Mathematics Island: The discovery of new geometries


The parallel postulate, a famous assertion of ancient Greek mathematician Euclid, was considered an absolute truth for more than 2000 years, until János Bolyai and, independently, Nikolai Ivanovich Lobachevsky, constructed new geometries, in which the postulate does not hold.

After all, no one doubts the truth of the parallel postulate.
(Giovanni Girolamo Saccheri, 1733)

I have discovered things so wonderful that I was astounded […] All I can say at present is that out of nothing I have created a strange new world.
(János Bolyai, 1823)