In March 1776, months before the Declaration, Adam Smith looked across the Atlantic and wrote what reads like a prophecy now: “From shopkeepers, tradesmen, and attornies, they are become statesmen and legislators, and are employed in contriving a new form of government for an extensive empire, which, they flatter themselves, will become, and which, indeed, seems very likely to become, one of the greatest and most formidable that ever was in the world.” No war had been won. No nation had even been declared yet. But a Scottish economist saw it coming.

The Overmountain Men surrounded the base of Kings Mountain. They attacked from every side at once. Long rifles cracked from behind trees and rocks as they climbed. Their accuracy deadly against the Loyalists’ smoothbore muskets. Ferguson's Loyalists answered with volleys and bayonet charges to drive the frontiersmen down the slope. The mountain men had no bayonets. They didn't need them. They fell back, then turned and shot the Loyalists on open ground. All while yelling and whooping like devils. Ferguson rode back and forth across the ridge, blowing a silver whistle to rally his men. He wore a bright checkered shirt so his troops could see him. He cursed the men he looked down on, calling them backwater men. And ordered charge after charge. But the Overmountain men would not break as easily as he thought. They reloaded on the run, took cover here, popped out there, and kept pressing upward. Again and again they surged up the slope, and each time they held more of the ridge. When the position began to collapse, Ferguson tried to cut his way out with a desperate charge. He was shot from his horse, his body riddled with bullets. With their commander dead, the Loyalist resistance crumbled. The Battle of Kings Mountain was over in barely an hour. It was a crushing victory for the Overmountain Men. October 7, 1780.

In 1876, a sitting congressman worked out a brand-new proof of the Pythagorean theorem during a casual math discussion with colleagues. His name was James Garfield. Seventh term from Ohio. Five years from the presidency. It appeared in the New England Journal of Education that April. Garfield remains the only U.S. president to have contributed something original to mathematics.

In the dark tunnels beneath 1800s Colorado, the miners weren't alone. They shared the mines with the Tommyknockers. Two feet tall. Wrinkled faces. White whiskers. Dressed in tiny mining clothes. Cornish immigrants brought the belief with them after the gold and silver rushes. Soon every mining camp in the state knew the stories. The Tommyknockers stole tools and lunches. They knocked over timbers holding the mines up. But they also warned. A knock on the rock could mean the roof was about to come down, or that a rich gold vein was just ahead. Miners left the last bite of their pasty in the dark. Part thanks. Part insurance. The mines are long closed now. But in Idaho Springs, the Tommyknocker Brewery still carries the name, so the legend lives on.