On symmetry as an underlying property of physics:

The relationship that eventually mattered most to Einstein’s legacy was symmetry. Scientists often describe symmetries as changes that don’t really change anything, differences that don’t make a difference, variations that leave deep relationships invariant. Examples are easy to find in everyday life. You can rotate a snowflake by 60 degrees and it will look the same. You can switch places on a teeter-totter and not upset the balance. More complicated symmetries have led physicists to the discovery of everything from neutrinos to quarks — they even led to Einstein’s own discovery that gravitation is the curvature of space-time, which, we now know, can curl in on itself, pinching off into black holes.

Symmetry has helped physicists predict eventual discoveries (like the Higgs boson and gravitational waves), but also doesn’t predict some symmetries we’d expect:

In some cases, symmetries present in the underlying laws of nature appear to be broken in reality. For instance, when energy congeals into matter via the good old E = mc2, the result is equal amounts of matter and antimatter — a symmetry. But if the energy of the Big Bang created matter and antimatter in equal amounts, they should have annihilated each other, leaving not a trace of matter behind. Yet here we are.

The perfect symmetry that should have existed in the early hot moments of the universe somehow got destroyed as it cooled down, just as a perfectly symmetrical drop of water loses some of its symmetry when it freezes into ice. (A snowflake may look the same in six different orientations, but a melted snowflake looks the same in every direction.)

“Everyone’s interested in spontaneously broken symmetries,” Trodden said. “The law of nature obeys a symmetry, but the solution you’re interested in does not.”