One hundred years ago, on Dec. 14, 1911, the Norwegian Roald Amundsen and four companions trudged through fog, bitter cold and lacerating wind to stand at the absolute bottom of the world, the South Pole. Nowhere was there a trace of their British rival, Robert Falcon Scott. No Union Jack mocked them, no ice cairn bespoke precedence. The Norwegians had won the race.

Amundsen and Scott were commanding forces driving early exploration of Antarctica, the ice-covered continent almost half again the size of the United States and unlike any other place on Earth. Both were driven by ambition to win fame by grabbing one of the few remaining unclaimed geographic prizes. Each was different, though, in temperament and approach to exploration, which may have been decisive in the success of one and the undoing of the other.

Earnest and methodical, Amundsen had previously wintered over with an expedition in Antarctica and succeeded in the first navigation of the Northwest Passage, north of Canada, as he learned well how to prepare for work on the planet’s coldest, most unforgiving continent....