Sunday, February 07th, 2010 | Author: Konrad Voelkel
MathOverflow is a relatively new place for mathematicians to ask and answer research questions or just watch other mathematicians' discussions to learn. Since it's growing like the arXiv, it's no longer possible for me to read everything interesting without investing "too much" time. Like for the arXiv, where we have the arXiv Blog that looks for some of the most interesting (physics) papers submitted, there ought to be an excerpt-of-MO, too. This way, you could subscribe to your special fields of interest in a feed reader and additionally read some not-that-specialised questions picked by someone else.
I'm not going to do this, but in this post I'll present some of my favourites from the last months at MathOverflow (omitting the more subject-specific ones):
- Success stories: Kevin Buzzard asked for errata on Cassel-Fröhlich's Algebraic Number Theory book and the London Maths Society (LMS) is going to reprint that book, including an erratum. See also the discussion on meta.MO if errata requests are appropriate for MO and the
Errata Wiki(now offline), an attempt to provide a common place for these things.
- Success stories: Timothy Gowers asked if MO has led to mathematical breakthroughs, and the answers list some cases where it at least helped a lot.
- Tools: Ilya Nikokoshev asked for tools that help in organising research notes.
- Tools: Elisha Peterson asked for tools that help in organising papers (toread, tocite, etc.) and the answers were helpful for my discussion on how to manage papers.
- Tools: Anton Petrunun asked for tools that help in collaborative paper writing.
- ToRead: Ilya Nikokoshev asked for "a single paper everyone should read" and there are some nice suggestions, if you don't have enough to read yet ;-)
- ToRead: David Hansen asked for papers that maximise the ratio importance:length and there are some suggestions which won't take much time to read!
- Teaching: Gil Kalai asked for fundamental examples in different branches of mathematics. The thread seems to me to be a very useful source to look for motivation.
- Teaching: Michael Hoffman asked what the undergraduate curriculum is missing and there are various answers and interesting controversies.
- Teaching: Ryan Budney asked for success stories with curriculum reforms (at average research universities).
- Fun: Mathematics in the real world - Theo Johnson-Freyd explains how to calculate using a very long frictionless one-dimensional billiard table.
- Fun: Andrew Stacey asked how to respond to "I was never much good at maths at school" and there are lots of serious answers, like this one by Andrew Tuggle which I like most.
- Understanding: Reid Barton explains how spectral sequences generalise long exact sequences.
- Understanding: Andrew Critch explains a geometric picture of flat modules where "flat" really means "flat" in an intuitive sense.
- Understanding: Scott Carnahan asked for a motivation for (higher) algebraic K-Theory.
- Understanding: Javier gives a rough idea about the field with one element (F_un en français)
- Understanding: Yuhao Huang asked "Why is the decomposition theorem awesome?", but there are not many helpful answers despite links to the de Cataldo and Migliorini article. Have a look at the "related questions" section in the sidebar. I put this question here only because of the decomposition theorem winter school in Freiburg, Germany this month (Feb 2010).
The software MO uses is very well suited for this kind of excerpt, since there are permalinks not only for questions but for answers, too.
So maybe someone who is already thinking about being a math blogger will adopt this idea and watch out for nice general-interest questions&answers on MO, to blog about them occasionally (I won't).