Euclid
Euclid (; – "Eukleídēs", ; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His "Elements" is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the "Elements", Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor.
Hilbert's axioms
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book "Grundlagen der Geometrie" (tr. "The Foundations of Geometry") as the foundation for a modern treatment of Euclidean geometry. Other well-known modern axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff.