Mihai Pătraşcu, cause of numerous flame wars on the complexity blog, as well as lonely campaigner for the rights of esoteric data structures everywhere, has a blog, self-billed as ‘Terry Tao without the Fields Medal‘.
Enjoy !
My Biased Coin: A New Blog !!
It’s been a while since I’ve been able to announce a new CS blog. Please point your bookmarks/RSS newsreaders/browsers to Michael Mitzenmacher’s new blog, My Biased Coin. Michael has occasionally posted over here, and has often had comments and suggestions for me. When he’s not brokering peace agreements between power law distributions and log normal distributions, Michael corrupts young grad students at Harvard for a living, filling their minds with all kinds of random bits that are occasionally error corrected.
8th carnival of mathematics
It’s back-to-school night at the carnival of mathematics. Time to revisit, reflect, and ponder on things we think we already know.
Estraven at Proving Theorems wishes that mathematicians today spent more time revisiting and bring up to date older, more inaccessible works of mathematics. This is discussed in the context of a re-publication of some of Grothendieck’s early work on schemes.
There’s a lovely quote at the end of the article, one that I cannot but help share:
I could of course keep writing paper after paper. But there is so much beautiful mathematics out there that I don’t know yet, and I want to read at least some of it before I die
I remember first sensing beauty when I first learnt Burnside’s Lemma: Leadhyena Inrandomtan at Viviomancy has a detailed post on this simple, and yet elegant result in combinatorics.
Burnside’s Lemma ultimately deals with counting symmetries: Ian Stewart has a new book out on the history of symmetry titled, “Why Beauty is Truth: A History of Symmetry”. In a post at the Brittanica blogs, he describes why he decided to write this book.
In an ongoing series, John Amstrong continues his unapologetic look at coloring knots. I’d say any topic that has phrases like ‘involuntary quandle’ is worth studying. Of course, the original tying-yourself-in-knots proof was the diagonalization method of Cantor, which Mark Chu-Carroll is kind enough to explain to us, while he takes a timeout from beating errant creationists with sticks of logic. Mark notes that he’s been going back to some old books on Set theory and is thoroughly enjoying them, another example of the theme of the day 
Godel’s incompletenes theorem is another of the tying-yourself-in-knots variety, and this year’s Godel prize winner is a result in the same vein, showing why certain “natural proof structures” cannot be used to prove P != NP. Siva and Bill Gasarch have the scoop.
Walt at Ars Mathematica catches up to the Bulletin of the AMS, highlighting some nice expository articles that should make Estraven happy.
It’s time to get educational now. Dave Marain helps high school math teachers everywhere with lesson plans for teaching quadratic systems and tangents without calculus. Mikael Johansson shows bravery far above and beyond the call of duty, explaining fundamental groupoids to a group of 9th graders. Heck, I don’t even understand what a groupoid is, and I read John Baez all the time !
jd2718 shows his students how Fermat is connected to them. It would be remiss of me not to give a shout out to the Mathematics Genealogy Project. We’ve all heard the horror stories about the students who write “dy/dx = y/x”; Dan Greene at The Exponential Curve talks of students who write “log 5/log 2 = 5/2″ and wonders if we need to change the notation for log to something more “mathematical”.
I am delighted, and surprised, to see the quality of reports produced in the undergraduate
automata class that Leo Kontorovich is TAing. Read more about what his students did here. Andy Drucker weaves tales (tails?) of dogs eating steak in mineshafts, and cats climbing GMO-compromised trees, to explain some of the subtler details of computability theory.
We’re almost ready to wrap up this edition of the carnival. Chew on some simple brainteasers that will excercise regions of your brain that you may not have known existed ! And review the history of calculating devices, with some speculation on what future calculators might look like.
Finally, no carnival of mathematics would be complete without a cartoon by XKCD:
And that’s all, folks ! Keep those posts coming. The next Carnival of Mathematics is in two weeks, hosted by JD2718.
The 7th Carnival of Mathematics is out
I’ll be hosting the next one, so if you have a submission you’d like to be publicized, send it to sureshv REMOVE at THIS gmail AND dot THIS com. Or, you can submit it at the master blog carnival site.
Miscellaneous links
It’s a good day for math blogging. Gil Kalai, guest blogging for Terence Tao, explains the weak -net conjecture for convex sets (and can I say that I’m very jealous of the impeccable LateX typesetting on wordpress.com). Leo Kantorovich presents an interesting example of the breakdown of discrete intuition from the Steele book on the Cauchy-(Bunyakovsky)-Schwarz inequality. Andy Drucker talks about why convexity arises naturally when thinking about multi-objective optimization.
An ending…
They say, “all good things come to an end”. What they don’t say is, “if good things didn’t end, you wouldn’t realize how good they were”.
Lance announces today that he’s shutting down the Computational Complexity blog. As far as I know, he’s the ur-TCS blogger, and was the direct inspiration for my starting the Geomblog. I’ve always had the Complexity blog on my must-read list, and have felt both pressured (to write better posts) and inspired (by the rich content) every time I’ve seen a new posting.
Another aspect of Lance’s blog that I envy is the rich commenter community: he was able to create a forum for discussion of TheoryCS, on matters both technical and non-technical, that will be hard to replace.
So thanks for all the posts, Lance, and hopefully you’ll be back one day !
Meta-posts
I was browsing my referrer logs and found a callback to Lance’s blog. In the comments for the post, I see this comment (emphasis mine):
Here’s one that I’ve found very vexing: Let A(d) denote the least surface area of a cell that tiles R^d via the translations in Z^d. Improve on the following bounds:sqrt(pi e / 2) sqrt(d)
(It’s a little more natural to consider A(d)/2 than A(d).)The lower bound is by considering a volume-1 sphere, the upper bound by monkeying around a little with a cube’s corner.
Any proof of A(d)/2 >= 10sqrt(d) or A(d)/2
For motivation: Either pretend I posted on Suresh’s blog (so it’s just a problem in geometry); or — it’s related to finding the best rate for parallel repetition of a simple family of 2P1R games.
It’s a meta post !!! And by the way, there’s no such thing as “JUST a problem in geometry”. Harumph !!
