There are very many irrational numbers but proving irrationality of a specific number is not a common event. A few weeks ago Frank Calegari, Vesselin Dimitrov, and Yunqing Tang posted a paper that proved the irrationality of
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.
In fact they proved even more: that Image may be NSFW.
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and Image may be NSFW.
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, are linearly independent over Image may be NSFW.
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. This is, of course, a fantastic result.
According to the short abstract, “The argument applies a new kind of arithmetic holonomy bound to a well-known construction of Zagier.”
h/t to Ido Kaminer and members of the “Ramanujan machine team” who told about this result in a recent workshop.
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Shana Tova to all the readers: happy new (Jewish) year!
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Some more links: Apéry’s 1979 theorem that ζ(3) is irrational. A blog post on Persiflage about the new irrationality result. A videotaped lecture by Frank Calegari.
