When you imagine the universe, you might think of a giant ball that’s filled with stars, galaxies and all sorts of interesting astrophysical objects. You may imagine how it looks from the outside, like an astronaut views the globe of the Earth from a serene orbit above.
But the universe doesn’t need that outside perspective in order to exist. The universe simply is. It is entirely mathematically self-consistent to define a three-dimensional universe without requiring an outside to that universe. When you imagine the universe as a ball floating in the middle of nothing, you’re playing a mental trick on yourself that the mathematics does not require.
Granted, it sounds impossible for there to be a finite universe that has nothing outside it. And not even “nothing” in the sense of an empty void — completely and totally mathematically undefined. In fact, asking “What’s outside the universe?” is like asking “What sound does the color purple make?” It’s a nonsense question, because you’re trying to combine two unrelated concepts.
It could very well be that our universe does indeed have an “outside.” But again, this doesn"t have to be the case. There’s nothing in mathematics that describes the universe that demands an outside.
If all this sounds complicated and confusing, don’t worry. The entire point of developing sophisticated mathematics is to have tools that give us the ability to grapple with concepts beyond what we can imagine. And that’s one of the powers of modern cosmology: It allows us to study the unimaginable.