> The paper soon set off a cascade of what Ellenberg called “math at Internet speed.” Within 10 days, Ellenberg and Dion Gijswijt, a mathematician at Delft University of Technology in the Netherlands, had each independently posted papers showing how to modify the argument to polish off the original cap set problem in just three pages.

This is a very interesting trend I've noticed. I wanted to cite a few papers on arXiv in one of my own research papers recently, but my advisor commented that none of the articles had been peer reviewed (since arXiv is a preprint server). I told him that in the last year alone, six papers on arXiv follow a "research trail" (i.e. a paper is put on arXiv in May that builds on results from a February paper that builds on results from December, etc.), and that the most recent peer-reviewed article in a published journal is so far behind the state-of-the-art that completing my paper without any mention to the arXiv works would put me significantly behind the rest of the field.

Of course, these papers all relate to math and computer science — whether a new algorithm or proof works is (usually) immediately evident upon implementation, and the papers on arXiv include the complete algorithm and often link to the author's code. Peer-reviewing their work yourself often takes no longer than a half hour or so (unlike, say, a research article in materials science, where a complete replication study could take over a year).