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A Russian mathematician named Nikolai Ivanovich Lobachevsky is the man credited with inventing hyperbolic geometry. Nikolai lived from 1792 to 1856.
The first recorded study of spherical geometry was by Autolycus of Pitane, in the 4th century BC.
Algebraic Geometry - book - was created in 1977.
Geometry has been studied in every civilization that we have written records of. In that sense, no mathematician can have created geometry. Euclid is generally recognized as having pioneered the use of the axiomatic method in mathematics. Of that work, his most famous is his work in geometry.
The Sumerians (Sumerian Civilization) was the first to develop algebra and geometry