What does it mean: “The Universe is most probably flat”?
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It’s rather easy to conceptualize “flatness” in 2D. You can visually see the difference between a flat piece of paper and a ball. But we can see that because when something 2D is curved, it curves *through* 3D space, and since we exist in 3D space, we can see the curvature.
If, however, we were 2D being living on the surface of those 2D objects, how could we tell if we were living on the paper vs the ball? Remember, that all lines of sight follow along the surface as well; they given no evidence that they are curving through 3D.
The answer is: triangles.
On a flat plane, the angles of triangles always sum to 180, but on a sphere they are greater than 180. So you could construct a triangle, measure its sides and angles and determine whether you are on a flat or curved 2D surface, all using methods available to you as a being constrained to that dimension.
The concept of curvature also applies to 3D, but since we’re 3D beings living in a 3D world, it’s hard to conceive how this might manifest itself. If our 3D world is curved, it would have to be curving through a 4th spatial dimension which we have no access to.
But we have access to triangles.
By picking out distant stellar objects, we can use them to construct imaginary triangles in space, measure their angles, and try to determine if our space is flat or not.
So far, all measurements imply that our universe is flat within a certain margin of error.
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