Hydrodynamics procreated complex analysis, partial derivative equations, Lie groups and algebra theory, cohomology theory and scientific computing. Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry. Second, as every natural science, mathematics is being developed by trial and error, modeling and experimentation, with proofs coming last as a method of hypothesis verification. Both aspects of mathematics must be reflected in mathematics education. In fact the trend of melding of theoretical physics with mathematics was reciprocated on the part of mathematics by fostering its experimental nature.
Triangle geometry serves as a good example.
Later triangle geometers include Euler, Pascal, Ceva, and Feuerbach. A huge wave of interest and publications in triangle geometry swept through the last years of the 19th century but then collapsed during the early years of the 20th. Kimberling's book Triangle Centers and Central Triangles published in 1998 describes nearly 400 various centers and his online encyclopedia currently lists in excess of 500 remarkable points. Most of these were first discovered with the help of computer. Computers open new horizons for experimentation while still keeping experiments inexpensive.