In 1915, two of the world’s top mathematicians, David Hilbert and Felix Klein, invited Emmy Noether to the University of Göttingen to investigate a puzzle. A problem had cropped up in Albert Einstein’s new theory of gravity, general relativity, which had been unveiled earlier in the year. It seemed that the theory did not adhere to a well-established physical principle known as conservation of energy, which states that energy can change forms but can never be destroyed. Total energy is supposed to remain constant. Noether, a young mathematician with no formal academic appointment, gladly accepted the challenge.

She resolved the issue head-on, showing that energy may not be conserved “locally” — that is, in an arbitrarily small patch of space — but everything works out when the space is sufficiently large. That was one of two theorems she proved that year in Göttingen, Germany. The other theorem, which would ultimately have a far greater impact, uncovered an intimate link between conservation laws (such as the conservation of energy) and the symmetries of nature, a connection that physicists have exploited ever since. Today, our current grasp of the physical world, from subatomic particles to black holes, draws heavily upon this theorem, now known simply as Noether’s theorem.