James Grime’s Numberphile videos

James Grime has “Numberphile”, a series of videos about various numbers and how they relate to more serious bits of maths. He goes outside with a big piece of paper, a marker, and a cameraman, and films himself talking and writing on the paper. (But you don’t have to watch him write! Thanks to the magic of film editing, the numbers appear one by one.) In this one on 220 and 284, “amicable numbers” — the factors of 220 add up to 284, and vice versa. Over at Maths Gear they’re selling pairs of keyrings with these numbers inscribed on them.

James points out that although the (220, 284) pair was known to the ancients, and Euler had found thirty pairs by 1747, it wasn’t until 1866 that B. Nicolò I. Paganini (as far as I know, no relation to the violinist) discovered the pair (1184, 1210). I’m a little surprised by this; you hear the story of great feats of calculation in that era, how did this one slip by? It reminds me of the fact that supposedly people thought 2^{11}-1 was prime when 2047 is trivial to factor by trial division. At least, if you have Arabic numerals…

The whole Numberphile channel is here (currently 19 videos, a couple hours in total). Some of my favorites are:

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