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"It is difficult to get through a day in an American school without hearing maxims such as these: "To succeed, you must believe in yourself," and "To teach, you must relate the subject to the lives of students." But the Brookings Institution is reporting today that countries such as the United States that embrace self-esteem, joy and real-world relevance in learning mathematics are lagging behind others that don't promote all that self-regard. Consider Korea and Japan. According to the Washington think tank's annual Brown Center report on education, 6 percent of Korean eighth-graders surveyed expressed confidence in their math skills, compared with 39 percent of U.S. eighth-graders. But a respected international math assessment showed Koreans scoring far ahead of their peers in the United States, raising questions about the importance of self-esteem. In Japan, the report found, 14 percent of math teachers surveyed said they aim to connect lessons to students' lives, compared with 66 percent of U.S. math teachers. Yet the U.S. scores in eighth-grade math trail those of the Japanese, raising similar questions about the importance of practical relevance. "

December 2005 Over the millennia, many mathematicians have hoped that mathematics would one day produce a Theory of Everything (TOE); a finite set of axioms and rules from which every mathematical truth could be derived. But in 1931 this hope received a serious blow: Kurt Gödel published his famous Incompleteness Theorem, which states that in every mathematical theory, no matter how extensive, there will always be statements which can't be proven to be true or false. Gregory Chaitin has been fascinated by this theorem ever since he was a child, and now, in time for the centenary of Gödel's birth in 2006, he has published his own book, called Meta Math! on the subject (you can read a review in this issue of Plus). It describes his journey, which, from the work of Gödel via that of Leibniz and Turing, led him to the number Omega, which is so complex that no mathematical theory can ever describe it. In this article he explains what Omega is all about, why maths can have no Theory of Everything, and what this means for mathematicians."

"In the beauty and geometric complexity of tile mosaics on walls of medieval Islamic buildings, scientists have recognized patterns suggesting that the designers had made a conceptual breakthrough in mathematics beginning as early as the 13th century. A new study shows that the Islamic pattern-making process, far more intricate than the laying of one's bathroom floor, appears to have involved an advanced math of quasi crystals, which was not understood by modern scientists until three decades ago. The findings, reported in the current issue of the journal Science, are a reminder of the sophistication of art, architecture and science long ago in the Islamic culture. They also challenge the assumption that the designers somehow created these elaborate patterns with only a ruler and a compass. Instead, experts say, they may have had other tools and concepts."

"Can men and women ever compete fairly in a sport like running? Yes, but it requires a little bit of maths know-how."

"Melvyn Bragg and guests John Barrow, Colva Roney-Dougal and Marcus du Sautoy explore the unintended consequences of mathematical discoveries, from the computer to online encryption, to alternating current and predicting the path of asteroids. In his book The Mathematician's Apology (1941), the Cambridge mathematician GH Hardy expressed his reverence for pure maths, and celebrated its uselessness in the real world. Yet one of the branches of pure mathematics in which Hardy excelled was number theory, and it was this field which played a major role in the work of his younger colleague, Alan Turing, as he worked first to crack Nazi codes at Bletchley Park and then on one of the first computers. Melvyn Bragg and guests explore the many surprising and completely unintended uses to which mathematical discoveries have been put."

"The economic forecasts are in for 2010, and there are mixed views about whether the economy will turn the corner this year. The consensus among leading economists is for 2.7 percent growth this year. A lot goes in to forecasting the economy and getting the math right is only one of them."

" By applying electrical current to the brain, researchers can enhance a person's mathematical ability for up to six months. "

"What is mathematics? It's neither physical nor mental, it's social. It's part of culture, it's part of history. It's like law, like religion, like money, like all those other things which are very real, but only as part of collective human consciousness. That's what math is. For mathematician Reuben Hersh, mathematics has existence or reality only as part of human culture. Despite its seeming timelessness and infallibility, it is a social-cultural- historic phenomenon. He takes the long view. He thinks a lot about the ancient problems. What are numbers? What are triangles, squares and circles? What are infinite sets? What is the fourth dimension? What is the meaning and nature of mathematics? In so doing he explains and criticizes current and past theories of the nature of mathematics. His main purpose is to confront philosophical problems: In what sense do mathematical objects exist? How can we have knowledge of them? Why do mathematicians think mathematical entities exist forever, independent of human action and knowledge? "

"Andrew Pole had just started working as a statistician for Target in 2002, when two colleagues from the marketing department stopped by his desk to ask an odd question: "If we wanted to figure out if a customer is pregnant, even if she didn't want us to know, can you do that? " Multimedia How to Break the Cookie Habit This article is adapted from "The Power of Habit: Why We Do What We Do in Life and Business," which will be published on Feb. 28. More in the Magazine » Readers' Comments Share your thoughts. Post a Comment » Read All Comments (35) » Pole has a master's degree in statistics and another in economics, and has been obsessed with the intersection of data and human behavior most of his life. His parents were teachers in North Dakota, and while other kids were going to 4-H, Pole was doing algebra and writing computer programs. "The stereotype of a math nerd is true," he told me when I spoke with him last year. "I kind of like going out and evangelizing analytics." As the marketers explained to Pole - and as Pole later explained to me, back when we were still speaking and before Target told him to stop - new parents are a retailer's holy grail. Most shoppers don't buy everything they need at one store. Instead, they buy groceries at the grocery store and toys at the toy store, and they visit Target only when they need certain items they associate with Target - cleaning supplies, say, or new socks or a six-month supply of toilet paper. But Target sells everything from milk to stuffed animals to lawn furniture to electronics, so one of the company's primary goals is convincing customers that the only store they need is Target. But it's a tough message to get across, even with the most ingenious ad campaigns, because once consumers' shopping habits are ingrained, it's incredibly difficult to change them. There are, however, some brief periods in a person's life when old routines fall apart and

Famed screenwriter Charlie Kaufman and theoretical physicist Brian Greene dissect time as we know it. What is the smallest unit of time, and what does it look like? For starters, you should stop looking at the clock, and start looking at the universe.

Parenting sites indicate many New York City parents want caregivers to teach their children a language.

Some interesting questions as to whether parents can "know" it's a good thing or a bad thing to have their children learn a second language. There are clearly cognitive and social costs and benefits that must be weighed.

Computers have become an extension of us: that is a commonplace now. But in an important way we may be becoming an extension of them, in turn. Computers are digital - that is, they turn everything into numbers; that is their way of seeing. And in the computer age we may be living through the digitization of our minds, even when they are offline: a slow-burning quantification of human affairs that promises or threatens, depending on your outlook, to crowd out other categories of the imagination, other ways of perceiving.

"For these days one of America's two great political parties routinely makes equally nonsensical promises. Never mind the war on terror, the party's main concern seems to be the war on arithmetic. On Thursday, House Republicans released their "Pledge to America," supposedly outlining their policy agenda. In essence, what they say is, "Deficits are a terrible thing. Let's make them much bigger." The document repeatedly condemns federal debt - 16 times, by my count. But the main substantive policy proposal is to make the Bush tax cuts permanent, which independent estimates say would add about $3.7 trillion to the debt over the next decade - about $700 billion more than the Obama administration's tax proposals. "

"Certain numbers have magical properties. E, pi and the Fibonacci series come quickly to mind - if you are a mathematician, that is. For the rest of us, the magic numbers are the familiar ones that have something to do with the way we keep track of time (7, say, and 24) or something to do with the way we count (namely, on 10 fingers). The "time numbers" and the "10 numbers" hold remarkable sway over our lives. We think in these numbers (if you ask people to produce a random number between one and a hundred, their guesses will cluster around the handful that end in zero or five) and we talk in these numbers (we say we will be there in five or 10 minutes, not six or 11). "

"Melvyn Bragg and his guests discuss imaginary numbers. In the sixteenth century, a group of mathematicians in Bologna found a solution to a problem that had puzzled generations before them: a completely new kind of number. For more than a century this discovery was greeted with such scepticism that the great French thinker Rene Descartes dismissed it as an "imaginary" number. The name stuck - but so did the numbers. Long dismissed as useless or even fictitious, the imaginary number i and its properties were first explored seriously in the eighteenth century. Today the imaginary numbers are in daily use by engineers, and are vital to our understanding of phenomena including electricity and radio waves."

"Dr. Mandelbrot coined the term "fractal" to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature. "Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you blew them up with a microscope the more complexity you found," said David Mumford, a professor of mathematics at Brown University. "He was one of the primary people who realized these were legitimate objects of study." "

From sociology to mathematics, the academic world as viewed through the lens of "purity."

Thanks to Catherine T. (Oberlin Class of 2014) for this one.

"The physiology of panic, fear and arousal in cinemagoers; the evolutionary psychology of leadership; plus, robonauts and holographic communications"