Big Primes, Small Numbers, Sarah Palin and the Financial Crisis

Nov. 2, 2008 — -- This month's "Who's Counting" will be an assortment drawn from mathematically flavored stories in the news.

A 13-Million-Digit Prime Number

The first concerns a number that easily swamps even the billions and trillions cited in recent financial stories. We know a lot about the existence of millions of subprime mortgages, but little media attention has been devoted to the existence of a just-discovered 13-million digit prime number. (A prime number, recall, is one divisible only by itself and 1. The numbers 3, 19 and 37 are prime, whereas 6, 33 and 49 are not.)

Mathematicians at UCLA won the $100,000 prize offered by the Electronic Frontier Foundation for discovering this humongously large prime number. It is a Mersenne prime number, a prime number of the form 2^P-1, where P is also prime. In this case P = 43,112,609, and the 13-million digit number is 2^43,112,609 - 1.

To find a Mersenne prime having more than 10 million digits and thus win the prize, people from around the world contributed the power of their underused computers in order to perform the complex and repetitive calculations required.

Such an accomplishment may strike many as pointless, but prime numbers and the difficulty of factoring nonprime numbers into primes is part of what allows the secure transfer via numerical code of trillions of dollars around the world.

Small Number Sense and Mathematical Ability

Another story that appeared recently concerns a study at Johns Hopkins University that established a connection between students' intuitive "number sense" and how well they performed in mathematics class.

Specifically, the researchers looked at the ability of 14-year-olds to look at collections of flashing blue and yellow dots on a computer screen and quickly determine which color dot was more numerous. If the difference is great -- say eight yellow and 20 blue dots -- this is easy, but if the numbers are closer, the task is more difficult.

A keen ability to discern the relative magnitudes of blue and yellow dots at a glance -- i.e., a good number sense -- correlated strongly with their past performance in math up to that time.

Whether this connection is causal, which direction it runs if it is, and whether number sense can be easily improved are unanswered questions.

In any case, this result is a little surprising because formal mathematics is abstract, whereas recognizing the relative magnitudes of small numbers seems much more intuitive and visceral, a skill that even some animals possess.

Another question occurs to me. In my classes, I often stress estimating and comparing large numbers -- the height of buildings, the number of coins in a jar, etc. -- and wonder whether there is a similar correlation between an ability to accurately estimate and compare large numbers and a facility with formal mathematics.

This latter skill is often useful in political discourse. A topical example: In an Oct. 24 speech in North Carolina on special needs children, vice presidential candidate Sarah Palin stated, "Sometimes these dollars, they go to projects having little or nothing to do with the public good, things like fruit fly research in Paris, France. I kid you not."

This, of course, is plain ignorant, because over the years research on fruit flies has played a seminal role in understanding human biology, particularly genetic disorders affecting children.

Numerically interesting is the fact that California congressman Mike Thompson recently obtained a $211,000 grant for USDA research in France to study the control of a kind of fruit fly.

Note that this is only $61,000 more than the cost of Palin's campaign wardrobe. I kid you not.

Did Mathematicians Cause the Financial Crisis?

Finally, I'd like to note that some commentators have blamed mathematicians and physicists for the financial crisis. The claim is that their introduction of derivatives and other unfathomably complex financial instruments somehow led to the credit crunch and related maladies.

The counterargument points out that mathematicians are not at fault if the various mathematical models they constructed are misused. For example, I often come across people who misinterpret some piece of statistical software and then draw absurd conclusions from their misinterpretations.

On the other hand, there might be a small bit of responsibility that can reasonably be assigned to mathematicians. If the assumptions underlying a particular mathematical model are unwarranted, then the mathematicians who constructed it are at least partially culpable.

An example of an earlier crisis, the collapse of the Long-Term Capital Management hedge fund in 1998, is relevant. Two of the fund's founding partners, Robert Merton and Myron Scholes, were Nobel Prize winners, but despite their presence on the board of LTCM, this earlier debacle roiled the world's financial markets and, had not emergency measures been enacted, might have seriously damaged them.

Here too, however, it's not true that the LTCM collapse was primarily the fault of the Nobel laureates and their models. Most analysts believe it was a consequence of a "perfect storm" in the markets, a vanishingly unlikely confluence of chance events. The specific problem encountered by LTCM was, as it is today, a lack of liquidity in world markets, and this was made worse by the disguised dependence of a number of factors that were assumed to be independent.

Consider, for illustration's sake, the probability that 3,000 specific people will die in New York on any given day. Provided that there is no connection among them, this is an impossibly minuscule number. But if most of these people work in a pair of buildings, the independence assumption fails. The 3,000 deaths are still extraordinarily unlikely, but not impossibly minuscule.

Bottom Line

So whether the topic, like 13-million-digit Mersenne primes, seems far removed from our everyday lives or, like the financial crisis, promises to affect our houses, jobs and well-being, mathematics is implicated. Let's hope there are enough young people who appreciate scientific research and are good at quickly discerning the difference between eight yellow dots and seven blue ones. Without them we'll end up behind the eight ball.

John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as of the just-released "Irreligion: A Mathematician Explains Why The Arguments for God Just Don't Add Up " His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.