You are pacing a huge hall in complete darkness. You walk from wall to wall, counting your steps, and suddenly realize that the distances don't add up as they should. It seems as if the floor is not flat but bulging like a hump or hollowed like a bowl. That's roughly what astronomers found when studying distant galaxies and sound waves frozen in the early Universe.
But any builder knows: if your ruler is rigid and the floor is actually perfectly level, any irregularity will look like a flaw in the floor itself. Same here. Scientists used data from telescopes that observed millions of galaxies, supernova explosions, and even how massive clumps of matter bend light. When they squeezed all these measurements into the simplest model, it stubbornly showed curvature, as if the expansion of space were not proceeding quite as expected.
As soon as they gave the model a bit more freedom, allowing it to vary the properties of dark energy or add other ingredients, the illusion vanished. Space became flat again, like a sheet of paper. So the curvature itself was not a discovery but a shadow cast by theoretical frameworks that were too tight. We didn't find a flaw in the cosmos; we found the limit of our old tools. And now, back in that dark hall, we know: the floor is level; our first steps were just too constrained.
If the Universe were open, like a saddle, two parallel beams of light would diverge, and distant galaxies would appear smaller than they do in flat space.
In the novel 'The Three-Body Problem', a civilization uses the curvature of space for travel, but if our Universe were open, such maneuvers might require entirely different physics.