# Cooperation counts for math professor

Martin Nowak sees math in some pretty unexpected places: in the evolution of verbs like "laugh," in the spread of cancer cells, and in the performance of professional bicyclists who trade the lead position with their competitors so they can save energy by drafting off the other's wind.

Nowak, 42, a Harvard University mathematician and biologist, is at the forefront of a new field called evolutionary dynamics, in which Darwin's idea of natural selection is formulated in terms of math equations.

Last week, a paper he worked on was featured on the cover of Nature, the science equivalent of People magazine's cover. And he's currently collaborating with Harvard Divinity School professor Sarah Coakley on the evolution and theology of cooperation.

"The strength of Martin's work is that he's gifted in considering very complex processes and then going to the very core of the problem and formulating, in very simple mathematical terms, a framework that can be easily understood," said Christoph Hauert, a research associate on the theology project. "He's been instrumental in proposing models that lead to new interpretations and insights."

Humans, Nowak believes, evolved to cooperate; and he's come up with the mathematical formulas to prove it.

"The most competitive scenario of natural selection, where everybody competes with everybody else, can actually lead to features like generosity and forgiveness," he said. "That I find great."

Nowak began to wonder about how he could uncover these formulas while still a graduate student at the University of Vienna. What if he used math to decode interactions between opponents? By weighing the relative value of costs and benefits, equations could capture the true value of cooperating in a given situation, depending on whether an opponent cooperates or not.

Consider two prisoners held separately and offered the same deal: If they cooperate with each other by staying silent, the prosecutor can send them to jail for only six months. If both talk, ratting each other out, they'll each get five years. But if one decides to testify and the other doesn't, the prisoner who talks will go free, while the other goes to jail for 10 years.

Without knowing what the other will choose, what should each do?

Their best bet is to testify, no matter what their opponent does. Yet if the prisoners cooperate, they could produce a better outcome for themselves - a six-month sentence. What emerges is mathematical proof that it can pay to work together.

The theory also works for athletes. Last year, cyclist George Hincapie came to a professional road race championship with only one teammate to help him set the pace and battle the wind; and both Levi Leipheimer and David Zabriskie came alone. Even though they were some of the best cyclists in the world, it would be nearly impossible for any one of them to win facing teams with many more riders. So all four worked together trading the lead, so three could conserve energy while one battled the wind. Hincapie and Leipheimer finished one-two.

"Cooperation means someone pays a cost and someone else gets a benefit," Nowak said. "I study what makes cooperation a winning strategy. I analyze it using a metaphor that comes from biological evolution natural selection and mutation," and these basic principles, he said, can be described by exact mathematical equations.

Nowak defines evolution more broadly than simply the changing of genes, which is what brought him into the study of language. The Nature paper, researched by some of his students, concludes that most English verbs behave in an extremely regular way, evolving, for instance, to end in "ed," such as "helped," "laughed," "reached," "walked," and "worked." Certain irregular verbs, including "be" and "think," haven't made that transformation, even though they are 38,800 and 14,400 years old respectively, because they are used so frequently. "The study reveals a simple mathematical law of language evolution," said Nowak. "If a verb is used 100 times less frequently, it regularizes 10 times faster."

Adding math to such a problem allows researchers to predict what will happen in the future, the paper suggests. "We measured something no one really thought could be measured and got a striking and beautiful result," first author Erez Lieberman said in a statement.

Nowak sees his work on cooperation as also closely related to his work on cancer.

"Cancer is a breakdown of cooperation among cells," he said. "Cells receive mutations, which revert them to their primitive program of selfish replication, often killing the organism and themselves."

To beat cancer, he said, scientists need to stop this process of "destructive evolution," re-establishing the cooperation among cells that is needed to protect the body against the disease.

Usually, said Nowak, cooperation leads to improvement, innovation, and productivity. "Molecules combined to form the first cells. Human societies are made up of individuals that cooperate. Whenever evolution is doing something amazingly new, cooperation is involved," he said.

The most successful cooperators, his equations show, choose generosity over greed, forgiveness over retaliation, but there's a message, he believes, that goes beyond his mathematical models.

"A winning strategy must be hopeful. I must assume that it will be possible to cooperate with you," he said. "In everyday life, you always want to believe, as long as possible, the best of the other person."

**Hometown:** Born in Vienna, Austria; lives in Cambridge.

**Education: **Graduated from the University of Vienna in 1987 with a degree in biochemistry; earned his doctorate in mathematics there in 1989.

** ****Other interests:** music (Mahler, Puccini, Beethoven, Mozart); tennis; table tennis.

**Why he doesn't watch the Tour de France: **"I have seen some brief glimpses, but I do not watch regularly because we have no television connection at home."

**Why there's strength in numbers: **"If you write down an equation, it's absolutely clear," said Arne Traulsen, a former postdoc with Nowak who now studies cooperation at the Max Planck Institute for Evolutionary Biology in Germany. "I agree with Martin when he says that mathematics is the language of all science."