how can scientists say the universe is flat, when it seems to go in all directions?
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They don’t mean “flat” in the sense of the universe being a two-dimensional plane. They mean that spacetime doesn’t ordinarily have its own curvature (though massive objects can force some curvature onto around them, as black holes do).
We grow up learning about Euclidean geometry in school: a straight line is the distance between two points, the angles in any triangle add up to 180, only lines with the same slope can be parallel, that sort of thing. Over short distances, this works out closely enough to be extremely useful, and for centuries it was thought to be the only way you could do geometry. This is the “flat space” scientists are talking about: geometry works more or less the same way in space as it does on a flat piece of paper.
But starting in the 19th Century, methematicians started tinkering with other possibilities. If you draw lines on, say, a horse’s saddle, parallel lines can start curving away from each other depending on their location, and there start being more ways for lines to be parallel. If you draw lines on a ball (and add the constraint that lines must pass through the center of the ball, eventually coming back to meet themselves on the other side), then there are *no* ways for lines to be parallel: any two lines must eventually intersect. These two weird geometries are called hyperbolic and elliptical geometry, respectively. They are *non-Euclidean* geometries, because they don’t fit the assumptions Euclid made when he first described the geometry we’re familiar with.
And the thing is, these geometries also work. They don’t work the same way Euclidean geometry does, of course -the rules are different, as are the properties of shapes- but you can find the rules and do things in them like you can in traditional Euclidean geometry. And that led to the question: sure, Euclidean geometry is close enough at small scales, but is that really how it works everywhere, on the scale of the universe as a whole?
We don’t currently know the answer to that. Again, at small scales, Euclid’s close. But let’s say the universe curves out like a saddle. A straight line is no longer the shortest distance between two points in this case, *if* you can figure out a way to jump off the saddle at one point and land on it at another point. Could we perhaps figure out a way to do that? A similar question holds if the universe curves in like a sphere: could we find a way jump *into* the sphere at one point and burrow through it, emerging at the destination having travelled a shorter distance than we were supposed to? Either way could be used to circumvent the speed of light, but only if the universe’s geometry actually works that way. If it’s flat, these shortcuts won’t work. But we don’t know if it’s flat or not.
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