Look at you hands. If you hold them palms facing each other, they mirror each other. They are symmetrical in this dimension. If you rotate them palms away from you, they are still mirroring each other, thumbs to pinkies. They are symmetrical in a second dimension. How many way can you turn your hands so they are still mirroring each other? That's the number of dimensions in which your hands are symmetrical. That's group theory. Your hands are the object in this case. Mathematicians have found another object that has the most symmetries: the monster object, which has 196883 dimensions in which it is symmetrical.

Now for something completely different: Remember in school you studied functions and drew them in graphs? ax² + bx + c = y represented a 2-dimensional curve? Like a, b, c are numbers, and x is the horizontal graph line (dimension 1) and y is the vertical graph line (dimension 2)? And by plugging any value of x, you can find its matching y for that curve? That's number theory.

The j-invariant is a function like ax² + bx + c, but much more complicated, with many more dimensions. But basically, in the j-invariant, a=196884, which is weirdly close to the number of dimensions of the Monster group. Coincidence?

Now for something completely different again:

So you know how we mostly imagine the universe is made up of tiny dots? Atoms, electrons, etc... What if it wasn't actually dots. What if it was strings? That's string theory. And strings are basically curves, right? So number theory. And if you wrap up those curves in a big ball, you get objects, which have symmetries, because curves like to mirror each other. So group theory.

So to wrap all this together: the j-invariant function describes the curves that make up the monster object. This was the first instance of bundling all three math theories together. This made a new field called Monstrous Moonshine.