The trouble was, Gauss was a man with a secret. In ancient times Euclid had made geometry the archetype of a rigourous mathematical system. To deduce all the theorems of geometry, Euclid needed some definitions and some rules of reasoning. It is possible to extend a finite straight line continuously in a straight line. It is possible to draw a circle with any centre and radius.
All right angles are equal to each other.
If a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles. While the first four seem the sort of concepts that could not be derived from more basic arguments, the fifth looks like something that ought to be provable, and for two thousand years mathematicians tried to do just that, but they never could. Gauss' secret was that he had realised that it really was impossible to prove the fifth postulate, and moreover, you could get an equally rigourous, but different, geometry if you made an alternative assumption. Once the possibility of non-Euclidean geometry has been raised, the first question is to ask whether it applies to our world. But you could do experiments in geometry, to see whether the straightest lines you could draw would agree with Euclidean plane geometry or not.