Celebrating Irrationality: Frank Calegari, Vesselin Dimitrov, and Yunqing Tang Proved the Irrationality of 1/1²-1/2²+1/4²-1/5²+1/7²-1/8²+ …

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 

.

In fact they proved even more: that and  , are linearly independent over . 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.

Shana Tova to all the readers: happy new (Jewish) year!

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.