One equation brings together the two cornerstones of modern physics: quantum mechanics and relativity

"Aesthetically it is elegant and simple," says Jim Al-Khalili of the University of Surrey in Guildford, UK. "This equation is very powerful, mainly because of what it signifies and the role it played in the history of 20th-century physics."

The Dirac equation predicted the existence of antimatter

The equation was discovered in the late 1920s by physicist Paul Dirac. It remains highly influential.

It brought together two of the most important ideas in science: quantum mechanics, which describes the behaviour of tiny objects; and Einstein's special theory of relativity, which describes the behaviour of fast-moving objects. As a result, Dirac's equation describes how particles like electrons behave when they travel close to the speed of light.

"It was the first step towards what's called quantum field theory, which has given us the standard model of particle physics and the Higgs boson," says Al-Khalili.

Physicist Jon Butterworth of University College London in the UK also picked the Dirac equation.

"I love the Dirac equation because it combines elegant mathematics with huge physical consequences," says Butterworth. "Paul Dirac was determined to come up with a proper relativistic quantum equation for electrons. He did it, but the consequences were more far-reaching that anyone could have dreamed."

Perhaps most dramatically, the Dirac equation predicted the existence of antimatter – the mirror image of all known particles. Antimatter was later found to exist in the real world.

"Not bad going, for one equation," says Butterworth.

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