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He also worked in analysis, solving the Hausdorff moment problem. His Picard-Lefschetz theory eventually led to the proof of the Weil conjectures. Several other important theorems are named after her,.g. His revolutionary nature was demonstrated at age twelve, when he began questioning the axioms of Euclid. Although most noted for number theory, he had great breadth. Hardy wrote that no one was ever more passionately devoted to mathematics than Landau. He was first to prove Taylor's Theorem rigorously, and first to prove Fermat's conjecture that every positive integer can be expressed as the sum of k k-gonal numbers for any. He may share credit with Alexander Gelfond for the solution to Hilbert's 7th Problem. Henry Smith was an outstanding intellect with a modest and charming personality. These ideas led to the schools of Plato, Aristotle and Euclid, and an intellectual blossoming unequaled until Europe's Renaissance. (Vieta wasn't particularly humble either, calling himself the "French Apollonius.

You can read a 1912 translation of parts of The Method on-line.) Top Eratosthenes of Cyrene (276-194 BC) Greek domain Eratosthenes was one of the greatest polymaths; he is called the Father of Geography, was Chief Librarian at Alexandria, was. He anticipated future advances including Darwin's natural selection, Newton's Second Law, the immutability of elements, the nature of the Milky Way, and much modern geology. (He acknowledged his limitation, writing "I admire the elegance of your Levi-Civita's method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot. (Like some of the greatest ancient mathematicians, Newton __flame photometer essay__ took the time to compute an approximation to ; his was better than Vieta's, though still not as accurate as al-Kashi's.) Newton is so famous for his calculus, optics, and. These two, along with Charles Hermite, are considered the founders of the important theory of invariants. Although the physical sciences couldn't advance until the discoveries by great men like Newton and Lavoisier, Aristotle's work in the biological sciences was superb, and served as paradigm until modern times. Cantor created modern Set Theory almost single-handedly, defining cardinal numbers, well-ordering, ordinal numbers, and discovering the Theory of Transfinite Numbers. His General Theory of Relativity has been called the most creative and original scientific theory ever. His early work in descriptive geometry has little interest to pure mathematics, but his application of calculus to the curvature of surfaces inspired Gauss and eventually Riemann, and led the great Lagrange to say "With Monge's application. In his spare time at Grenoble he continued the work in mathematics and physics that led to his immortality.

Among these are Fermat's conjecture (Lagrange's theorem) that every *flame photometer essay* integer is the sum of four squares, and the following: "Given any positive rationals a, b with a b, there exist positive rationals c, d such that a3-b3 c3d3." (This latter "lemma". Newton published the Cooling Law of thermodynamics. Other great Chinese mathematicians of that era are Li Zhi, Yang Hui (Pascal's Triangle is still called Yang Hui's Triangle in China and Zhu Shiejie. (This was of little use in ocean navigation since a ship's rocking prevents the required delicate observations. 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. (It is sometimes said that he knew that the Earth rotates around the Sun, but that appears to be false; it is instead Aristarchus of Samos, as cited by Archimedes, who may be the first "heliocentrist. He proved several important systems to be incomplete, but also established completeness results for real arithmetic and geometry. This difficulty, which almost disappears once Newton's First Law of Motion is accepted, was addressed before Newton by Jean Buridan, Nicole Oresme, Giordano Bruno, Pierre Gassendi (1592-1655) and, of course, Galileo Galilei. Others might place Laplace higher on the List, but he proved no fundamental theorems of pure mathematics (though his partial differential equation for fluid dynamics is one of the most famous in physics founded no major branch of pure mathematics, and wasn't.

Galileo once wrote "Mathematics is the language in which God has written the universe." Top Johannes Kepler (1571-1630) Germany Kepler was interested in astronomy from an early age, studied to become a Lutheran minister, became a professor of mathematics instead. (Christiaan Huygens, the other great mechanist of the era, had independently deduced that Kepler's laws imply inverse-square gravitation, but he considered the action at a distance in Newton's theory to be "absurd. He was also noted for his poetry. After the war he helped design other physical computers, as well as theoretical designs; and helped inspire von Neumann's later work. 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. Weyl studied under Hilbert and became one of the premier mathematicians and thinkers of the 20th century. He also proved many new theorems, such as the Erdös-Szekeres Theorem about monotone subsequences with its elegant (if trivial) pigeonhole-principle proof. This seems appropriate since, as the man "who reinvented mathematics his advances have sometimes been compared to Einstein's. In evaluating the genius of the ancient Greeks, it is well to remember that their achievements were made without the convenience of modern notation.

He developed the concept of skew curves (the earliest precursor of spatial curvature he made very significant contributions in differential equations and mathematical physics. He invented the Chebyshev polynomials, which have very wide application; many other theorems or concepts are also named after him. Without this reluctance I might demote Newton, though he'd still be in the Top Five. The guiding principle behind much of Grothendieck's work has been Topos Theory, which he invented to harness the methods of topology. His most famous identity (which Richard Feynman called an "almost astounding. He is also noted for the notion of dimensional analysis, was first to describe the Greenhouse Effect, and continued his earlier brilliant work with equations. He was also first to prove theorems named after others,.g. Euler was first to explore topology, proving theorems about the Euler characteristic, and the famous Euler's Polyhedral Theorem, FV E2 (although it may have been discovered by Descartes and first proved rigorously by Jordan). Weyl once said he was embarrassed to accept the famous Professorship at Göttingen because Noether was his "superior as a mathematician." Emmy Noether is considered the greatest female mathematician ever. Cayley once wrote: "As for everything else, so for a mathematical theory: beauty can be perceived but not explained." Top Charles Hermite (1822-1901) France Hermite studied the works of Lagrange and Gauss from an early age and soon developed. He was also one of the first to build on Riemann's innovations. David Hilbert had kinder words for it: "The finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity" and addressed the critics with "no one shall expel us from the paradise that Cantor has created.". He was first to note remarkable facts about Heegner numbers,.g.

Euclid ranks #14 on Michael Hart's famous list of the Most Influential Persons in History. The Theorem is sometimes called the "Cat's Cradle" or the "Mystic Hexagram." Pascal followed up this result by showing that each of Apollonius' famous theorems about conic sections was a corollary of the Mystic Hexagram; along with G?rard. Please e-mail and tell me! Top Vladimir Igorevich Arnold (1937-2010) Russia Arnold is most famous for solving Hilbert's 13th Problem; for the "magnificent" Kolmogorov-Arnold-Moser (KAM) Theorem; and for "Arnold diffusion which identifies exceptions to the stability promised by the KAM Theorem. He worked on the theory of area-preserving transformations, with applications to map-making. Eventually one of his papers was published in a journal; he was immediately given an honorary doctorate and was soon regarded as one of the best and most inspirational mathematicians in the world. Early Vedic mathematicians, the greatest mathematics before the Golden Age of Greece was in India's early Vedic (Hindu) civilization. Penrose formulated the Censorship Hypotheses about black holes,.g. Landau was the inventor of big-O notation. By imposing metrics on manifolds Riemann invented differential geometry and took non-Euclidean geometry far beyond his predecessors. Referring to this system, Gauss was later to exclaim "To what heights would science now be raised if Archimedes had made that discovery!" Some histories describe him as bringing Islamic mathematics to Europe, but in Fibonacci's own preface to Liber. Jean le Rond, named after the Parisian church where he was abandoned as a baby, played a very key role in that development.

Ptolemy wrote on trigonometry, optics, geography, and map projections; but is most famous for his astronomy, where he perfected the geocentric model of planetary motions. (By the way, the ranking assigned to a mathematician will appear if you place the cursor atop the name at the top of his mini-bio. He proved several important theorems about numbers, for example that Riemann's zeta function has infinitely many zeros with real part 1/2. But several others on the list had more historical importance. the Greatest Mathematicians of the Past ranked in approximate order of "greatness.". His proofs are noted not only for brilliance but for unequaled clarity, with a modern biographer (Heath) describing Archimedes' treatises as "without exception monuments of mathematical exposition. He was first to discover Cramer's Paradox, as Cramer himself acknowledged. The Lefschetz Fixed-point Theorem left Brouwer's famous result as just a special case. Chern was an important influence in China and a highly renowned and successful teacher: one of his students (Yau) won the Fields Medal, another (Yang) the Nobel Prize in physics. The Langlands Dual Group LG revolutionized representation theory and led to a large number of conjectures. He invented a method of L-series to prove the important theorem (Gauss' conjecture) that any arithmetic series (without a common factor) has an infinity of primes.

Despite opposition from the Roman church, this discovery led, via Galileo, Kepler and Newton, to the Scientific Revolution. He is also famous for the Plya Enumeration Theorem. Which is now linked with the name Fibonacci. Leonardo was also a writer and philosopher. He once wrote "To isolate mathematics from the practical demands of the sciences is to invite the sterility of a cow shut away from the bulls." Top Arthur Cayley (1821-1895) England Cayley was one of the most prolific mathematicians. With his "question mark function" and "sausage he was also a pioneer in the study of fractals. He provided key ideas about foundations and continuity despite that he had philosophic objections to irrational numbers and infinities. Top Johann Carl Friedrich Gauss (1777-1855) Germany Carl Friedrich Gauss, the "Prince of Mathematics exhibited his calculative powers when he corrected his father's arithmetic before the age of three. (It's possible that Galileo's pursuit of Venus' phases was inspired in part by Galileo's student, Benedetto Castelli.) Just as modern inventors sometimes mail sealed envelopes to an arbiter to establish precedence, Galileo sent an anagram to Kepler, to later. Several theorems bear his name, including the formula for the area of a cyclic quadrilateral: 16 A2 (abc-d ab-cd a-bcd -abcd) Another famous Brahmagupta theorem dealing with such quadrilaterals can be phrased "In a circle, if the chords. (Despite these comments, it does appear that Galileo ignored experimental results that conflicted with his theories.

His love of music and painting may have motivated some of his mathematics: He studied vibrating strings; and also wrote an important treatise on perspective in drawing which helped develop the fields of both projective and descriptive geometry. (Thabit __flame photometer essay__ shows how to construct a regular heptagon; it may not be clear whether this came from Archimedes, or was fashioned by Thabit by studying Archimedes' angle-trisection method.) Other discoveries known only second-hand include the Archimedean semiregular solids reported. Maxwell did little of importance in pure mathematics, so his great creativity in mathematical physics might not seem enough to qualify him for this list, although his contribution to the kinetic theory of gases (which even led to the first. He collaborated with Grothendieck and Pierre Deligne, helped resolve the Weil conjectures, and contributed indirectly to the recent proof of Fermat's Last Theorem. Lie became a close friend and collaborator of Felix Klein early in their careers; their methods of relating group theory to geometry were quite similar; but they eventually fell out after Klein became (unfairly?) recognized as the superior of the two. (For his experiments he started with a water-clock to measure time, but found the beats reproduced by trained musicians to be more convenient.) He understood that results needed to be repeated and averaged (he minimized mean absolute-error for his curve-fitting.

(Aristarchus guessed that the stars were at an almost unimaginable distance, explaining the lack of parallax. His theory unifying electricity, magnetism and light was supplanted by Maxwell's theory; however modern physics, beginning with Einstein's relativity, relies on Riemann's curvature tensor and other notions of the geometry of space. Johann insisted that Daniel study biology and medicine rather than mathematics, *flame photometer essay* so Daniel specialized initially in mathematical biology. He is most noted for his many contributions to the theory of functions of several complex variables. Following are the top mathematicians in chronological (birth-year) order. Remarkably, he stated that the cubic solution could not be achieved with straightedge and compass, a fact that wouldn't be proved until the 19th century. He had poor physical health and died at an early age, yet is still considered to be among the most productive mathematicians ever. D'Alembert was also a forerunner in functions of a complex variable, and the notions of infinitesimals and limits. His ephemeris was used by Columbus, when shipwrecked on Jamaica, to predict a lunar eclipse, thus dazzling the natives and perhaps saving his crew.