There was a time, not long ago, when computers—mere assemblages of silicon and wire and plastic that can fly planes, drive cars, translate languages, and keep failing hearts beating—could really, truly still surprise us.

One such moment came on February 10, 1996, at a convention center in Philadelphia. Two chess players met for the first of six tournament matches. Garry Kasparov, the Soviet grandmaster, was the World Chess champion, famous for his aggressive and uncompromising style of play. Deep Blue was a 6-foot-5-inch, 2,800-pound supercomputer designed by a team of IBM scientists.

“There was no way that this tin box was going to defeat a reigning world champion,” says Maurice Ashley, an American grand chessmaster who provided live commentary for the game that day.

Kasparov thought so, too. He’d previously scoffed at the suggestion that a chess-playing computer might defeat a grandmaster before the year 2000, which, back then, probably seemed pretty ridiculous to most people. Personal computers were just over a decade old, and looked liked this. Commercial companies had begun providing Internet access to the general public only the year before. Chess required guile, wit, and foresight—distinctly human traits—and a hunk of hardware, the chess community thought, could not replicate all that—at least not well enough to beat Kasparov.

But the tin box won that game, becoming the first computer to defeat a sitting world chess champion.

Chess players and computer scientists alike were stunned. Computers were by then known for doing some things better than humans could, like solving complex math problems or processing employees’ paychecks. “But everybody knew that chess required intelligence to play well, so to see that a computer could do this and compete with the best player in the world—that was sort of a wakeup call,” says Murray Campbell, one of the IBM computer scientists who developed Deep Blue, and a competitive chess player himself. “It was a sign that a lot more was coming.”

The concept of chess-playing machines dates back centuries. One of the first iterations was rather dishonest: an automaton created by Wolfgang von Kempelen, a Hungarian inventor, in the 1760s only managed to win because the human player hidden inside was pulling levers to move pieces across the board. It took humans until the 1950s to program machines to observe the rules of chess. By the 1980s, computers could conduct basic searches of potential moves and strategies, but at considerably quick speeds, searching several thousands positions per second. They started competing against skilled human players—and winning. In 1987, Deep Thought, the precursor to Deep Blue, defeated British chessmaster David Levy.

“Deep Thought sees far but notices little, remembers everything but learns nothing, neither erring egregiously nor rising above its normal strength,” the IBM scientists wrote in 1990. “Even so, it sometimes produces insights that are overlooked by even top grandmasters.”

Deep Blue was considerably more advanced. At its core, the computer was built to solve complex numerical problems. In front of a chess board, Deep Blue, equipped with data from hundreds of existing master games, would scan the board for features it recognized. Like a human player, the computer thought ahead, exploring potential moves in terms of sequences, envisioning future positions. It numerically rated the moves as it went, finally making the one that came out with the highest rating—the “best” move. Deep Blue was capable of evaluating 100 million positions per second.

Kasparov went into the historic game in 1996 feeling confident, but it soon became clear Deep Blue was a tougher competitor than he’d expected. Kasparov, already known for being an animated player, was visibly frustrated during the game, often shaking his head, says Jeffrey Popyack, a computer science professor at Drexel University who was in the room. At one point, Kasparov spent 27 minutes deliberating before moving his queen. “The thing that really sticks with me now was just the anguish that Kasparov was going through,” Popyack recalls.

Toward the end of game, Kasparov and Deep Blue were like “two sumo wrestlers battling one another at the edge of a high cliff,” as Monty Newborn, chairman of the computer chess committee for the Association of Computing Machines, once put it. Kasparov was mounting an aggressive attack on Deep Blue’s king when the machine made an unusual move—going after a pawn across the board—that suggested the machine was unaware it was in trouble. (“It would be kind of like your house was burning down and you decided to go grocery shopping,” Ashley, the American grandmaster, said.) Turns out the computer had calculated that Kasparov’s move—a bold bluff that would have intimidated a human player—wasn’t going to work. The world champion, visibly distraught, resigned a few moves later.

Modern, game-playing artificial intelligence is, well, even scarier. In 2011, Watson, an IBM super computer capable of answering open-ended questions posed in human language defeated Ken Jennings on Jeopardy! Last month, a computing system developed by Google researchers bested the top human player of Go, a complex 2,500-year-old game that depends heavily on intuition and strategy. (Popyack points out that, despite all that, computers are still not very good at programming other computers.)

Human players are successful if they can spot their opponents’ blind spots, and supercomputers are built to find even the smallest of errors and exploit them. “It’s never going to get tired, and it’s never going to get overconfident, and it’s just going to kill you,” Ashley said. “That’s the difference now. It’s like playing the Terminator.”

Kasparov rebounded in the second game against Deep Blue, and went on to win the whole six-game series. But the scales had been tipped. And in a subsequent matchup in 1997, Deep Blue triumphed. Humans were no longer winning the battle between man and machine.

“It’s a really dangerous business to say, ‘computers will never,’ and then say something after that,” Campbell says.