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Jeff Dekofsky explains Hilbert’s paradox of the Grand Hotel, a thought experiment proposed in the 1920s by German mathematician David Hilbert to illustrate some surprising properties of infinite sets, in this TED-Ed animated lecture

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As a special bonus, another amusing video (via Kottke)– an explanation of why it is that the sum of all positive integers (1 + 2 + 3 + 4 + 5 + …) = -1/12…  Euler actually proved this result in 1735, but the result was only made rigorous later; and now physicists have been seeing this result actually show up in nature.  (Spoiler alert: the answer turns on what one means by “sum” mathematically…)

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As we pray for more fingers and toes, we might spare a thought for Harald August Bohr; he died on this date in 1951.  While materially less well-known than his brother Niels, Harald was a formidable mathematician (founder of the field of almost periodic functions), a gifted athlete (an accomplished footballer who won a silver medal at the 1908 Summer Olympics as a member of Denmark’s team), an inspirational teacher (the annual award for outstanding teaching at the University of Copenhagen is called “the Harald” in his honor), and an out-spoken critic of the anti-Semitic policies that took root in the German mathematical establishment in the 1930s.

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