I promise I’ve been mathematically active this summer, despite my little blogging vacation (I do get the summers off, you know!). So, in one post, let me highlight some of the nice stuff I’ve seen around the web recently:

• An island on an island on an island.  Dave Richeson highlights Taal Volcano in the Philippines, a curious and (I think) unique geographical feature.

• The left-handed boy problem. Another post by Dave Richeson (can you tell I’m a fan of his blog?). The post is inspired by this kind of probability question:

Given a randomly selected family that has two children, one of whom is a boy, what is the probability that the other is a boy?

The post is great, but the conversation in the comments is just as great. You’ll notice that I’m a heavy participant. I really liked thinking about this class of problem. It highlights some of the most treacherous territory in mathematics, probability theory. I’ll probably end up devoting an entire post to this topic sometime in the future.

• P ≠ NP. The Math Less Traveled blog hosted this announcement of a possible proof that P ≠ NP, by Vinay Deolalikar. It’s a Clay Mathematics Institute Millennium Problem, which has a $1 million prize attached to its (vetted) solution. Unfortunately, fatal flaws have already been found. Oh well. So it’s still an open problem and perhaps one of my students will solve it someday!

• Stars and Stripes. Slate.com has a fun US flag generator, given any almost number of stars between 1 and 100. It’s great fun to play with the little interactive flag. And the task might provide you countless hours of entertainment, coming up with these arrangements on your own, without its help. A mathematician developed this, so that makes it appropriate for this blog :-).

And now for a bunch of books I read this summer which are all good, all of which I recommend.

• The Mathematical Universe, by William Dunham. It’s not new, I know. But I finally finished reading it this summer and I highly recommend it. I love his lighthearted tone and all the wonderful anecdotes sprinkled throughout the book. It’s the perfect mix of fascinating history and little mathematical facts & puzzles that will make you hungry for more! Feel free to come and borrow it from me.

• Outliers, by Malcolm Gladwell. It’s not purely mathematical–I call these books “pop research” books. Very good read. Tons of great tidbits that you can bring up in conversation, sure to fascinate your next dinner guests.

• Freakonomics, by Steven Levitt & Stephen Dunbar. Another book that’s not really new but that I’ve only recently read. It’s also a “pop research” book–mind candy, if you will.

• Godel, Escher, Bach, by Douglas Hofstadter.  Actually, I’m only half way through this book. But I can already tell you it’s absolutely classic; truly brilliant. Maybe someone will write another book, Godel, Escher, Bach, Hofstadter, someday. Citing books within books would be the kind of recursion that Hofstadter loves. Can’t wait to finish the book…I’m sure to post about again later, and in more detail.