Three Ways to Make Six—and a 100-Year-Old Mystery

Estimated duration: ~6 minutes There are three ways to make six by adding whole numbers that differ by at least two: one plus five, two plus four, or six by itself. Three. What happens if we change the rule? Use only numbers ending in one, four, six, or nine. Now the choices are six ones; one plus one plus four; or six. Still three. A coincidence for the number six? No. The two rules give the same count for every whole number. That surprising equality is a way to understand one of the Rogers–Ramanujan identities. Scientific American reports that mathematicians have now connected those identities to the geometry of a trefoil knot—and proved a result that yields infinitely many related families of identities.

Full episode: https://youtu.be/N7vonaVkm2U

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