As a group of young students troops by, their laughter echoing off display cases of African wildlife, Stephen Wolfram sits in New York's American Museum of Natural History and debunks 160 years of science. I'm scribbling fast and straining not to miss a word from this renowned thinker--a prodigy whose first physics paper was published when he was 15, who earned a PhD in physics from California Institute of Technology at age 20, and who won a MacArthur Foundation "genius" grant a year later, in 1981. Then, after making a mint by creating a software package used by scientists worldwide, he virtually dropped out of sight for a decade.

Moments before, Wolfram and I were standing in front of one of the dioramas, studying a stuffed zebra. Now, parked on a hard bench, he's pointing to photographs in his new 1,200-page book to make his case against natural selection. Conventional wisdom holds that the vast diversity of zebra-stripe patterns is produced by some complicated genetic mechanism and confers a survival advantage. Not so, says Wolfram. The stripes actually result from a simple set of coloring instructions. In essence, Wolfram contends, Mother Nature said: "They're not disastrous for the animal. They're easy to make. So what the hell--let's keep on making stripes."

That may not sound outrageous. But Wolfram is only getting started. He asserts that all complex phenomena are produced by simple rules. Scientists, he says, should be striving to uncover the underlying simplicity--not just searching for explanations by carving complex phenomenon into smaller and smaller, more digestible pieces.

In fact, Wolfram insists, that approach has led to lots of misleading answers. As we wander through the museum, he refutes much of what gets taught in science classrooms. For example, he says he can prove that physics' Second Law of Thermodynamics--that order inevitably disintegrates into disorder--isn't always true. It just seems that way because we haven't been able to concoct the right experiments to show that the second law is reversible.

No doubt his most controversial notion is the radical claim that most of what happens in nature, from the way leaves flutter in the breeze to the thought patterns of our brains, may spring from the same computational processes. "The aphorism that the weather has a mind of its own may be less silly than you might imagine," Wolfram says. "The weather represents computations as sophisticated as anything in our brains."

All this stems from an 11-year odyssey during which Wolfram was holed up at his computer, searching for nothing less than a unifying explanation for every branch of science. Along the way, he tells me, he made several discoveries that lay the foundations for a scientific revolution.

In science as we now know it, great thinkers hatch mathematical formulas to explain how things work, from the pull of gravity to the speed of light. Many of their equations are deceptively simple, like E=mc2. But solving some of them in exquisite detail could take decades, even with the world's fastest supercomputers. So scientists have devised elaborate shortcuts that provide "good enough" approximations. As science probes ever more deeply into nature's enigmas, their shortcut formulas have grown increasingly clever. But they still leave many basic issues unresolved, such as the relationship between gravity and quantum physics.

Now this 42-year-old, self-made multimillionaire declares that he has found a methodology for solving such riddles, explained meticulously in his hefty book, A New Kind of Science. Here, Wolfram posits that virtually everything--the patterns on seashells, the ticks of financial markets, even the universe itself--is the result of instructions as simple as an eight-step software program (table). Unearthing all these rules, he declares, could lead to a new scientific renaissance. Biologists, for instance, could pinpoint the code governing the complex shapes and folding patterns of proteins.

Within a generation or two, Wolfram predicts, his new kind of science will be taught in schools along with chemistry and math. He says his theory may even supplant today's physics; because it doesn't require calculus, it will attract smart researchers who don't want to learn advanced math. Wolfram also foresees a day, perhaps in his lifetime, when his name will be enshrined alongside those of Isaac Newton, Charles Darwin, and Albert Einstein.

Time out! Wolfram makes his claims in such a matter-of-fact way, as if he were passing on the weather forecast, that it takes me a moment to grasp just how audacious they are. No offense, I say, but do you really think you've unlocked the secret to the universe? "Oh, yes," he answers instantly. "I haven't been as bold as this before, but I've been right. There are a lot of things that I've figured out that have been big mysteries for a long time."

Some scientists agree that Wolfram may be blazing a trail. Gregory J. Chaitin, a renowned mathematical theorist at IBM Watson Research Center, hails Wolfram's thesis as "revolutionary." Richard E. Crandall, former chief scientist at NeXT Software Inc. and now at Reed College's Center for Advanced Computation, calls Wolfram's book "a masterpiece."

Not everyone in the scientific community concurs. Some dismiss the book as a rehash of Wolfram's breakthrough work in the 1980s on so-called cellular automata, a type of elementary computer program that generates line after line of black-and-white squares, varying each addition based on the pattern in the preceding line.

For Wolfram, the old science ended in 1984 when he was doing particle-physics research at the Institute for Advanced Study in Princeton, N.J. Fiddling around with cellular automata, he decided to write new rules for producing the successive lines of squares, or cells. At first, the results were symmetrically predictable. Then came Rule 30. This time, the symmetry disappeared: The orderly portion was clearly giving birth to disorder--simplicity was spawning complexity.

Eager to share his discovery, Wolfram flew to California and showed a printout to Richard P. Feynman, a Nobel laureate and former collaborator at Caltech. The two got down on the floor and laid a meter stick at various angles, trying to spot some sign of order--perhaps a hidden fractal pattern that would pop out by examining progressively smaller features. Next, Wolfram says, Feynman spent a week in Hawaii on vacation, mainly holed up with his son, searching for some pattern. He never found one.

That Wolfram would write such a confounding program probably shouldn't have been a surprise. The older son of a novelist father and a mother who was a philosophy don at Oxford University, Wolfram left Eton in 1976 (bored, he says), and St. John's College, Oxford, in 1978 without graduating (still bored). Wolfram left Caltech for a different reason: a legal dispute erupted over the rights to software that he had developed. "I admire Steve enormously for his work on software," says Tommaso Toffoli, a cellular-automata pioneer at Boston University. "But he has been suing everyone forever."

The Institute for Advanced Study was Wolfram's next stop. After three years, he got into another fight, this time over his academic role, and quit in a huff. Even Wolfram's admirers concede that he's a publicity hound. "He has a very robust sense of self-esteem," notes Rudolf Rucker, a computer scientist at San Jose State University. Feeling underappreciated, Wolfram put himself up for bid. The University of Illinois won the auction. It made him a professor of physics, math, and computer science and granted clear intellectual-property rights on his discoveries.

With seed money from his $128,000 genius grant, he founded Wolfram Research Inc. in 1987. Only a year later, he launched Mathematica, a comprehensive program that makes it easy to do higher math, such as symbolic manipulation. It became a runaway hit despite a hefty price tag--the latest version sells for $1,495. Because it can help engineers and scientists gain new insights into complexity, "Mathematica is one of the most important pieces of scientific software ever written," says Larry L. Smarr, head of the California Institute for Telecommunications & Information Technology at the University of California's San Diego campus.

Running a high-tech startup took Wolfram away from academic research. No matter, Wolfram remembers thinking at first. Others would recognize the importance of Rule 30 and take the research forward. But they didn't.

That's mainly because many researchers working in the field of chaos and complexity science don't agree that cellular-automata mechanisms can really explain all complex phenomena. "There must be a missing step," says Raymond C. Kurzweil, author and president of Kurzweil Technologies Inc. "Ultimately, the patterns are not that complex. They're all kind of similar and too low-level to explain the evolution of higher levels of intelligence."

When Wolfram realized that other researchers just weren't getting the message, he decided he needed to do the work himself if his discoveries were to advance. In 1991, Wolfram unplugged from the world. Working alone at home, he sat at his computer for hours on end, running scores of rules to explore how they apply to all branches of science. Typically, he'd work from 10 p.m. until sunup, sleep till mid-afternoon, then spend time with his wife, a former mathematician, and their three children.

The life of a recluse came naturally. Even with the book finally in print, Wolfram doesn't unwind with colleagues or employees at a bar. He doesn't play sports or follow politics. Rare for a mathematician, he doesn't even listen to music, except in his car, if he can find something by Mozart.

According to those who have worked with him, Wolfram was often impatient and condescending. "He wouldn't hesitate to tell you that you're full of it," recalls Theodore Gray, who has known Wolfram since 1987 and is a member of Wolfram Research's executive committee. But Gray swears the man has mellowed in his role as a manager. "He has realized there is no point exploding at people in the production department. That's counterproductive."

Yet arrogance lingers on, and it has carried over to his book. No part was offered for the usual peer-review process. Nor was the manuscript scrutinized by a book editor. Indeed, he balked at taking it to a publisher, preferring to release it himself through Wolfram Media Inc. He notes that other pioneers took a similar course. Both Newton and Darwin spent years in isolation before delivering their bombshells in a single volume.

Past the dioramas of African wildlife, he and I stop at a display of fish. Their sheer variety, Wolfram says, backs up his premise that a simple formula can yield an unexpected profusion of shapes and patterns. While Kurzweil and others don't believe Wolfram has proved that cellular automata also can account for intelligence, Kurzweil admits he's fascinated by their application to certain problems in physics, such as fluid turbulence. "Some aspects of physics actually fit quite neatly," he says, "but the book often doesn't get very far into this."

Perhaps that means Wolfram's ideas won't catch on any faster now than they did before. His book is readable, and its rich illustrations help make his points understandable to nonscientists. Still, he may need to elucidate further to reap scientific acclaim or practical payoffs similar to Mathematica. Cryptography may be the readiest application. The random sequences generated by Rule 30 could work well at encoding information, he expects. Other rules might also yield Mathematica-like tools for understanding the flow of fluids, which could help engineers design better aircraft and buildings.

Mostly, though, the book points to far-off benefits. "This is really basic research--as basic as it gets," says IBM's Chaitin. "This kind of stuff can have practical offshoots, but they could be 50 or 100 years down the road."

Fair enough, responds Wolfram. Now that he has created Mathematica, become rich, started a family, and published a 1,200-page tome, he again has time to return to research and prove that his theories are right. "One of the biggest challenges in doing a project like this is having the confidence to believe that you can do something meaningful," he says--then quickly adds: "This is my piece of philanthropy to the world."

It's much too early to place a value on his gift. But by challenging scientific orthodoxy, Wolfram may force scientists to explore new avenues in their quest for knowledge. That, by itself, could be quite a present. By Michael Arndt

With Peter Coy and Otis Port in New York