The Dutch physicist and astronomer Christiaan Huygens was educated at home by his father and private tutors until he was about 16 years old. From 1645 until 1647, Huygens studied law at the University of Leiden and mathematics at Frans van Schooten. Then, from 1647 until 1649, he studied law at the newly founded Collegium Arausiacum (College of Orange) at Breda. During the 1650s, Huygens concentrated on mathematics, studying algebraic problems inspired by Pappus of Alexandria's work. In 1656, Huygens invented a reliable pendulum clock, succeeding where many had failed, including Galileo himself. He worked on the more general theory of harmonic oscillating systems throughout his life, finally publishing his Horologium Oscillatorium (1673). Huygens then began to work extensively on optics and dynamics. His greatest achievement was his development of the wave theory of light, published in 1678 in his Traite de la Lumiere (Treatise on Light). This was written to counter Sir Isaac Newton's particle (or "corpuscular") theory of light. Huygens proposed that light travels in successive spherical shells from its source in space and that, when one shell hits a barrier, the point of contact becomes another source of light, in turn radiating light spheres. Using these ideas, Huygens successfully deduced Willebrod van Roijen Snell's law and explained the phenomenon of interference. His wave theory became accepted over Newton's corpuscular theory when it correctly predicted a decrease in the speed of light when refracted into a medium denser than air. Huygens left Holland for Paris in 1681. He continued his optical studies, constructed numerous clocks, and wrote Cosmotheoros. However, during his last years, Huygens once again returned his attention to mathematics.