One of the reasons that I can market my company’s products and offerings around the world is that the underlying automated rule sets on which they are based utilize the universal language of numbers. An article in The Economist asserts that “the eternal language of numbers is reborn as a form of communication that people all over the world can use—and, increasingly, must use [“Let’s talk about figures,” 22 March 2008 print edition]. The article begins with a Kevin Bacon-like, six degrees of separation story about a Hungarian mathematician who should be well known, but remains mostly anonymous outside of mathematical and scientific circles.
“Brilliance with numbers is a curious thing. Paul Erdos, a Hungarian who died in 1996, used to travel the world and stop briefly at the offices and homes of fellow mathematicians. ‘My brain is open,’ he would announce as, with uncanny intuition, he suggested a problem that, without realising it, his host was already half-way to solving. Together they would find the solution. In a discipline-wide joke, grateful mathematicians still use ‘Erdos numbers’ to indicate how close they were to contact with the great man: ‘Erdos 1’ describes his co-authors, ‘Erdos 2’ indicates their co-authors, and so on. And in all seriousness, the fruits of Erdos’s 83-year life include more than 1,500 jointly authored publications, and a network that extends via his collaborators not only into most areas of mathematics but into many other fields—physics, biology, linguistics and more. With his determination to overcome all the difficulties posed by immigration authorities or language (gestures and formulas were enough, if he and his hosts shared little vocabulary), the Hungarian epitomised many things about his subject. More than most other sorts of knowledge, mathematics has always transcended the limits of time and space. The genius of ancient Greek geometry not only stands the test of time (Pythagoras’s theorem is as valid now as when it was first proved); its discoveries can suddenly find new applications in the 21st century.”
Erdos epitomizes the benefits of connectivity and the ripples of productivity that results. Erdos was a “connector.” In his book The Tipping Point, Malcolm Gladwell defines connectors as “people with a special gift for bring the world together. What makes someone a Connector? The first — and most obvious — criterion is that Connectors know lots of people. … Their importance is also a function of the kinds of people they know.” Gladwell goes on to assert that when it comes to finding “new information, or new ideas — ‘weak ties’ are always more important than strong ties.” The fact that mathematicians created the Erdos number is testament to what Gladwell argues. Erdos also had the advantage of being an expert in the universal language of mathematics. That opened up his opportunities to make acquaintances around the world. The Economist argues that globalization, represented by Internet communication, makes mathematics even more universal and opens up even more opportunities for those with a facility with numbers.
“In an age of e-communications, continent-hopping scholars (not usually as eccentric as Erdos), and journals whose authors and readers come from every corner of the earth, mathematics is coming into its own as a sort of global dialogue in which anybody can take part—and whose fruits are not just beneficial, but indispensable, in just about every area of science. In years past, people with a gift for numbers often overcame vast odds to find an outlet for their genius. Srinivasa Ramanujan was a humble clerk in British India when, in 1912, he began sending theorems to Cambridge professors. Just one recipient saw the work’s value and invited Ramanujan to England. The internet gives today’s Ramanujans a better chance. But in any case, by comparison with the arts, doing well at maths was always much less dependent on cultural or economic factors. A talented number-spinner doesn’t need to be nurtured by visits to art galleries or the opera, or access to a parental library. Nor are the rules of algebra governed by social conventions: a gawky 14-year-old who clams up in interviews can still do well. And pure mathematics, at least, needs no fancy facilities like particle accelerators or wind tunnels. Sometimes a pen and paper is enough. Many a researcher has returned from an international conference with a napkin or beer-mat covered in jottings from a spontaneous and convivial late-night collaboration.”
There is a difference between so-called “pure math” and “applied math.” Businesses tend to be much more familiar with the latter than the former. But the boundary between the two is blurring.
“Admittedly, there is less of a distinction these days between pure maths and the applied sort; that is one of the consequences of a world where all sorts of knowledge seem to spread and fuse in unpredictable ways. For example, the kind of theoretical maths that would terrify a layman has become an indispensable key to understanding the way that living things behave. Anything that grows and disseminates—from single-celled organisms to malignant tumours, from rainforests to the pigments that form stripes or spots in the animal kingdom—can be modelled with the latest computational tools. At a time when the volume of data about every form of life is vast and crying out to be processed, ‘some kinds of pure maths are remarkably useful for biology,’ says Philip Maini, a mathematician who divides his time between Oxford, China, Australia and American campuses.”
The Economist writes about the fact that mathematicians from around the world meet and collaborate in ways that make them one of the most mobile groups in the world — comparable to executives of multinational corporations.
“The world of mathematics is not exactly a market, in the sense of a forum where people always sell to the highest bidder. … But international maths is a form of marketplace, where all sorts of people trade their intellectual wares to enormous mutual benefit. In an age where you need to be numerate to do almost anything else (from building bridges to conquering disease), governments anxiously compare their performance in mathematics with that of competitor nations. This month a new cry of alarm came from America, where a National Mathematics Advisory Panel, established by George Bush in 2006, reported that ‘without substantial and sustained change’ the country was doomed to ‘relinquish its leadership’ in the world of numbers as the century wears on. America has long masked its difficulty in educating enough mathematicians by importing lots of ready-made talent, especially from East Asia and the former Soviet Union. But the problems are real enough. As the panel noted, the share of American students doing degrees in maths or related areas fell from 32% in 1994-95 to 27% in 2003-04. And the share of maths-related doctorates at American universities that went to American citizens or residents fell over the past four decades from 80% of the total to less than 60%. The panel concluded that America’s problems become apparent when students start to study algebra—for most, their first encounter with genuinely abstract thinking.”
This concerns the technical community in the United States. The Tech Council of Maryland (TCM) is set to hold the first National STEM (Science, Technology, Engineering, and Mathematics) Summit 2008: The State of STEM on June 5, 2008. The summit, one of the east coast’s largest, will bring together national and regional experts to network, learn and collaborate about the growing need for developing a STEM initiative in the U. S. This is critical if American scholars are going to remain integral participants in international math discussions.
“For really high-flying mathematicians, the very idea of a national maths culture sounds dated. It comes naturally to them to find collaborators in one continent, publish in another and teach all over the world. But governments cannot help worrying; and the trick of importing fully-trained brains will become less viable as ‘exporting’ countries develop their own systems of higher learning. Among the communist or ex-communist countries whose brightest sons and daughters have often found their way to America, Canada or Australia, there are some interesting differences. As Ari Laptev, the (Soviet-born) president of the European Mathematical Society, points out, Tsarist Russia had a fine maths culture, and even in the darkest Soviet days, pure maths was an island of excellence and integrity. In the post-communist slump, Soviet mathematicians emigrated in droves, leaving a lack of mentors for today’s brainy kids. But in the new mood of nationalism and oil wealth, the mathematicians who stayed in Moscow are walking taller. Their challenge is how to keep youngsters in academia when they could be making money. In China, the cultural revolution hurt maths more than Russia’s Bolsheviks ever did; but these days, Chinese teenagers do superbly in global maths contests, and most of the Chinese doctoral students who people the maths faculties of the world will probably bring their talents home. Opportunities are expanding in China and narrowing elsewhere. China’s output of original mathematical work is still mediocre, but it is improving rapidly. New Chinese journals are being started; inventive minds will soon be filling them.”
There are some interesting initiatives that those in the U.S. (and elsewhere) should consider joining. The Economist puts it this way:
“In any case, it may be time to rethink the very idea of national teaching systems that with varying success prepare youngsters to join a global conversation when they grow up. Already, some of the solutions to school-teaching challenges are as global as could be. Take HeyMath!—an interactive maths-education package co-designed by Britain’s Cambridge University and some bankers in the south Indian city of Chennai: it has served 250,000 children in 33 countries; 2,000 teachers are using it now. Having gained an American foothold in Massachusetts, HeyMath! programmes honed in India (with help from partners in Singapore) are now being tried out by three schools in Connecticut. If only Ramanujan were alive to see it.”
Even those who possess little inclination for mathematics understand its importance. The earlier we expose our children to math the less scary and more intriguing it will become. In its 7 April 2008 print edition, BusinessWeek published a short sidebar titled, “Science? What’s Science?” by Cathernine Arnst. It reported the results of a new Harris Interactive poll that helps explain why children aren’t introduced to science earlier.
“A new Harris Interactive poll may explain why U.S. high schoolers rank 16th out of 30 countries on standardized science exams: Their parents don’t know much about science, either. Harris asked 1,304 U.S. adults to name the most influential role models for today’s youth; 31% picked entertainers (3% named Britney Spears), and 19% named an athlete. Not one chose a scientist. Only 11% could even name a living scientist. Stephen Hawking earned the most mentions. (The fact that a Hawking character appeared on an episode of The Simpsons may have helped.) Three out of four adults also admitted they do not have a good understanding of science. But they’d like their kids to do better. Eight in ten said science is not receiving the attention it deserves in schools.”
In other words, parents recognize the importance of math and science but are so ignorant in those subjects that they don’t know how to begin introducing their children to them or they are afraid to expose their lack of knowledge. As a result, the challenge of getting children interested in math and science will probably remain the task of America’s public school teachers. Professional golfer Phil Mickelson and his wife Amy identified this as an issue and a few years ago teamed with ExxonMobil to establish The Mickelson ExxonMobil Teachers Academy which trains teachers of third through fifth graders in innovative teaching methods and hands-on applications of math and science. The U.S. could use a lot more such initiatives. Until adults get excited about science and math, they shouldn’t expect their children to get excited either.