Which mathematicians are associated with the founding of geometry?

Answer 1

Euclid is the founder of Euclidean geometry, which is the most common form of geometry which is known to to the general populace and is based on the (unprovable) axiom there exists one and only one line though a given (distinct) point which is parallel to another given line.

However, there are other geometries which reject the Euclid's parallel postulate, such as Riemann geometry, created by the mathematician Riemann. First would be unnamed Egyptians and Babylonians, going back to 2000 BC. When we move to the ancient Greeks, starting around 600 BC we have names: Thales and Pythagoras, and then Eudoxus (around 370 BC). The great philosopher Plato encouraged the study of geometry around the time of Eudoxus. Geometrical proof was established some time earlier than 400 BC.

Euclid came a bit later (around 300 BC). The statement that Euclid founded Euclidean geometry needs interpretation. Euclid wrote his famous Elements, (The Elements of Geometry, in thirteen books) which were so successful that they displaced earlier books of Elements, which have not survived. Euclid made two contributions: * There is evidence that he laid out his own postulates and reworked the basis of the subject. * He collected together results from the people before him is a systematic way, including work by Eudoxus and by the Pythagoreans. The Elements basically make up an advanced textbook reporting on main results from a couple of centuries of previous work. They don't contain everything that was known at the time.

After Euclid comes Archimedes (around 250 BC), who among other things, worked on areas and volumes, and Apollonius (around 210 BC), who worked on conic sections.

[Note: In my country BC is common usage. In yours it may be BCE.]