David Hilbert, the patron saint of math teachers
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Mark A. Wilson
David Hilbert, besides his immense contribution to functional analysis, may as well be the patron saint of math teachers.
He is one of the founders of proof theory and was a leader in the mathematics field. One of his most important accomplishments was creating, in 1900, a legendary collection of 23 unsolved problems. The problems would go on to set the syllabus for the entire field for the 20th century. In doing so, Hilbert inspired and motivated generations of mathematicians.
Euclid, an ancient Greek mathematician alive during the reign of Ptolemy I in 323-283 BC, was the author of Elements, which served as the primary textbook for mathematics until the dawn of the 19th century. He originated Euclidean Geometry, and while perhaps not demonstrably responsible for the modern era, Euclid was certainly responsible for most of the elementary mathematics that led to it.
Euclid was among the first to formalize mathematical proofs, the primary method of exposition for the discipline.
Reference:
http://www.businessinsider.com/important-mathematicians-modern-world-2012-7?IR=T#euclid-of-alexandria-prover-of-math-9
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