In the winter of 1604, a man with ruined eyesight and crippled hands sat in a rented room in Prague, comparing a column of numbers against a curve he had drawn by hand, and found that the two disagreed by an amount roughly equal to the width of a coin seen from across a wide room. Everyone he knew would have called that agreement. He called it a problem, and spent the next five years destroying the most beautiful idea he had ever had in order to fix it.

Johannes Kepler has been reduced, in most retellings, to three tidy statements in a physics textbook. The man himself cast horoscopes for a warlord, was denied communion by his own church, wrote what may be the first work of science fiction, invented a better telescope than Galileo's, described the shape of a snowflake, worked out how to measure a wine barrel, and spent six years defending his mother against a charge of witchcraft while the Thirty Years' War burned through the towns where he had lived. He also proposed a model of the solar system built from the five perfect solids of Greek geometry. It was breathtaking. It was wrong. He never took it back.

This book follows him through all of it—the plague years, the unpaid salaries of three emperors, the burned printing house, the eleven months of borrowed data that changed astronomy—and asks a question that turns out to be sharper than it looks. The same mind that refused to overlook a discrepancy in the orbit of Mars cheerfully overlooked a discrepancy of the same kind in his own cherished geometry, twenty-five years later, in print, on purpose. What made the difference?

The answer is not that he grew careless. The answer says something uncomfortable and useful about how anyone decides which errors are worth honoring, and it applies as directly to a research laboratory this morning as it did to a cold room in Prague four centuries ago.