Electricity, fuels, heating: energy is all around us. Physicists talk about it all the time to decode the mechanisms behind basically every process. Yet a good definition of energy is hard to come by: what is this “energy”?

The reason why this concept seems vague is pretty simple actually: there is no good definition of energy. There is no picture, however abstract, we can point to and say “energy looks like that”. At its core, energy is but a mathematical quantity.
But a very useful one! First and foremost because we know how to compute it as long as we know what the system in question looks like. Furthermore, we know that things evolve spontaneously to reduce their energy: things high up fall down, hot things cool, but also less trivial things, like how a molecule takes shape.
We also know that energy comes in many forms: gravitational for things in gravity fields, kinetic of things moving, light, heat, electricity, chemical bonds, and many more. Even the mere fact of having a mass is a part of something’s total energy.

Maybe the most important thing about energy is that its total never changes. Energy can change form, enter or exit a specific object, pass from one to another, but it will remain the same amount. Always. So if we drop a ball from a certain height, we can tell exactly how fast it will hit the ground.
Dropping balls seem, again, a trivial example. But calculating how energy moves and transforms is also the basic to predict the output of a power plant, or decipher what happens in a particle accelerator.

So even if we can’t quite point out what energy is, its calculation is the backbone and foundation of basically everything people do in physics.
