How did a checkers program that never learned anything prove the game a draw?

It did it with brute force and a lot of patience. Chinook was built from 1989 to 2007 at the University of Alberta by a team led by Jonathan Schaeffer. It combined an opening book, a deep search, an evaluation function and an end-game database for all positions with eight pieces or fewer, and all of its knowledge was programmed by its creators, not learned. In 2007 the team announced that checkers was weakly solved: from the standard starting position, both players can guarantee a draw with perfect play.

The human in the story is Marion Tinsley. Widely considered the greatest checkers player ever, he had a doctorate in combinatorial analysis and lost only seven games between 1950 and his death in 1995, two of them to Chinook. In one game Chinook made a mistake on move ten and Tinsley told it, "You're going to regret that." Schaeffer later checked the database and found that Tinsley had picked the only strategy that could have beaten Chinook, seeing the win 64 moves ahead.

In 1994 Tinsley withdrew from a rematch after six drawn games because of pancreatic cancer, and Chinook was declared Man-Machine World Champion, though it had never beaten him in a match: it had won two games against him, but lost their 1992 match 4 to 2. After a 1995 title defense against Don Lafferty, Schaeffer stopped letting Chinook compete and tried to solve checkers instead. The proof needed about 10^14 calculations over 18 years, using from 200 desktop computers at its peak down to around 50, across a search space of about 5×10^20 positions.