Bolyai, János’ Absolute Geometry (non-Euclidean) – Up to modern times scientific geometry was based on the determinations, axioms and especially on the postulate, found in the beginning of Euclid’s elements, which stated that two straight lines on the selfsame plain always intersects each other, when a third straight line cutting them subtends the inner angles on one side, the sum of the angles being less than two right angles. János (John) Bolyai (1802-1860), independently from the Russian mathematician Lobachevsky, established an alternative system of geometry completely logical and watertight, at least the equal of the 2000-year old Euclidean System. In a paper written in 1823 Bolyai described a geometry in which several lines can pass through the point P without intersecting the line L. Thus, at the same time and independently of each other, a Hungarian and a Russian mathematician laid the foundations of absolute geometry. The great German mathematician, K. F. Gauss, as well as G.F.B. Riemann concurred with this fundamental finding. Einstein used this non-Euclidean (hyperbolic) geometry to develop his General Theory of Relativity. Bolyai’s hyperbolic geometry, the non-Euclidean geometry, where the Parallel Axiom is not valid as demonstrated by János (John) Bolyai, thus heralding a new age for the history of geometry – B: 1078, T: 7456.→Bolyai, János.