Nowak’s bald rejection of a sacrosanct evolutionary theory provoked fury in the ranks. Soon after his 2010 paper appeared, 137 scientists signed a letter to Nature expressing their outrage. Many of them condemned the journal for giving Nowak a voice and suggested that the paper was published only because its authors came from Harvard.

“I find this reaction so interesting,” Nowak says today in his heavily German-inflected English, sounding disconcertingly like Arnold Schwarzenegger. “Why adhere to a theory that doesn’t do anything?” He shrugs as if to imply that the flap hasn’t caused him untoward angst. After all, he has been developing his ideas for decades, his research most recently distilled in a 2011 book called SuperCooperators: Altruism, Evolution, and Why We Need Each Other to Succeed.

Ironically, Nowak was raised by his parents to be a fierce competitor. As an only child growing up in Austria, he loved solving the kind of problems that presented themselves in chess and math, a passion that his father encouraged. By the time he reached college in 1983, he didn’t see math as useful, and he declared his intention to be a biochemist so he could understand the foundations of life. But then Nowak reencountered mathematics in a physics class. “The professor posed questions about nature, and we had to answer them through calculations,” he says. “I found this fascinating—the idea that to understand something means to calculate it—and realized I wanted to do theoretical work.”

At the University of Vienna, Nowak began working with the theoretical chemist Peter Schuster, focusing on the mathematics of rna replication. Schuster liked to organize a yearly jaunt to the mountains with his best students, where they would ski all day, then retreat to a cabin for lectures, a communally prepared dinner, and more lectures at night. On one of these retreats, Nowak was transfixed by Karl Sigmund, a mathematician from the University of Vienna. With a crackling fire burning in the hearth, Sigmund presented them with the prisoner’s dilemma, a game theory model devised in 1950.

The prisoner’s dilemma focuses on the choice between cooperation and selfishness. Superficially it seems quite simple: You and another person have been caught by the police on suspicion of criminal activity and are being held in separate cells. The prosecutor visits each of you separately and offers a deal. If you confess and incriminate your accomplice while he or she remains silent, you will be convicted of a lesser crime, serving just one year in prison while your accomplice serves four. In the parlance of the game, you have “defected” from your friendship.

If you and your accomplice both refuse the deal and stay true to each other—remaining “cooperators” in the game’s lingo—you will both be convicted of a lesser crime and serve two-year sentences, since the police do not have enough evidence to convict either one of you of the more serious crime. If you both testify against each other—that is, if you mutually defect—then the police will convict both of you for the serious crime but give you only three years, since you provided some evidence.

Clearly, the best choice for you as an individual is to defect. You get only one year in prison if you rat on your accomplice and he doesn’t rat on you. Even if you both rat on each other, the penalty is three years, not the maximum sentence. It is only the sucker who doesn’t defect while his accomplice does who spends four years in the slammer, the maximum sentence. On the other hand, both prisoners are worse off when they turn on each other than they would be if they both kept silent.

Nowak was fascinated by the prisoner’s dilemma because it provides a mathematical way to study human behavior and, more broadly, the evolutionary costs and benefits of cooperation. Each round of the game generates numbers (the number of years in prison can be considered points), there can be different results based upon different strategies, and all of this can be turned into calculations. With the prisoner’s dilemma, Sigmund said, one could use math to examine the thorniest conundrum of our social lives: how to weigh personal gain against the common good.

For the rest of the alpine weekend and all the way back to Vienna, Nowak talked to Sigmund about the game. He visited him the following day at his office at the Institute for Mathematics in Vienna, which shared a building with a seminary, the priests on the first floor and the mathematicians on the second. “It was total tranquility,” says Nowak, a Roman Catholic who holds fast to his faith. “In biochemistry, we were always breaking things, and there were bad smells. But here there were just empty corridors with someone occasionally walking by, deep in thought. I was amazed that someone could make a living just by thinking.”

In 1987 Nowak decided to do doctoral work with Sigmund on the mathematics of evolution. Their focus was the prisoner’s dilemma and its endless iterations, now parsed with computers and math.

Others had already studied cooperation using the prisoner’s dilemma, notably political scientist Robert Axelrod, who held virtual tournaments in the 1970s. Scientists around the world sent Axelrod strategies for the “prisoners”—instructions for when they would cooperate and when they would defect—to wield in round after computerized round. Each round, the strategies received points; the shorter the prison term, the higher the score.

Over the course of hundreds of computerized rounds, the winning strategy was one called Tit for Tat: Whatever you did in the last round of the game, I will do to you in this round. This strategy relies on direct reciprocity and abounds in the real world, especially in communities where creatures have a history with one another. For instance, Neighbor Jones is more likely to change a flat tire for Neighbor Newell if Newell helped fix Jones’s broken lawn mower last week. It holds true in the animal world as well: A vampire bat is more likely to share a blood meal with others in the cave if those others shared a blood meal with it the last time it failed to find prey.

Nowak and Sigmund regarded Axelrod’s work as an elegant exercise of mathematics but wanted to change the game so that it applied more directly to specific questions in evolution. The classic Darwinian theory of natural selection suggests that individuals who cooperate threaten their own evolutionary fitness, since cooperation always involves a cost to the self (the vampire bat that shares blood has less food for itself). Still, life is full of cooperation, from the single cells that joined to form higher organisms to the construction of cities by humans and intricate communal nests by ants. If cooperation exists so widely, Nowak wondered, what mechanisms were at work to increase cooperation when natural selection seemed to argue against it?

A paper published in Nature in 1976 by Lord Robert May, a British physicist who has made notable contributions to theoretical biology, introduced some new ideas for changing the game and teasing out those mechanisms. May argued that virtual tournaments like Axelrod’s might not accurately replicate the interplay of cooperation and defection in real life. “I pointed out that many of the results from computer modeling depended on [virtual] people deciding on a strategy and following it exactly,” May says. “In reality, there is going to be a lot of noise and error. You need to allow for this.”

In other words, real creatures rarely follow a strategy perfectly. Neighbor Jones usually repays Neighbor Newell’s helpfulness, but if Jones has just had an argument with his wife when he sees Newell coming to ask for help with the flat tire, he may decide he doesn’t want to get his hands dirty. So Nowak and Sigmund set out to create virtual tournaments that allowed for noise and error by conferring probabilistic behavior on the virtual players. Some might defect 80 percent of the time after their partner defected in a previous round; others might cooperate 50 percent of the time even when their previous partner defected. This probabilistic behavior added in the kind of noise that May deemed lacking in pristine models that came before.

To further put the terms of the game into a plausible evolutionary context, Nowak and Sigmund gave winning players and their strategies the power of reproduction. In this new version of the game, the virtual players didn’t just accumulate points when they won; they were rewarded with a duplicate of themselves equipped with the same winning strategy. Their offspring then took the place of another player in the population. The game now mimicked what happens to real organisms: Random mutations resulted in some players having winning strategies that allowed them to triumph and spread those strategies while others died off. After thousands of rounds of the computer playing the game, Nowak and Sigmund would see what kind of strategy for cooperation or defection dominated the population.

As Nowak and Sigmund expected, an approach called Always Defect triumphed for 100 generations. Then it gave way to Tit for Tat for generations, with the two scientists cheering as they watched the gimlet-eyed Always Defectors fizzle out. The game churned on even after Nowak finished his Ph.D. in 1989. He then moved to England to do postdoctoral research with May at the University of Oxford. The first breakthrough in his work with Sigmund happened when Nowak returned to Vienna for a vacation, toting his computer with him. Checking in on his virtual world, he was amazed to see the emergence of a new winning strategy. Later named Generous Tit for Tat, players with this strategy occasionally cooperated, even after the other one had defected.

Nowak saw a huge evolutionary message emerging from these simulations. “What we were seeing was the evolution of forgiveness,” he says. “Generous Tit for Tat suggests that we never forget a good turn, but we occasionally forgive a bad one. It makes a lot of sense. Tit for Tat can create a vendetta, but Generous Tit for Tat allows you to move on.”

As the game continued, Nowak saw that even though Generous Tit for Tat was a long-lived strategy, it didn’t hold sway forever. There were still some Always Defectors that survived, and they were ultimately able to break down the new highly cooperative status quo. A society filled with happy cooperators becomes easy pickings for the selfish, who can tip things back toward dog-eat-dog. But that state, too, will have a few remaining cooperators who eventually tip things back to mass generosity.

We see this pattern all the time in human society. Peace is followed by war, which is followed by peace again. Empires rise and fall. Companies grow, attract the attention of competitors, and lose their market share, but can then reorganize (requiring internal cooperation) and dominate the market again. Every trend of cooperation and defection, it seems, contains the seeds of its opposite. But no matter what happens, Nowak realized that there is always selective pressure toward cooperation.

One day when Nowak was back in Austria, hiking the mountains with Sigmund, they began to talk about cooperation between people who barely knew each other, a behavior called indirect reciprocity. While some experiments have a long and arduous genesis, Nowak in three weeks developed a computer simulation that explained indirect reciprocity. In this game, as in the prisoner’s dilemma, the players either defected or cooperated with each other, but only once—they couldn’t decide how to behave on the basis of previous experience with the other player. But Nowak also added a mechanism by which the players built up a reputation, one that rose or fell according to their history of cooperative behavior. As he expected, the players with good reputations experienced more cooperation than those with bad reputations.

Nowak became convinced that the power of reputation, or indirect reciprocity—being willing to cooperate with someone despite not knowing him personally—is a hugely important factor in human cooperation. And because cooperation has been so important in human development, he concluded that the need to grapple with reputation was a major factor driving the development of language and our powerful brains.

“From very early on, the selection pressure was about social interactions in a group,” Nowak says. “You need to be smart enough to monitor the social interactions in the group, to understand motives and intentions for action. You need to be able to keep it in memory, and you need to be able to talk about it. One theory before this had been that big brains make language possible, but I believe it was the opposite—that the need for language created big brains.”

After nearly two decades of studying the rise of cooperation in populations, Nowak sees the entire world through the prism of the prisoner’s dilemma: He is always looking at the tension between cooperation and defection. In 2006 he had an epiphany of sorts while sitting in a meeting in Japan, jet-lagged from his trip. Working in his head, like the mathematicians at the seminary, he counted five crucial mechanisms that drove cooperation in highly social species like ours.

The first mechanism is Tit for Tat, or direct reciprocity—“I will if you will”—which represented the first outbreak of cooperation in the prisoner’s dilemma simulation.

Next comes the much more advanced mechanism of indirect reciprocity, or reputation, when one individual is willing to help another not because of personal experience but because others have described having good prior encounters with that person.

Nowak identifies the third mechanism as “spatial selection”—interaction born of living in proximity. Within a small area, social networks aid survival and cooperation flowers.

The fourth is multilevel selection, involving larger groups like towns, tribes, or companies. These structures encourage cooperation among their members.

The fifth mechanism is a version of the familiar kin selection, the tendency to cooperate with blood relations. Nowak believes blood ties might play a role—but one defined more by social cooperation than by the propagation of family genes.

Nowak is also open to the possibility of an additional cooperative strategy he has missed. “It would be exciting if we found one. It would make me very happy—I’d have to figure out why it developed and why I missed it. The beauty of all this is how it’s so open-ended,” he says.

Today Nowak is defending and refining his retooled theory of evolution in Cambridge. Visitors trying to find his lair can be put off by the first floor, which is occupied by a large sporting goods store. How could this be a building containing a hub of scientific research? The view is no more convincing when one reaches the sixth floor, where the elevator opens to a Ping-Pong table, a pile of battered paddles, and some bicycles. Just beyond that, a doorway flanked by ornate Roman pillars leads to classrooms and offices along purple hallways studded with folk masks from around the world. “I want people to come in and not really know what’s going on here,” Nowak says when asked about the decor.

The Roman columns are a visual pun: His research center has a program called Research Opportunities in Mathematical Evolution (ROME). “The people participating are called the Romans,” he says. “If many people apply, we say it’s not surprising because all roads lead to Rome. If a project doesn’t work out, we say it’s ok because Rome wasn’t built in a day.”

Nowak’s Program for Evolutionary Dynamics now has 15 colleagues working on diverse subjects for which the mathematics of evolution has been extended to topics as far afield as the spread of infection. Applied to HIV, the model showed that the virus spread so rapidly within the body that the best way to treat it was to attack it quickly with multiple drugs, providing support for the approach used with the aids cocktail.

While first putting together the ROME program, Nowak happened to read one of E. O. Wilson’s papers dismissing inclusive fitness, a paper other scientists seemed to have largely ignored. Nowak knew from his own work with the prisoner’s dilemma that the development of cooperation did not begin with or require kinship, as Hamilton’s advocates believed; in his simulations of the game, it could flourish among any players who interacted with one another. He had read the papers produced by other scientists who were applying inclusive fitness to their work and found the mathematics to be nonsense.

Nowak and Wilson started to talk about their mutual dissatisfaction with the theory. Soon Corina Tarnita joined the fold. As the three elaborated on their points, Wilson pulled out a bobble-head doll of Darwin, which he manipulated to agree with them. “We knew, as the English say, that this would ‘flutter the dovecote,’ ” Wilson says. “We expected it. We took comfort in an article published in 1921 entitled ‘100 Physicists Against Einstein.’ ”

Like Einstein’s 1905 paper on special relativity, the 2010 Nature paper had a simple message: Sacrificing oneself to protect the genes of relatives does not drive the evolution of social creatures. Instead, cooperation emerges to protect the social group, regardless of how closely related members may be.

Such full-scale attacks on the status quo tend not to go down well. “I…don’t know what the editors at Nature were thinking when they published this paper,” wrote biologist Jon Wilkins of the nonprofit Ronin Institute. Inclusive fitness “really changed the kind of data that field biologists who are interested in social traits were collecting,” says his colleague Joan Strassmann, who studies how inclusive fitness governs the behavior of slime molds. Until Hamilton introduced his theory, “people had no idea that so many animals down to microbes could say, ‘You’re my relative; you’re not.’ ” Biologist Jerry A. Coyne of the University of Chicago summed up the views of many colleagues when he wrote, “If [Nature] had gotten decent reviewers, and followed their advice, [the paper] never would have seen print.”

The virulence of the reaction stunned those in Nowak’s camp. “There’s a weird level of anger about this,” says Roger Highfield, a chemist and former editor of New Scientist magazine who was Nowak’s coauthor on the SuperCooperators book. “I’ve been covering scientific controversies since the mid-1980s. Usually if other researchers don’t like your paper, they bend over backward not to come across as swivel-eyed, foaming-at-the-mouth furies, but that’s exactly the response.”

Highfield wonders if some of the rage stems from fear that any challenge to accepted evolutionary theory could be used to undermine evolution itself. “There’s an unease from some quarters that you will give ammunition to the creationists and intelligent design people—that they’ll say, ‘Ah, this shows flaws in Darwinian theory,’ ” he says. Perhaps Nowak became a lightning rod because, as a practicing Roman Catholic, he stands out in a field where most people keep their religious proclivities (if any) under a hat. But May, Highfield, and others who have worked with Nowak contend his faith doesn’t influence his science. “Martin is just trying to put evolution on a rigorous mathematical foundation,” Highfield says.

Even though the fight over inclusive fitness has sucked up a lot of the air recently, Nowak’s broader ideas seem to be taking hold. “What Martin is saying is that cooperation is to be expected,” says David Krakauer, an evolutionary theorist at the University of Wisconsin at Madison. “We think of prosocial behavior as requiring institutions that reward and direct our behavior. Churches, legal structures, and bureaucracies are all there to temper the so-called innate proclivities of human beings. Martin’s big point is that that’s not the complete picture. Cooperation doesn’t require a magistrate’s court.”

It is an innate part of the biology that helped us evolve. Cooperation lies at the core of who we are.

TRIBAL COOPERATION Biologist Martin Nowak has identified five mechanisms that drove the evolution of cooperation. One of the most powerful is group selection: In a competition between groups such as tribes, the one that has tighter bonds and more cooperative members will tend to win out.

ALL IN THE FAMILY Since the 1960s, most evolutionary biologists have thought that cooperative behavior arose from the individual’s need to ensure the survival of the genes of close family members. Nowak disagrees: He argues that so-called kin selection is just one of several mechanisms driving a more general impulse toward cooperation.

A NEIGHBOR IN NEED Studies have shown that individuals have a tendency to sacrifice themselves for the good of those living in close proximity, regardless of how closely related they are.

I WILL IF YOU WILL The most basic form of cooperation, dubbed direct reciprocity, arises when an individual will do another a good turn in the expectation that sometime in the future she can expect similar ?treatment in return.

Kristin Ohlson is a freelance journalist, essayist, and fiction writer based in Cleveland.