Abel Prize 2019 goes to Karen Uhlenbeck

The Abel Prize for 2019 has been awarded to Karen Uhlenbeck. The citation reads: for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.

π calculated to 31 trillion digits

This Pi Day, Emma Haruka Iwao has announced calculation of $\pi$ to $\pi \times 10^{13} = 31,\!415,\!926,\!535,\!897$ digits, exceeding the previous record of 22 trillion digits set in November 2016.

This used y-cruncher, running Chudnovky’s algorithm. Chudnovky’s algorithm is $\mathcal{O}(n(\log n)^3)$, making each record more impressive. In a blog post, Emma writes about the benefits of using a cloud cluster, saying the calculation ran on a virtual machine cluster, using

25 nodes for 111.8 days, or 2,795 machine-days (7.6 machine-years), during which time Google Cloud performed thousands of live migrations uninterrupted and with no impact on the calculation process.

Ways to access the digits and fun related bits and bobs are outlined in the blog post.

Aperiodical guest author Andrew Taylor writes about an intriguing piece of number theory which turns out to also be something else. How many ways are there of writing some natural number $n$ as the sum of two squares? $$n = p^2 + q^2$$ I don’t want an answer for some particular $n$. I…