Another fortnight has passed.
The past 3 weeks we were hosting the IMAGINARY exhibition at the University of Antwerp, and one of the items was related to the fact that there are 27 lines on a cubic surface. John Baez now has a description and some pretty visualisations of the Clebsch surface on his AMS Blog "Visual Insight". There are other really cool visualisations on this blog, new ones are posted every 1st and 15th of the month.
I like using MathSciNet and zbMath, and sometimes a review (often negative) can be fun to read. There is a page dedicated to these exceptional MathReviews. You'll need a subscription to read the actual reviews though. Related to this is Edward Dunne's Beyond Reviews blog, which discusses reviews that are really worth reading (and not because the reviewer eloquently describes where the authors went wrong as for the first link).
The Aperiodical has a post in which Christian thumbs through a beautiful and intriguing book of Georges Papy about group theory. It gets interesting at the 1:20 mark, where he reads the preface and the author turns out this book is supposedly written to be used by high school teachers.
It gets even more interesting when you realise that Georges Papy actually was responsible for the reform of the mathematics education in Belgium in the 1960s! When I was in elementary and secondary school in the late 1990s, early 2000s there were still some remnants of his influence visible (I can only presume). For example: I guess (or hope) that no-one outside Belgium had to learn the lists of axioms for groups, rings and fields by heart at the age of 11--12 without ever seeing any example of these (at that time) besides the integers and the rationals. Although I do fear that Bourbaki's influence might have scarred the maths education outside Belgium too in this particular way.
Also, some older people in Belgium, when you confess that you are a mathematician, will tell you stories of how they were either subjected to the wonders (or horrors) of Papy's "New Maths", or how they were just a few years too old and were raised in the ignorance that is a maths education not firmly based on Bourbaki whilst their younger siblings became part of the horde of the mathematically enlightened.
There is another article about Grothendieck, this time featuring recollections by 12 mathematicians who were (very) close to him.
One story I'd like to highlight is from Robin Hartshorne, who wrote "Residues and duality" based on notes of Grothendieck. After its publication, Grothendieck asked him
"Well, those lecture notes were a good rough account, but when are you going to write the book on duality?"
It was published 3 weeks ago, but I only discovered it today: a news update from the arXiv. Interesting point: they will update their TeX installation and improve its documentation this year. Hurray! See also the 2016 roadmap for more information.