Jascha Hoffman

Yes, Virginia, there is a Santa Claus. And, no, Virginia, children don't always smile when they first visit him.

More than 95% of children were visibly indifferent or hesitant when they approached Santa, according to research just performed by a business school professor. While few of the children were smiling, most parents seemed quite happy and excited.

"I thought more kids would be smiling," said John Trinkaus, of the Zicklin School of Business at Baruch College, noting that the children seemed passive and suspicious.

Last week, he observed 300 children at two large shopping malls on Long Island and 30 children at the Macy's department store at Herald Square, noting each child's facial expression - on a scale running from exhilarated to terrified - as they waited to visit Santa Claus.

When asked whether she was afraid of Santa Claus, Jasmine Ghorbani, a grade-school student coming out of Macy's, seemed almost insulted. "It's the 2-year-olds who cry," she said.

At the malls, Mr. Trinkaus found that the overwhelming majority of kids - 82%, to be exact - showed stone-faced indifference in the face of Santa.Sixteen percent showed signs of hesitation, 1% looked happy, and 1% were terrified.

In the smaller survey conducted outside Macy's Santaland in Herald Square, Mr. Trinkaus's research yielded more encouraging results. While the vast majority of children again were indifferent or hesitant, none were terrified, and two were even smiling.

"I wouldn't dispute those numbers," said "Kris Kringle," 737, who lives at the North Pole,but has been working at Macy's since 1862."Some kids take one look, start screaming, and hide behind their parents' legs."

"For kids under the age of 3, I can be a very imposing figure," Mr. Kringle said, adding that a big, hairy man in a bright-red outfit is not what most infants expect to see.

If children aren't ready, he never tries to force a conversation, but rather waits for them to warm up to him. One frightened child, for example, was only willing to conduct the visit after hiding underneath his bushy white beard, Mr. Kringle said.

On the way out of Macy's, 4-year-old Sissel Soderblom looked a bit shaken. "He did a very good job of saying, it's okay to be scared," said her mother, Karen Soderblom of San Diego. "This is the best Santa we've seen."

On the bus to Manhattan, Callie Griffon, a 7-year-old from Guatemala, was sure she didn't want to sit on Santa's lap at Macy's. But after he told her what she would be receiving for Christmas, she told him she loved him, and he returned the compliment, she said.

Around the age of 10, children who no longer believe in Santa Claus may feel too grown-up to ask him for presents, Mr. Kringle said. Once, a group of unbelieving teenagers ambushed him, holding toy guns to his head. Mr. Kringle was unperturbed, saying, "Santa Claus knows a toy when he sees one."

In the study, Mr. Trinkaus suggested that his findings "might suggest a loss of 'innocence' - that kids are growing up too fast, that 'childhood' is vanishing, that the culture is changing and that pragmatism is what counts."

"I don't think I'm as magical a being as I used to be," said Mr. Kringle with a sigh, when asked about the large number of indifferent stares recorded in the study. "Over the last 30 years, the media has been filled with images of me, earlier and earlier.... Christmas has become too commercial."

BERKELEY, Calif. - A reclusive Russian mathematician appears to have answered a question that has stumped mathematicians for more than a century.

After a decade of isolation in St. Petersburg, over the last year Grigory Perelman posted a few papers to an online archive. Although he has no known plans to publish them, his work has sent shock waves through what is usually a quiet field.

At two conferences held during the last two weeks in California, a range of specialists scrutinized Perelman's work, trying to grasp all the details and look for potential flaws.

If Perelman really has proved the so-called Poincare Conjecture, as many believe he has, he will become known as one of the great mathematicians of the 21st century and will be first in line for a $1 million prize offered by the Clay Mathematics Institute in Cambridge.

Colleagues say Perelman, who did not attend the California conferences and did not respond to a request for comment, couldn't care less about the money, and doesn't want the attention. Known for his single-minded devotion to research, he seldom appears in public; he answers e-mails from mathematicians, but no one else.

"What mathematicians enjoy is the chase of really difficult problems," said Hyam Rubinstein, a mathematician who came from Australia to attend meetings at the Mathematical Sciences Research Institute in Berkeley and the American Institute of Mathematics in Palo Alto, Calif., hoping to better understand Perelman's solution. "This problem is like the Mount Everest of math conjectures, so everyone wants to be the first to climb it."

The Poincare Conjecture, named after the Frenchman who proposed it in 1904, is the question that essentially founded the field of topology, the "rubber-sheet geometry" that looks at the properties of surfaces that don't change no matter how much you stretch or bend them.

To solve it, one would have to prove something that no one seriously doubts: that, just as there is only one way to bend a two-dimensional plane into a shape without holes - the sphere - there is likewise only one way to bend three-dimensional space into a shape that has no holes. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe.

Dozens of the best mathematicians of the last century tried with all kinds of approaches to solve the conjecture. Some thought they had it for months, even years, but counter-examples and flaws just kept springing up. Simply-stated but elusive to prove - like Fermat's Last Theorem - this conjecture has spurred the development of whole branches of mathematics.

A decade ago, after some work in the United States that colleagues described as "brilliant," Perelman gave up a promising career to work in seclusion in St. Petersburg. Although he appears occasionally, most recently for lectures at the Massachusetts Institute of Technology and several other US schools last spring, he keeps a very low profile.

Even in mathematical circles, surprisingly little is known about him, and those who know him often don't want to speak publicly about his work.

At any rate, he seems to have used his time alone wisely. While working out the Poincare Conjecture, Perelman also seems to have established a much stronger result, one that could change many branches of mathematics. Called the "Geometrization Conjecture," it is a far-reaching claim that joins topology and geometry, by stating that all space-like structures can be divided into parts, each of which can be described by one of three kinds of simple geometric models. Like a similar result for surfaces proved a century ago, this would have profound consequences in almost all areas of mathematics.

As the foundation for his proof, Perelman used a method called Ricci flow, invented in the mid-1980s by Columbia University mathematician Richard Hamilton, which breaks a surface into parts and smooths these parts out, making them easier to understand and classify.

Although some mathematicians find it disturbing that Poincare's simple question could have such a complicated answer, Hamilton is not worried. After so many failed proofs, he said, "no one expected it to be easy."

Hamilton calls Perelman's work original and powerful - and is now running a seminar at Columbia devoted to checking Perelman's proof in all its detail.

If the proof is vetted, the Clay Mathematics Institute may face a difficult choice. Its rules state that any solution must be published two years before being considered for the $1 million prize. Perelman's work remains unpublished and he appears indifferent to the money. Hamilton, on the other hand, did the foundational work on which the proof is based - but that was over a decade ago. And, as with any major finding, many people have contributed in some degree.

Huge financial prizes raise the stakes for assigning credit for major proofs like this one. For the time being, however, researchers are sharing their approaches with a sense of openness. And the mood is one of cautious optimism that Perelman's approach, even if flawed, will eventually be the one that works.

It takes years for a solution to make the leap from being just another claim to actually being considered "true." Perelman's work will be digested by a wide range of mathematicians in the next few years, said University of California at Davis mathematician Joel Hass. Steps that Perelman pushed through by brute force will be replaced with simpler methods, and his work will be integrated into other fields, Hass said.

And while the equivalent of the Poincare conjecture has already been proven for dimensions four and up, no one yet has any idea how to classify all the spaces that appear in higher dimensions. This state of ignorance is what prods mathematicians to keep working.

"It's interesting how a really good problem can sometimes be much better than a really good answer," Rubinstein said with a grin.