linear equation accidentally has acquired a non-standard second meaning. In particular: old-sense linear equationnew-sense linear equationany old-sense equation.

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Mathematical Aphorisms. Part 2.

One should intentionally take an intensional view on the things one cares about.

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Mathematical Aphorisms. Part 1.

It is by design that it has no content.        

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Mathematical Aphorisms. Part 0.

In Constructive Mathematics, proof-by-exhaustion is not in general exhaustive, though often still exhausting.

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