A French mathematician and scholar named Nicole Oresme used the rectangular coordinate system and perhaps the first time-velocity-distance graph. He was also the first to use fractional exponents and also worked on infinite series, being the first to prove that the harmonic series (1⁄1 + 1⁄2 + 1⁄3 + 1⁄4 + 1⁄5.) is an infinite series divergent. Harmonic series help understand wavelengths in music, which also relates to physics. Another great invention originated and improved by Europeans is the invention of the logarithm in the early 17th century by John Napier. It was later improved by John Napier and Henry Biggs. This invention represented a major breakthrough and contribution to the advancement of science, astronomy and mathematics, making some difficult calculations relatively easy. It was one of the most crucial mathematical developments of the time. It also helped physicists like Kepler and Newton who probably could never have performed such complex calculations that they really needed for their innovations