• Urs Schreiber, Why supersymmetry? describes what Deligne's work on Tannakian has to do with elementary particles. The crux of the story is that elementary particles seem to behave a lot like tensor categories, the main example of which is the category of representations of a group. Then the question is how to describe any such tensor category as something coming from a group, and it turns out that it is enough to use supergroups for this, i.e. you sprinkle some $\mathbb{Z}/2\mathbb{Z}$-grading everywhere. The question of course is whether you do need funny stuff in odd degree to describe physics.
• Degtyarev, Smooth models of singular K3 surfaces is a fun paper regarding the Fermat quartic $x^4+y^4+z^4+w^4=0$ in $\mathbb{P}^3$, which is a (smooth) K3 surface. It is classical that in this case there are 48 lines on the K3 surface (the number 48 comes from 3 partitions of the four coordinates in 2 sets of 2, and then 16 choices of 4th roots of unity). In the paper is shown that it can be embedded into $\mathbb{P}^3$ in two other essentially different ways, and that in these embeddings there are 56 lines! For more information there is also David Roberts' Google+ post.
• Emannuel Kowalski, Trying to understand Delign's proof of the Weil conjectures is an absolutely brilliant exposition on the Weil conjectures, why étale cohomology is what it is, and how Lefschetz pencils are used to reduce the proof.
• Weapons of Math Destruction is the brand new book of Cathy O'Neil. The various reviews I've read (of course, there might be a small selection bias at work here) are very positive, and I'm looking forward to read the actual book. Based on the descriptions I think it might be the case that people who like John Oliver's Last Week Tonight will like the book, or vice versa.