his own set of axioms for geometry; it is his axioms that are often found in today's high school texts. The first-century AD philosopher Apollonius of Tyana sought to emulate Pythagoras and live by Pythagorean teachings. His work on Pell's equations has been called "brilliant" and "marvelous." He proved the Brahmagupta-Fibonacci Identity (the set of sums of two squares is closed under multiplication). Hardy provided rigorous proofs for several of Ramanujan's conjectures, including Ramanujan's "Master Theorem" of analysis. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus. J'ai besoin de tout mon courage pour mourir vingt ans!" This tormented life, with its pointless early end, is one of the great tragedies of mathematical history. And areas of applied math including quantum mechanics, general relativity, and image processing. He was also an accomplished gambler and chess player and wrote an early book on probability. Hermite's most famous result may be his intricate proof that e (along with a broad class of related numbers) is transcendental.

The Unknown Pythagoras

(The other "theorems" were probably more like well-known axioms, but Thales proved Thales' Theorem using two of his other theorems; it is said that Thales then sacrificed an ox to celebrate what might have been the first mathematical proof in Greece.) Thales noted that, given. The number three also features prominently: the Divine Comedy has three parts and Beatrice is associated with the number nine, which is equal to three times three. Top Andrey Nikolaevich Kolmogorov (1903-1987) Russia Kolmogorov had a powerful intellect and excelled in many fields. Their teachings did not make their way to Europe, but were read by the Japanese mathematician Seki, and possibly by Islamic mathematicians like Al-Kashi. 214 In the Greek architectural orders, every element was calculated and constructed by mathematical relations. He also believed in the "musica universalis" (or the "harmony of the spheres" the idea that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a kind of symphony. Nine Chapters (known in Chinese as Jiu Zhang Suan Shu or Chiu Chang Suan Shu ) was apparently written during the early Han Dynasty (about 165 BC) by Chang Tshang (also spelled Zhang Cang). Weyl studied under Hilbert and became one of the premier mathematicians and thinkers of the 20th century. When he followed up Augustus de Morgan's earlier work in symbolic logic, de Morgan insisted that Boole was the true master of that field, and begged his friend to finally study mathematics at university. He excelled at mechanics, worked in cartography, helped Pascal with vacuum experiments, and invented the Roberval balance, still in use in weighing scales to this day.