Just to complement Gerhard Paseman's answer. The story of how Girolamo Saccheri in early 1700's "almost" discovered hyperbolic geometry is quite amusing. Actually he died thinking he had proved the fifth postulate, but his argument was weak: "the hypothesis of the acute angle is absolutely false; because it is repugnant to the nature of straight lines". The sentence referesrefers to his construction of a quadrilateral with two sides of equal length perpendicular to a given one. The acute angles are the ones opposite to the right ones. But Wikipedia explains this too...
In this example an ideological bias prevented the discovery of beautiful mathematics... I wonder if this still happens now a days, probably yes.