He has begun by supposing that light has a constant velocity... the same in all directions. This... could never be verified directly by experiment...… - Henri Poincaré

Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as, upon taking my seat in the omnibus, I went on with a conversation already commenced, btu I felt a perfect certainty. On my return to Caen, for conscience's sake I verified the result at my leisure.

Tout le monde y croit cependant, me disait un jour M. Lippmann, car les expérimentateurs s'imaginent que c'est un théorème de mathématiques, et les mathématiciens que c'est un fait expérimental.

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think.