Some time ago, I wrote an article on the optimal way to select a mate, assuming you know how many eligible partners exist, and that once you’ve dated someone, you can’t go back and date them again (sorry, Drew Barrymore and that dude from the Apple commercials). This is less romantically known as the secretary problem. Let me briefly recall the problem and its solution: suppose you have n candidates, from which you want to pick the best one. This applies to a variety of situations, from hiring a secretary to finding a girlfriend to apartment hunting. In either case, the outcome is the same: you should look at roughly the first n/e of them (yes, that e), and then select the first one after those n/e which is better than all that you have seen so far. While this strategy won’t guarantee you get the best choice, it . . . → Read More: Finding Love with a Modified Drake’s Equation
Late last year, a study was published in Proceedings of the National Academy of Sciences which tried to pin down origins for the gender gap in mathematics education. As I’ve discussed before, the gender gap in math education is shrinking, and has been shown to be less about biology and more about culture – in cultures where gender equality is weaker, the gender gap is stronger. Nevertheless, even in American culture, the gender gap still persists, and this study by Sian Beilock and others has tried to figure out how, if the gender gap is culturally based, it comes about in young students. The original study can be found here, while a discussion of the study that was featured in the news can be found here.
Professor Beilock and her colleagues tried to correlate young students’ math anxiety with the math anxiety of their teachers. In particular, they looked . . . → Read More: Gender Gap Genesis
In the aftermath of the Super Bowl, some of you fans may be dreading the next six months. To kick off this football drought, I’d like to highlight this article, which was featured on Yahoo yesterday. The article says that Saints quarterback Drew Brees should hope to lose the coin toss at the start of the game, because in the past 43 Super Bowls, the team that won the coin toss had only won 20 times.
An unlucky coin? Unlikely.
Um…what? Who cares? While 20/43 is slightly less than the expected 50%, this difference is not even close to being statistically significant. Actually, the fact that this ratio is only 1 1/2 games shy of the mean is pretty good. Matt Springer has posted an article that discusses why we shouldn’t really care about this difference.
Of course, the sample size is naturally restricted by the small number of . . . → Read More: Lying with Statistics in Football
Big ups to Liz Landau for bringing attention to one of the most important unsolved math problems of our time, the Riemann Hypothesis. Over at the CNN SciTechBlog, she has written a nice article on the problem aimed at a general audience. This year marks the 150th anniversary of the publication of Riemann’s manuscript, where he proposed the now famous conjecture on the zeros of the Riemann-zeta function, and November was the month in which it was published. However, as Landau points out, the exact date of publication isn’t known, which makes having a birthday celebration a little tricky. The American Institute of Mathematics picked today to celebrate, and in honor of Riemann talks were held all around the world.
The Riemann Hypothesis has held the attention of the mathematical community for a century and a half, but it’s also made occasional forays into the realm of popular culture. For . . . → Read More: Happy Birthday, Riemann Hypothesis!
Last month marked the release of Superfreakonomics, a sequel by economist Steven Levitt and journalist Stephen Dubner to the 2005 bestseller Freakonomics. The fanfare surrounding this prefix-enhanced release has been marred, however, by controversy surrounding a chapter on global warming. Starting with this entry on ClimateProgress.org, the debate has drawn a few responses on the Freakonomics blog, but nothing has seemed to blunt the allegations that Dubner and Levitt wrote the chapter from a contrarian perspective without understanding even the fundamental principles of climate science, and as a result, what they’ve written is garbage.
Much of the writing back and forth has been quite heated, and being a student of mathematics I am averse to conflict. However, one response resonated with me a great deal, and as a case study of the arguments that can be made using only simple calculations, it’s quite effective. The response in question comes from . . . → Read More: Debating Superfreakonomics
As you may have heard, last week Martin Gardner celebrated his 95th birthday. Gardner, who authored the “Mathematical Games” column in Scientific American for a quarter of a century, is often credited for introducing generations of young students to the beauty and charm inherent in mathematics. My favorite quote in this vein comes from professor Ron Graham, who is quoted in a recent New York Times article on Gardner as saying that “Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children.” A warm brain is the key to mathematical dexterity.
Both Scientific American and Wired ran articles on Gardner last week, and each one used a different expression to represent his age. Scientific American congratulated him on reaching an age of 25 x 3 – 1, while Wired proclaimed that Gardner had turned 5! – 25. Upon reflection I think I prefer the latter expression . . . → Read More: Martin Gardner and the Three Way Duel
I’m not sure, but this seems like a good candidate for a new bar. According to a recent study out of the University of Washington, as many as half of the population may fail to understand simple probability statements, in the context of weather forecasts.
Here’s the summary:
If, for example, a forecast calls for a 20 percent chance of rain, many people think it means that it will rain over 20 percent of the area covered by the forecast. Others think it will rain for 20 percent of the time, said Susan Joslyn, a cognitive psychologist at the University of Washington who conducted the study.
Coming out of Washington, one would think that the participants would have a better than average understanding of rain forecasts, but now I certainly hope that’s not the case.
That’s American math education for you. Maybe everyone should just move to LA – . . . → Read More: How Low Can We Go?
For those who don’t believe we can actually use math to fight crime, the story of Harry Markopolos, the man who blew the whistle on Bernie Madoff, shows that a dream of using math to catch criminals need not be untenable. In a recent interview for 60 Minutes, Mr. Markopolos describes how he harnessed the power of mathematics to discover that whatever Mr. Madoff was doing, it had to be illegal.
Bernie’s luck was bound to run out sooner or later, as he must’ve known. His seeming success was really nothing more than a giant Ponzi scheme – in other words, he was able to pay his investors amazing returns by taking money from new investors, rather than by creating new wealth. It doesn’t take a mathematician to realize that such a plan is unsustainable, since the more successful your scheme becomes, the more new investors you require in . . . → Read More: Numb3rs in Real Life