Mathematics

I'm afraid I have to blog and run today. I have to scamper off to Dulles Airport an hour from now to retrieve a friend. (Don't worry, I've already set the VCR to tape the premiere of Prison Break!) So why not have a look at Slate's take on the Poincare conjecture. It includes this memorable description, attributed to mathematician Christina Sormani, of what the conjecture actually says: The Poincare Conjecture says, Hey, you've got this alien blob that can ooze its way out of the hold of any lasso you tie around it? Then that blob is just an out-of-shape ball. [Grigory] Perelman and […
A reader asked me, in response to yesterday's post, why I failed to make any mention of the Mobius Strip. Addressing that topic seemed like a good way to close the week's blogging. Imagine that you take a long thin strip of newspaper. Hold it at the top with your thumb and index finger, and let the bottom dangle loosely. Now grab the bottom and give it a half-twist. Take the narrow side at the bottom, and bring it up so the short edge meets up with the corresponding short edge where you are holding the newspaper. Tape these ends together. The result is a Mobius Strip. Click here for…
Tuesday's New York Times had this lengthy article about progress on one of the great open problems in mathematics: Poincare's conjecture. Actually, it looks increasingly likely that the problem is no longer open: Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincaré conjecture, about the nature of space. After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back…
In a recent post, I mentioned the common confusion between randomness and stochasticity. A couple of commentors brought this issue up, so I'll discuss it further (I really do read your comments...). Needless to say, with mathematicians and philosophers lurking around these ScienceBlogs, I'm giving one biologist's amateur perspective on what these terms mean. Let's start with randomness. I don't mean random in an existential 'does life have any meaning?' sense (Yawn. You bore me. Stop worrying about that and go do something meaningful. Or have an ice cream cone). By random, I mean…
Polymathematics has posted another excellent essay on the subject of whether .9999...repeating equals one. This time he is responding, very effectively, to various counter arguments raised by commenters. One small comment of my own, though: The name of the blog is “EvolutionBlog.” One word. Reading the various comments left to the post reveals two kinds of skeptics. Some are people who are perfectly willing to accept that .9999...=1, but find the logic justifying this conclusion to be hard to follow. No shame in that. The idea of the limit of an infinite series is not a simple one,…
I've always liked soccer balls -- and not just because you can play soccer with them. The arrangement of pentagons and hexagons to form a surfaces that's reasonable spherical always seemed outstandingly clever. Who was the genius who first realized you could do that? Well, my world has been rocked. I still think the soccer ball is clever, but in and entirely different kind of way. Tonight I was flipping through the copy of American Scientist that arrived with today's mail, looking at the pictures*, and I came across this article on the topology (and combinatorics) of soccer balls. (The…
There's an interesting blog discussion going on about the age-old question of whether .99999..., where the nines go on forever, is actually equal to one. The answer is: Yes, it does, and if you think it does not then you are mistaken. Polymathematics got the ball rolling with several arguments establishing the equality of the infinite decimal on the one hand and the number one on the other. Mark Chu-Carroll offered some follow-up thoughts here. One way to prove that .9999... repeating equals one is to realize that the notation “.9999...” is really just a short-hand way of writing the…
The New York Times is reporting that President Bush has chosen Larry Faulkner, a chemist and a former President of the University of Texas at Austin to head the National Math Panel: The former president, Larry R. Faulkner, who led the university from 1998 until early this year, will be chairman of the National Math Panel, which President Bush created by executive order in mid-April. The panel is modeled on the National Reading Panel, which has been highly influential in promoting phonics and a back-to-basics approach to reading in classrooms around the nation. Though that panel has been…