James Gregory (1638-1675) was a Scottish mathematician and astronomer. He described an early practical design for the reflecting telescope, the Gregorian telescope. Today Gregorian optics are used in radio telescopes such as Arecibo, which features a "Gregorian dome". He made advances in trigonometry, discovering infinite series representations for several trigonometric functions. He showed how the areas of the circle and hyperbola could be obtained in the form of infinite convergent series. Gregory was among the first to speculate about the existence of what are now termed transcendental numbers. The first proof of the fundamental theorem of calculus and the discovery of the Taylor series can both be attributed to him. He suffered a stroke while viewing the moons of Jupiter with his students. He died a few days later at the age of 36.