19th-century philosophy of complexity from mathematics, astronomy, physics, chemistry, biology, and a new discipline called "sociology", which is the study of the "dynamics and statics of society". The American philosophers Charles Sanders Peirce and William James developed the pragmatist philosophy in the late 19th century. The twilight years of the 19th century in Britain saw the rise of British idealism, a revival of interest in the works of Kant and Hegel. Transcendentalism was rooted in Immanuel Kant's transcendence and German idealism, led by Ralph Waldo Emerson and Henry David Thoreau. The main belief was in an ideal spiritual state that 'transcends' the
19th century in science later in the 19th century by the German mathematician Bernhard Riemann; here no parallel can be found and the angles in a triangle add up to more than 180°. Riemann also developed Riemannian geometry, which unifies and vastly generalizes the three types of geometry. The 19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, William Rowan Hamilton in Ireland developed noncommutative algebra. The British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were