# On the hunt for mathematical beauty

##### March 23, 2012 by Helen Knight

For anyone who has ever taken a commercial flight, it’s an all-too-familiar scene: Hundreds of passengers sit around waiting for boarding to begin, then rush to be at the front of the line as soon as it does.

Boarding an aircraft can be a frustrating experience, with passengers often wondering if they will ever make it to their seats. But Alexei Borodin, a professor of mathematics at MIT, can predict how long it will take for you to board an airplane, no matter how long the line. That’s because Borodin studies difficult probability problems, using sophisticated mathematical tools to extract precise information from seemingly random groups.

“Imagine an airplane in which each row has one seat, and there are 100 seats,” Borodin says. “People line up in random order to fill the plane, and each person has a carry-on suitcase in their hand, which it takes them one minute to put into the overhead compartment.”

If the passengers all board the plane in an orderly fashion, starting from the rear seats and working their way forwards, it would be a very quick process, Borodin says. But in reality, people queue up in a random order, significantly slowing things down.

So how long would it take to board the aircraft? “It’s not an easy problem to solve, but it is possible,” Borodin says. “It turns out that it is approximately equal to twice the square root of the number of people in the queue.” So with a 100-seat airplane, boarding would take 20 minutes, he says.

Borodin says he has enjoyed solving these kinds of tricky problems since he was a child growing up in the former Soviet Union. Born in the industrial city of Donetsk in eastern Ukraine, Borodin regularly took part in mathematical Olympiads in his home state. Held all over the world, these Olympiads set unusual problems for children to solve, requiring them to come up with imaginative solutions while working against the clock.

It is perhaps no surprise that Borodin had an interest in math from an early age: His father, Mikhail Borodin, is a professor of mathematics at Donetsk State University. “He was heavily involved in research while I was growing up,” Borodin says. “I guess children always look up to their parents, and it gave me an understanding that could be an occupation.”

In 1992, Borodin moved to Russia to study at Moscow State University. The dissolution of the USSR meant that, arriving in Moscow, Borodin found himself faced with a choice of whether to take Ukrainian citizenship, like his parents back in Donetsk, or Russian. It was a difficult decision, but for practical reasons Borodin opted for Russian citizenship.

Times were tough while Borodin was studying in Moscow. Politically there was a great deal of unrest in the city, including a coup attempt in 1993. Many scientists began leaving Russia, in search of a more stable life elsewhere.

Financially things were not easy for Borodin either, as he had just \$15 each month to spend on food and accommodation. “But I still remember the times fondly,” he says. “I didn’t pay much attention to politics at the time, I was working too hard. And I had my friends, and my \$15 per month to live on.”

After Borodin graduated from Moscow State University in 1997, a former adviser who had moved to the United States invited Borodin over to join him. So he began splitting his time between Moscow and Philadelphia, where he studied for his PhD at the University of Pennsylvania.

He then spent seven years at the California Institute of Technology before moving to MIT in 2010, where he has continued his research into probabilities in large random objects.

Borodin says there are no big mathematical problems he is desperate to solve. Instead, his greatest motivation is the pursuit of what he calls the beauty of the subject. While it may seem strange to talk about finding beauty in abstract mathematical constructions, many mathematicians view their work as an artistic endeavor.

“If one asks 100 mathematicians to describe this beauty, one is likely to get 100 different answers,” he says.

And yet all mathematicians tend to agree that something is beautiful when they see it, he adds, saying, “It is this search for new instances of mathematical beauty that largely drives my research.”

Explore further: Deciphering hidden code reveals brain activity

## Related Stories

#### Deciphering hidden code reveals brain activity

March 28, 2011

(PhysOrg.com) -- By combining sophisticated mathematical techniques more commonly used by spies instead of scientists with the power and versatility of functional magnetic resonance imaging (fMRI), a Penn neurologist has ...

#### Want to solve a problem? Don't just use your brain, but your body too

June 1, 2011

When we’ve got a problem to solve, we don’t just use our brains but the rest of our bodies, too. The connection, as neurologists know, is not uni-directional. Now there’s evidence from cognitive psychology ...

#### The math of the Rubik's cube

June 29, 2011

Last August, 30 years after the Rubik’s cube first appeared, an international team of researchers proved that no matter how scrambled a cube got, it could be solved in no more than 20 moves. Although the researchers ...

#### Eyes are windows to more than a child's soul

September 1, 2011

Nearly 80 percent of what children learn during their first 12 years is through their vision. Though vision problems may seem easy to identify, they actually can be difficult for parents to discern. Still, parents need to ...

#### Is there a hidden bias against creativity?

November 18, 2011

CEOs, teachers, and leaders claim they want creative ideas to solve problems. But creative ideas are rejected all the time. A new study, which will be published in an upcoming issue of Psychological Science, a journal of ...

#### The quantifier: Building software that interprets medical images

January 12, 2012

Polina Golland’s parents tell the story that, sometime in the early 1980s, when Polina was in junior high, she announced that she wanted to go to MIT. That’s an unusual plan for any 13- or 14-year-old to hatch independently, ...

## Recommended for you

#### Is divorce seasonal? Study shows biannual spike in divorce filings

August 21, 2016

To everything there is a seasonâ€”even divorce, new research from University of Washington sociologists concludes.

#### Researchers plumb the secrets of tissue paper

August 24, 2016

Canada's tissue manufacturers are now much closer to producing the perfect paper, thanks to new UBC research.

#### More than a few good men: Study finds counterintuitive outcomes of gender imbalance

August 24, 2016

Contrary to traditional expectations of unbalanced sex ratios, places with more men than women do not typically experience higher rates of family and social instability, according to a University of Utah study. The study, ...

#### Urban sociologists call for expanding concepts of 'livable cities'

August 24, 2016

A commentary in the current issue of the journal Nature, co-written by Hillary Angelo, UC Santa Cruz assistant professor of sociology, argues that while big cities appear to be islands of sustainable living, issues of social ...

#### An inflexible diet led to the disappearance of the cave bear

August 23, 2016

Senckenberg scientists have studied the feeding habits of the extinct cave bear. Based on the isotope composition in the collagen of the bears' bones, they were able to show that the large mammals subsisted on a purely vegan ...

#### New tiny species of extinct Australian marsupial lion named after Sir David Attenborough

August 23, 2016

The fossil remains of a new tiny species of marsupial lion which prowled the lush rainforests of northern Australia about 18 million years ago have been unearthed in the Riversleigh World Heritage Area of remote north-western ...