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Math of the Rubik’s Cube

It’s rare for mathematical research to break into the mainstream media. New papers are posted on the arXiv every day, and published in journals all over the world throughout the year, but unless a famous problem is purported to have been solved (in this case, a famous problem is usually one that has a cash prize associated with its solution), knowledge of such advances is only found by those specifically seeking it. Last week, however, there an exception to this general rule was made for a new result concerning the Rubik’s cube.The conclusion, reached by an international team of mathematicians, is that the Rubik’s cube can always be solved in 20 moves or less, and that, moreover, their result is in some sense the best possible. This result was featured on the front page of Yahoo News for a couple of days, which I found surprising.

What do I mean . . . → Read More: Math of the Rubik’s Cube

Let’s Make a Deal with Paul the Octopus

As summer reaches its midpoint, we come to the end of another rousing year of World Cup soccer. As with any international sporting event, fans all over the world have undoubtedly had their share of ups and downs. Of all the countries in this year’s tournament, however, I think Germany may be receiving the most attention, for even though they didn’t make it into the finals, the Germans have one thing no other country has: a precognitive octopus.

At least, that is what the media would have us believe. For the past several weeks, Paul the Octopus has captured the hearts, minds, and stomachs of people around the world. He’s a charming octopus, to be sure, but it isn’t his good looks that have gotten him this far. Instead, it’s his seeming ability to correctly predict the outcome of soccer matches. As time has gone on and Paul’s predictions have . . . → Read More: Let’s Make a Deal with Paul the Octopus

A New Birthday Problem

Last week, Slashdot posted an interesting link to a problem posed at the most recent Gathering 4 Gardner, a mathematical (or perhaps I should say mathemagical) convention created in honor of the late Martin Gardner. The question, posed by Gary Foshee, is as follows: you have a friend with two children, one of whom is a boy born on a Tuesday. What is the probability that the other child is a boy?

Forget about the Tuesday fact for a moment – if you have a friend with two children, one of whom is a boy, what is the probability that the other child is a boy? You might expect that the answer should be 50%, since the sex of one child shouldn’t affect the sex of the other. But this is not quite right, because you’re not told whether the boy is the older or younger child.

There are only . . . → Read More: A New Birthday Problem

Love and Marriage

I’ve previously discussed some mathematical approaches to dating. Specifically, we have seen how choosing a partner can be modeled as a type of secretary problem, and, if you like, you can estimate the number of candidates you should consider by using a modified Drake’s equation. However, as you know, building a lasting relationship is about more than choosing the right partner; maintaining a happy relationship takes work. And even though most people go into a relationship believing they will not end up as a statistic, the unfortunate reality is that nearly half of all marriages in this country will end in divorce.

How can it be that despite the best intentions of many couples, such a significant proportion will not endure? As one always should, we can turn to mathematics for possible answers. In fact, José-Manuel Rey of the Department of Economic Analysis at the Universidad Complutense in Madrid has . . . → Read More: Love and Marriage

RIP Martin Gardner

Not long ago, I wrote an article in commemoration of Martin Gardner’s 95th birthday. Sadly, it seems this will be my last article in celebration of his birth, as he passed away late last month.

Through his passing, though, his influence has become even more apparent. Perhaps because he published mathematical games in Scientific American for 25 years, the magazine has been the most visible in its veneration of him. There are no less than six articles on Gardner at the SciAm website; while some are reprints of earlier articles, there is also new material from writers and mathematicians who were influenced in some way by Gardner’s unique career. Since I can’t do justice to Gardner the way others already have, let me summarize what you can find if you’re interested in learning more about this stand-up fellow.

If you’d like to learn more about Gardner’s life, SciAm has reprinted . . . → Read More: RIP Martin Gardner

RIP Mr. Escalante

I’d just like to take a moment to remember Jaime Escalante, who died today at the age of 79. I’ve talked about this East LA math teacher whose antics were given a national stage in the film Stand and Deliver before, and out of all the films I’ve seen that try to do justice to mathematics, this one does the best job. So thanks again, Kimo, for reminding us that skill in mathematics, just as with anthing else worth doing, comes from hard work and dedication. Although, I’m sure that a cool hat certainly helps.

Mathematical badass.

Math Really Goes Pop

This morning my good friend Gabe of Motivated Grammar, who is secretly addicted to celebrity gossip, sent me this link to an article from Perez Hilton which is all about mathematics. No, I am not joking – Mr. Hilton apparently loves Grigori Perelman, the mathematician who solved the famous Poincaré conjecture and recently refused a $1 million dollar prize from the Clay Mathematics Institute for his solution.

I'm fairly confident that this is the first time a mathematician has been branded with the Perez Hilton logo.

The Poincaré conjecture, first posed by Poincaré over 100 years ago, is a question about conditions under which an object is essentially a hypersphere, that is, a sphere sitting inside 4 dimensional space. More specifically, it asks whether or not every simply connected, closed 3-manifold is homeomorphic to the 3-sphere (the answer is affirmative). Believe it or not, there is a fairly accessible . . . → Read More: Math Really Goes Pop

Math in the News(paper)

Last year, Professor Steven Strogatz of Cornell University wrote a series of op-eds for the New York Times that discussed the presence of mathematics in unlikely places. I discussed one of these columns here. Now, either those articles were well-received, or Professor Strogatz is well-connected, because this year he’s back in the Times with a much more ambitious series of articles. This time around, Strogatz is attempting to “[write] about the elements of mathematics, from preschool to grad school, for anyone out there who’d like to have a second chance at the subject.”

Preschool to grad school is a significant amount of ground to cover, but thus far Strogatz has used his articles to assault this goal with gusto. To date, he has tackled counting, patterns in addition, negative numbers, division, and basic high school algebra. This doesn’t really do justice to his content, though. Along the way he . . . → Read More: Math in the News(paper)