![]() ![]() Twentieth-century mathematics flowered in the belief that it had transcended completely the limitations imposed by its natural origins. The mathematicians who created the monsters regarded them as important in showing that the world of pure mathematics contains a richness of possibilities going far beyond the simple structures that they saw in Nature. … as a “gallery of monsters,” akin to the cubist paintings and atonal music that were upsetting established standards of taste in the arts at about the same time. These new structures were regarded … as “pathological,”. ![]() Historically, the revolution was forced by the discovery of mathematical structures that did not fit the patterns of Euclid and Newton. Modern mathematics began with Cantor’s set theory and Peano’s space-filling curve. Classical mathematics had its roots in the regular geometric structures of Euclid and the continuously evolving dynamics of Newton. A great revolution of ideas separates the classical mathematics of the 19th century from the modern mathematics of the 20th. ![]() Fractal is a word invented by Mandelbrot to bring together under one heading a large class of objects that have … an historical role … in the development of pure mathematics. ![]()
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