calculations. Bolzano gave the first analytic proof of the Fundamental Theorem of Algebra; the first rigorous proof that continuous functions achieve any intermediate value (Bolzano's Theorem, rediscovered by Cauchy the first proof that a bounded sequence of reals has a convergent subsequence (Bolzano-Weierstrass theorem was first. (He also showed that the rationals have the same cardinality as the integers; and that the reals have the same cardinality as the points of N-space and as the power-set of the integers.) Although there are infinitely many distinct transfinite numbers, Cantor conjectured that. He developed the theory of manifolds, a term which he invented. The Antikythera mechanism is an astronomical clock considered amazing for its time. He also produced two very influential conjectures: his conjecture about the zeta function in finite fields developed into the field of arithmetic geometry; Artin's Conjecture on primitive roots inspired much work in number theory, and was later generalized to become Weil's Conjectures. He facilitated David Hilbert's early career, publishing his controversial Finite Basis Theorem and declaring it "without doubt the most important work on general algebra the leading German journal ever published." Klein is also famous for his book on the icosahedron, reasoning from its symmetries.

### The 100, greatest Mathematicians

Markov had a research papers on stock market son, also named Andrei Andreyevich, who was also an outstanding mathematician of great breadth. Top Albert Einstein (1879-1955) Germany, Switzerland,.S.A. He had ideas similar to Pythagoras about numbers ruling the cosmos (writing that the purpose of studying the world "should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language. His theories of physics would seem quaint today, but he seems to have been the first to describe magnetism and static electricity. But although their base-60 system survives (e.g. The book was a major influence in promoting the axiomatic approach to mathematics which has been one of the major characteristics of the subject throughout the 20th century. Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. He was knowledgeable in a broad range of fields unrelated to mathematics; his University even insisted he run for Parliament. (Rademacher and Selberg later discovered an exact expression to replace the Hardy-Ramanujan approximation; when Ramanujan's notebooks were studied it was found he had anticipated their technique, but had deferred to his friend and mentor.) In a letter from his deathbed, Ramanujan introduced his mysterious "mock.

If his writings had survived he'd surely be considered one of the most brilliant and innovative geometers of antiquity. This construction (which introduced the Archytas Curve ) has been called "a tour de force of the spatial imagination." He invented the term harmonic mean and worked with geometric means as well (proving that consecutive integers never have rational geometric mean). Hamilton's Principle of Least Action, and its associated equations and concept of configuration space, led to a revolution in mathematical physics. This page is copyrighted by James Dow Allen. Top Ghiyath al-Din Jamshid Mas'ud Al-Kashi (ca ) Iran, Transoxania (Uzbekistan) Al-Kashi was among the greatest calculaters in the ancient world; wrote important texts applying arithmetic and algebra to problems in astronomy, mensuration and accounting; and developed trig tables far more accurate than earlier tables. Dedekind was far ahead of his time, so Noether became famous as the creator of modern algebra; but she acknowledged her great predecessor, frequently saying "It is all already in Dedekind." Dedekind was concerned with rigor, writing "nothing capable of proof ought to be accepted.