When we think of the universe, we think of stars, planets and galaxies suspended in a huge dark void. But what if the universe can be visualized in a single mathematical equation? That equation is Einstein’s field equation of general relativity, published in his landmark paper of 1915. It remains as one of the most beautiful equations in physics.

Here is the field equation:

In just one “simple” line of symbols, Einstein captures not just the essence of our universe but what animates it. Before we look at the individual parts of the equation, here are three reasons why it is so fundamental to our understanding of the universe. First, it shows that we can explain gravity without invoking a mysterious invisible force (as Newton did). In particular, Einstein proved that gravity is the result of the bending and warping of space and time (spacetime) caused by anything that has energy and mass. Second, the equation predicts that black holes are real and not just science fiction. Third, the equation predicts that the universe is not static but expanding. Without going into details, it suffices to say that all three predictions have been verified by highly precise experiments. That a one-line equation can describe so much of the universe is nothing short of breathtaking.

Now, let’s go the individual parts of the equation in a short video.

In short, Einstein’s field equation summarizes general relativity by noting that mass-energy dictates geometry and geometry dictates motion. As the famous American physicist John Wheeler puts it: “spacetime tells matter how to move and matter tells spacetime how to curve”.

Beyond its sheer beauty, Einstein’s field equation is a powerful reminder that nature is fundamentally mathematical, suggesting that mathematics is not something humans invent but discovered.