The 10 best mathematicians.

Pythagoras, from a 1920s textbook. Photograph: © Blue Lantern Studio/Corbis

Pythagoras (circa 570-495BC)

Vegetarian mystical leader and number-obsessive, he owes his standing as the most famous name in maths due to a theorem about right-angled triangles, although it now appears it probably predated him. He lived in a community where numbers were venerated as much for their spiritual qualities as for their mathematical ones. His elevation of numbers as the essence of the world made him the towering primogenitor of Greek mathematics, essentially the beginning of mathematics as we know it now. And, famously, he didn’t eat beans.

Hypatia (cAD360-415)

Hypatia (375-415AD), a Greek woman mathematician and philosopher. Photograph: © Bettmann/Corbis

Women are under-represented in mathematics, yet the history of the subject is not exclusively male. Hypatia was a scholar at the library in Alexandria in the 4th century CE. Her most valuable scientific legacy was her edited version of Euclid’s The Elements, the most important Greek mathematical text, and one of the standard versions for centuries after her particularly horrific death: she was murdered by a Christian mob who stripped her naked, peeled away her flesh with broken pottery and ripped apart her limbs.

Girolamo Cardano (1501 -1576)

Girolamo Cardano (1501-1576), mathematician, astrologer and physician. Photograph: SSPL/Getty

Italian polymath for whom the term Renaissance man could have been invented. A doctor by profession, he was the author of 131 books. He was also a compulsive gambler. It was this last habit that led him to the first scientific analysis of probability. He realised he could win more on the dicing table if he expressed the likelihood of chance events using numbers. This was a revolutionary idea, and it led to probability theory, which in turn led to the birth of statistics, marketing, the insurance industry and the weather forecast.

Leonhard Euler (1707- 1783)

Leonhard Euler (1707-1783). Photograph: Science and Society Picture Library

The most prolific mathematician of all time, publishing close to 900 books. When he went blind in his late 50s his productivity in many areas increased. His famous formula eiπ + 1 = 0, where e is the mathematical constant sometimes known as Euler’s number and i is the square root of minus one, is widely considered the most beautiful in mathematics. He later took an interest in Latin squares – grids where each row and column contains each member of a set of numbers or objects once. Without this work, we might not have had sudoku.

Carl Friedrich Gauss (1777-1855)

Carl Friedrich Gauss (1777-1855). Photograph: Bettmann/CORBIS

Known as the prince of mathematicians, Gauss made significant contributions to most fields of 19th century mathematics. An obsessive perfectionist, he didn’t publish much of his work, preferring to rework and improve theorems first. His revolutionary discovery of non-Euclidean space (that it is mathematically consistent that parallel lines may diverge) was found in his notes after his death. During his analysis of astronomical data, he realised that measurement error produced a bell curve – and that shape is now known as a Gaussian distribution.

Georg Cantor (1845-1918)

Georg Ferdinand Cantor (1845-1918), German mathematician. Photograph: © Corbis

Of all the great mathematicians, Cantor most perfectly fulfils the (Hollywood) stereotype that a genius for maths and mental illness are somehow inextricable. Cantor’s most brilliant insight was to develop a way to talk about mathematical infinity. His set theory lead to the counter-intuitive discovery that some infinities were larger than others. The result was mind-blowing. Unfortunately he suffered mental breakdowns and was frequently hospitalised. He also became fixated on proving that the works of Shakespeare were in fact written by Francis Bacon.

Paul Erdös (1913-1996)

Paul Erdos (1913-96).

Erdös lived a nomadic, possession-less life, moving from university to university, from colleague’s spare room to conference hotel. He rarely published alone, preferring to collaborate – writing about 1,500 papers, with 511 collaborators, making him the second-most prolific mathematician after Euler. As a humorous tribute, an “Erdös number” is given to mathematicians according to their collaborative proximity to him: No 1 for those who have authored papers with him; No 2 for those who have authored with mathematicians with an Erdös No 1, and so on.

John Horton Conway (b1937)

John Horton Conway.

The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles. In 1970, he came up with the rules for the Game of Life, a game in which you see how patterns of cells evolve in a grid. Early computer scientists adored playing Life, earning Conway star status. He has made important contributions to many branches of pure maths, such as group theory, number theory and geometry and, with collaborators, has also come up with wonderful-sounding concepts like surreal numbers, the grand antiprism and monstrous moonshine.

Grigori Perelman (b1966)

Russian mathematician Grigory Perelman. Photograph: © EPA/Corbis

Perelman was awarded $1m last month for proving one of the most famous open questions in maths, the Poincaré Conjecture. But the Russian recluse has refused to accept the cash. He had already turned down maths’ most prestigious honour, the Fields Medal in 2006. “If the proof is correct then no other recognition is needed,” he reportedly said. The Poincaré Conjecture was first stated in 1904 by Henri Poincaré and concerns the behaviour of shapes in three dimensions. Perelman is currently unemployed and lives a frugal life with his mother in St Petersburg.

Terry Tao (b1975)

Terry Tao. Photograph: Reed Hutchinson/UCLA

An Australian of Chinese heritage who lives in the US, Tao also won (and accepted) the Fields Medal in 2006. Together with Ben Green, he proved an amazing result about prime numbers – that you can find sequences of primes of any length in which every number in the sequence is a fixed distance apart. For example, the sequence 3, 7, 11 has three primes spaced 4 apart. The sequence 11, 17, 23, 29 has four primes that are 6 apart. While sequences like this of any length exist, no one has found one of more than 25 primes, since the primes by then are more than 18 digits long.

Alex Bellos selects the maths geniuses whose revolutionary discoveries changed our world.

Dilemma for China’s one-child generation: where to spend New Year.

By Keith B. Richburg,

BEIJING – This week begins China’s annual mass pilgrimage, as hundreds of millions of people pack the trains and highways to return to their hometowns for the Chinese New Year holiday known as the Spring Festival.But for one particular group — young urban married couples who grew up as only children — the yearly ritual can also mean tough decisions, sometimes-painful arguments, and a modern-day test for one of China’s most enduring centuries-old family traditions.

These young couples are part of the generation of only children born during the 34 years of China’s “one child policy”. Following the typical pattern, they migrated to the larger cities from the outlying provinces to go to university. They stayed for work, then got married.And now they must decide which set of parents to go visit. It’s a decision fraught with emotion, especially for China’s growing elderly population, who often live alone and far from their children, who have historically been caregivers in a country with little social safety net.

“Both of us want to go back to our home to celebrate Chinese New Year,” said Lin Youlan, 30, a government worker who married her husband, Li Haibin, 33, four years ago. “We always fight about this problem.” She is from Chongqing in southwest China, and he is from Shangdong, on China’s east coast. They live in Beijing, and they are both only children.

Li said as the only son, he is under intense family pressure to visit his parents, who are not in good health. “In Shandong Province, men must celebrate the Spring Festival with their own families. And the wives should spend the Lunar New Year at their husbands’ homes,” he said. “I worry how others will look at my parents if I don’t go back home every year.”

In ancient times, the Lunar New Year’s Eve and the first day of the New Year were spent at the home of the husband’s parents, and the second day was spent with the parents of the wife. But that was in a time when couples largely married from the same village or town, or a relatively short distance away.

Now China’s 1.3 billion people are mobile and rapidly urbanizing. The government announced Tuesday that the country’s urban population had surpassed those living in rural areas, compared to just a quarter of the population living in cities in 1990.

That shift, coupled with the one-child policy and other societal changes, has left tens of millions of elderly people living alone, and often with little in the way of government aid. China also has few nursing homes, and no tradition of professional caretakers to look after the elderly when they become infirm.

China now has 178 million people over the age of 60, according to government census figures. Li Liguo, the minister of social affairs, said that number of over-60s will jump to 216 million, or 16.7 percent of the population, by 2015. At that time, Li said, there will be 51 million “empty nester” old people over 65 and living alone.

But while the older population is growing, China’s current birthrate of about1.54 children per woman is considered far below the normal replacement rate, which is 2 children per woman. (The United States, by comparison, is 2.06).

“The elderly in the countryside is really worrying,” said Therese Hesketh, a professor of global health at the University College London who has studied the impact of China’s population policies.

The problem comes vividly into focus now, with the annual Chinese New Year trek home — a time of year when, psychologists say, many “empty nest” parents grow lonely and depressed.

“Even in the U.K. at Christmastime, this is an issue that comes up,” with smaller families and couples deciding whose parents to visit for the holidays, Hesketh said. “This is a universal issue magnified in China by the one-child policy.”

Some Chinese couples try to resolve the annual conflict by visiting both sets of parents.

Chen Juan, who is 29, and her husband Huang Feilong, 31, met in Beijing through an online dating site, when they saw they were both from Hunan province, from cities about three hours drive apart. They got married in 2008 and spent four Chinese New Years together — 3 at his parents home, and only one with her family. “We fight about this almost every year,” Chen said.

This year, for the first time, they are dividing the weeklong holiday in half, the first and most important days with his family, then the remainder with hers.But the country’s size, and the difficulty of finding bus and train tickets over the holiday period, makes traveling to two sets of parents impractical for many.

Chinese economists and academics have recently been engaged in a vigorous and surprisingly public debate over whether it is time to scrap the one-child policy and allow couples to decide themselves, with some pointing to the empty nester problem as a reason to relax the policy.

But so far, the central government has shown no signs of altering the policy. In a speech last year marking World Population Day, Li Bin, Director of National Population and Family Planning Commission, said China’s growing population remained a challenge, and the government would continue the policy to keep birthrates low.

The policy actually only covers about 35 percent of Chinese, mostly those living in urban areas, with a series of exemptions for many others. Farmers are allowed to have more children, for example, and members of ethnic minority groups are excluded.

The law was implemented in 1978, as a way to control overpopulation and the strain on scarce resources. Authorities estimate the policy prevented 400 million births, and it is credited with helping lift the country out of poverty by reducing the number of mouths to feed.

But the law, which is implemented on the provincial level, also has been harshly criticized. There were reports of some provinces forcing women who were pregnant in violation of the policy to undergo forced late-term abortions or sterilizations. There were also earlier stories of female infants being killed because of a preference for boys. China now has a gender imbalance due to the policy. And the one-child policy takes one of the most basic life decisions — what size family to have — away from individuals.

The law has also been said to have a harder impact on the poor. Some wealthy families now have as many children as they want, since the penalty is a fine they can usually easily pay.

Economists now see another reason to scrap the policy. After three decades of the one-child policy, China is now facing a future labor shortage.

Others here have argued that Chinese families’ increasingly urban lifestyle makes a one-child policy obsolete; most would likely choose to have just one child, this argument goes, since the expense of raising children is so high.

But some young couples who see their own struggles over questions like visiting relatives over the holidays say they are committed to having more than one child.

“I want two children in the future — one boy and one girl,” said Chen Juan.

 

 

 

Which Is America’s Best City?

Based on metrics like school performance, green space, and cultural amenities, Raleigh, N.C., ranks No. 1 in Businessweek.com’s first Best Cities ranking.
:By Venessa Wong.

Ask most people which city they would most want to live in and usually their answers would be shaped by such realities as proximity to their jobs and what they can afford. But suppose you could choose to live anywhere you wanted regardless of cost? What if you could live in a city that offered a wealth of culture, entertainment, good schools, low crime, and plenty of green space? Many people might opt for obvious choices such as New York or San Francisco, but great as they are, data reveal other cities are even better.

Businessweek.com spent months working with data that would help us to identify the best cities in the U.S. We looked at a range of positive metrics around quality of life, counted up restaurants, evaluated school scores, and considered the number of colleges and pro sports teams. All these factors and more add up to a city that would seem to offer it all. When we began the process we had no idea which cities would come out on top. The winner? Raleigh, N.C.
Raleigh No. 1

To most residents of Raleigh, it may not come as a surprise that their city earned the title of America’s Best City. Raleigh shows the cultural graces that go along with anchoring the so-called Research Triangle, home to North Carolina State University, Duke University, and the University of North Carolina at Chapel Hill. Among its many attributes the city sports 867 restaurants, 110 bars, and 51 museums, according to Onboard Informatics, as well as a thriving social scene, good schools, and 12,512 park acres, equal to several times the green space per capita in cities like New York and Los Angeles, according to the Trust for Public Land. It also offers a great deal on nights and weekends—from concerts and opera, to the NHL’s Carolina Hurricanes and college sports, to the 30,000-square-foot State Farmers Market.

Raleigh may have a population of only about 400,000 and span about 144 square miles, yet data show it still offers a lot, if only in a smaller package. True, Raleigh may not be the center of the tech universe like San Francisco, a hub of higher education on the same scale as Boston, or a vibrant 24-hour metropolis like New York, but all those cities also offered higher unemployment, a dearth of parks, worse public education, and other negative factors that weighed against them.

“We’ve always said, you can find about every amenity that you want, even in a city of our size,” says James Sauls, director of Raleigh Economic Development, a partnership between the City of Raleigh and the Greater Raleigh Chamber of Commerce.

The city has been home to an array of celebs including Olympic champion Kristi Yamaguchi, Dexter star Michael C. Hall, and singer Clay Aiken (whose dog was even named Raleigh).
Better, Not Bigger

With help from Bloomberg Rankings, Businessweek.com evaluated 100 of the country’s largest cities based on 16 criteria including: the number of restaurants, bars, and museums per capita; the number of colleges, libraries, and professional sports teams; the income, poverty, unemployment, crime, and foreclosure rates; percentage of population with bachelor’s degrees or higher; public school performance; park acres per 1,000 residents; and air quality. Greater weighting was placed on recreational amenities such as parks, bars, restaurants, and museums per capita, educational attainment, school performance, poverty, and air quality. As living in great cities can be expensive, affordability was not taken into account.

The data for this ranking came from the U.S. Census Bureau, U.S. Bureau of Labor Statistics, Sperling’s BestPlaces, GreatSchools, Onboard Informatics, RealtyTrac, Bloomberg, and the Trust for Public Land.
After Raleigh, the next highest-ranked cities were Arlington, Va.; Honolulu; Scottsdale, Ariz.; and Irvine, Calif. Larger cities placed lower: New York was 14th, while Los Angeles ranked 53rd and Chicago 75th. The highest-ranked city with a population greater than 1 million was San Diego, at seventh. Washington, D.C., which has 588,433 people, came in sixth. Since some criteria were evaluated on a per population basis, places did not necessarily score higher for having a larger number of establishments or amenities.

At the bottom of this ranking of 100 cities were Detroit; Stockton, Calif.; Akron, Ohio; Laredo, Tex.; and Cleveland.
A Park With a City in It

Many urbanites appreciate cities’ bustling streets and constant activity. Raleigh, though active, is often described as “a park with a city in it,” according to the city tourism site, and the downtown area has wide sidewalks, public art, and outdoor cafes, according to the Downtown Raleigh Alliance. With several colleges in the area, it is also a young city and about one-fifth of the population are in their 20s, compared to a national rate of 13.8 percent, show 2010 Census data.

“The Raleigh area features a cluster of great universities, so education is part of the culture of the community,” says Ford W. Bell, president of the American Association of Museums. “Integral to this culture are the region’s museums, rooted as they are in education and lifelong learning.”

Most residents drive, though Raleigh also has a public bus system, including a free bus service downtown.

High quality of life combined with new and expanding business in the region have attracted more residents to Raleigh, one of the fastest-growing U.S. cities: The population in the metro area expanded by an estimated 12.2 percent from 2009 to 2010, according to economic and demographic data company Woods & Poole Economics.
Growing Economy

The city’s largest employers are the state and public school system, according to Raleigh Economic Development. Strong technology, defense technology, biotechnology, and life sciences sectors and emerging cleantech and smart grid industries have bolstered the local economy, says Sauls.

In the weak U.S. economy, Raleigh’s unemployment rate increased to 7.6 percent in July 2011 from an annual average of 4.4 percent in 2008, BLS data indicate, but joblessness in the city remains lower than the metro area, which reached 8.4 percent, and lower than the U.S. rate of 9.1 percent.

Even in today’s tough environment, a number of Raleigh companies are expanding, including software company Red Hat (RHT), which announced in January that it would add 540 jobs. The company had looked at other cities, but as Chief Executive Officer Jim Whitehurst told reporters, Raleigh offered the best overall package.

“It’s a combination of things: There’s a great university system here so it’s easy to find qualified talent and it’s a great place to hire people. The relative cost of living is low, the cost of real estate is dramatically lower [than other cities], and the state is pro-business,” says Whitehurst, who moved to the area in 2008 from Atlanta. And with most of the benefits of a major metropolitan area, he says, “it’s a wonderful lifestyle.”

Indian Republic Day 2012: Thailand PM to be chief guest at parade.

Thailand’s first woman Prime Minister Yingluck Shinawatra will be the chief guest at India’s Republic Day parade celebrations on January 26, Thai trade representative Nalinee Thaweesin said here on Tuesday. Yingluck, who became Thailand’s first woman prime minister last July, will arrive in India on January 24 on a three-day official visit.