61. Pierre De Fermat -- Facts, Info, And Encyclopedia Article Together with (french philosopher and mathematician; developed dualistic Through his correspondence with (french mathematician and philosopher and http://www.absoluteastronomy.com/encyclopedia/p/pi/pierre_de_fermat.htm

Pierre de Fermat [Categories: Number theorists, Basque mathematicians, French mathematicians, 17th century mathematicians, 1665 deaths, 1601 births] Pierre de Fermat (The Romance language spoken in France and in countries colonized by France) French (A professional person authorized to practice law; conducts lawsuits or gives legal advice) lawyer of (A member of a people of unknown origin living in the western Pyrenees in France and Spain) Basque origin at the Parliament of (A city on the Garonne River in southern France southeast of Bordeaux; a cultural center of medieval Europe) Toulouse and a (A person skilled in mathematics) mathematician who is given credit for the development of modern (A hard lump produced by the concretion of mineral salts; found in hollow organs or ducts of the body) calculus . In particular, he is the precursor of (The part of calculus that deals with the variation of a function with respect to changes in the independent variable (or variables) by means of the concepts of derivative and differential) differential calculus with his method of finding the greatest and the smallest ordinates of curved lines, analogous to that of the then unknown

62. Math Chronology Table AD 1637, french mathematician and philosopherRene Descartes introduced coordinate AD 1812, french mathematician Pierre Simon Laplae published the first http://library.thinkquest.org/C007273/mathcronos.html

Mathematics History Prehistoric human beings probably learned to count at least up to ten on their fingers. The Chinese, Hindus, Babylonians, and Egyptians all devised methods of counting and measuring that were of practical importance in their everyday lives. The first theoretical mathematician is held to be Thales of Miletus (c. 580 BC) who is believed to have proposed the first theorems in plane geometry. His disciple Pythagoras established geometry as a recognized science among the Greeks. The later school of Alexandrian geometers (4th and 3rd centuries BC) included Euclid and Archimedes. Our present decimal numerals are based on a Hindu-Arabic system that reached Europe about AD 100 from Arab mathematicians of the Middle East such as Khwarizmi. Mathematics Chronology Table 2500 BC The people of Mesopotamia ( now Irq) developed a positional numbering (place-value) system, in which the value of a digit depends in its position in a number 2000 BC Mesopotamian mathematicians solved quadratic equations (algebraic equations in which the highest power of a variable is 2) 0876 BC A symbol for zero was used for the first time, in India

63. World4a Both Bernoulli and the french mathematician Abraham De Moivre, in his Doctrineof Chances in 1718, applied the newly discovered calculus to make rapid http://library.thinkquest.org/C006364/ENGLISH/history/historyw4a.htm

IV. Mathematics Since the 16th Century Europeans dominated in the development of mathematics after the Renaissance. A. 17th Century During the 17th century, the greatest advances were made in mathematics since the time of Archimedes and Apollonius. The century opened with the discovery of logarithms by the Scottish mathematician John Napier, whose continued utility prompted the French astronomer Pierre Simon Laplace to remark, almost two centuries later, that Napier, by halving the labors of astronomers, had doubled their lifetimes. (Although the logarithmic function is still important in mathematics and the sciences, logarithmic tables and their instrumental form¡ªslide rules¡ªare of much less practical use today because of electronic calculators.) The science of number theory, which had lain dormant since the medieval period, illustrates the 17th-century advances built on ancient learning. It was Arithmetica by Diophantus that stimulated Fermat to advance the theory of numbers greatly. His most important conjecture in the field, written in the margin of his copy of the Arithmetica, was that no solutions exist to an + bn = cn for positive integers a, b, and c when n is greater than 2. This conjecture, known as Fermat's last theorem, stimulated much important work in algebra and number theory before it was finally proved in 1994. Another major step in mathematics in the 17th century was the beginning of probability theory in the correspondence of Pascal and Fermat on a problem in gambling, called the problem of points. This unpublished work stimulated the Dutch scientist Christiaan Huygens to publish a small tract on probabilities in dice games, which was reprinted by the Swiss mathematician Jakob Bernoulli in his Art of Conjecturing. Both Bernoulli and the French mathematician Abraham De Moivre, in his Doctrine of Chances in 1718, applied the newly discovered calculus to make rapid advances in the theory, which by then had important applications in the rapidly developing insurance industry.

64. Indo-French Cooperation In Mathematics Applicants should require a french mathematician to write a letter of supportincluding his agreement to take care of the nominee during his visit in France http://iml.univ-mrs.fr/infrcoop/grants.html

GRANTS A first call from the french Ministry of National Education, Research and Technology had be made in April 1999. The two following applications which we made have been accepted: - the other for a high level position for three months for R. Balasubramanian (The Institute of Mathematical Sciences, Chennai) who came to the Institut de Mathématiques de Jussieu from September to December 1999 . A second call from the french Ministry of National Education, Research and Technology had been issued in January 2000. A new call for offer (Appel d'Offre) from the french Ministry of Research has been issued in November 2000.Under this scheme, the application should be made by a french mathematician who wishes to invite an indian researcher. For a postdoc fellowship (one year), the deadline is February 28, 2001, while for a high level position (from 1 to 6 months), the deadline is December 31, 2000. Further Visiting Positions in France.

65. Geometry Quotes. Geometry Step By Step From The Land Of The Incas - Antonio Guti french lawyer and mathematician. Concerning the lost proof of his Last Theorem. french mathematician, philosopher and physicist. http://agutie.homestead.com/files/Quotes_B.htm

Geometry Quotes: See also: Quotes Quiz Alexander, Jane. Chairman, National Endowment for the Arts (1993-1997) "When we teach a child to sing or play the flute, we teach her how to listen. When we teach her to draw, we teach her to see. When we teach a child to dance, we teach him about his body and about space, and when he acts on a stage, he learns about character and motivation. When we teach a child design , we reveal the geometry of the world. When we teach children about the folk and traditional arts and the great masterpieces of the world, we teach them to celebrate their roots and find their own place in history." Alger, William R. 1823-1905. U.S. minister, writer. The line of life is a ragged diagonal between duty and desire Archimedes. 287-212 BC. Greek mathematician, engineer, and physicist. Soldier, stand away from my diagram Supposedly spoken by Archimedes to the Roman soldier who killed him. Perhaps the best indication of what Archimedes truly loved most is his request that his tombstone include a cylinder circumscribing a sphere , accompanied by the inscription of his amazing theorem that the sphere is exactly two-thirds of the circumscribing cylinder in both surface area and volume!"

66. Tensen Physics Dictionary (biographies) Andre Marie Ampere (17751836) was a french mathematician, chemist, John-BaptisteJoseph Fourier (1768-1830) was a french mathematician who developed http://www.mcm.edu/~christej/dictionary/bib.html

A B C D ... Z Niels Henrik Abel ) was a Norwegian mathematician. ( pg.703) Andre Marie Ampere ) was a French mathematician, chemist, and physicist who experimentally quantified the relationship between the electrical current and the magnetic field . His works were summarized in a treatise published in , The units of electrical current are named after him. ( pg.5) The Bernoulli Family consisted of nine Swiss mathematicians in three generations. The father, Johan , lived from to Daniel has been called the "Father of Mathematical Physics." All were followers of Leibniz Charles A. Coulomb ) was a French engineer and physicist who published the laws of electrostatics in seven memoirs to the French Academy of Science between and . His name is associated with the units of electrical charge pg.5) ) was a French mathematician who "fathered" modern mathematics." ( Pierre de Fermat ) was a French lawyer, linguist and amateur mathematician who extended ideas about algebra and contributed to optics with his "Principle of Least Time." ( Leonard Euler ) (rhymes with boiler not ruler ) was probably the most prolific mathematician (student of Johan Bernoulli , friend of Daniel Bernoulli ) of all time, known for the quality of his vast works. (

67. Pasquale Who? “Blaise Pascal,” David said. “He was a 17thcentury french philosopher andmathematician. He laid out the basic principles of probability theory with Fermat http://www.cardplayer.com/poker_magazine/archives/?a_id=13508&m_id=73

68. List Of Jewish Scientists And Philosophers - Enpsychlopedia German mathematician; Benoit Mandelbrot, Polishborn french mathematician,creator of fractal geometry; Herman Minkowski, German mathematician http://psychcentral.com/psypsych/List_of_Jewish_scientists_and_philosophers

home resource directory disorders quizzes ... support forums Advertisement ( List of Jewish scientists and philosophers List of Jewish scientists and philosophers Main article: List of Jews See also List of Jewish Nobel Prize winners This list is incomplete ; you can help by expanding it Contents showTocToggle("show","hide") 1 Biologists and Chemists 2 Cognitive scientists and psychologists 3 Computer scientists 4 Mathematicians ... edit Biologists and Chemists See Biology and Chemistry Gistav Victor Rudolf Born , Professor of Pharmacology Ernst Chain , winner of 1945 Nobel Prize for work on penicillin Karl Djerassi , Austrian-American chemist Hans Krebs German-born English biologist, discovered Krebs Cycle Gregory Pincus , U.S. biologist, inventor of the birth-control pill Jonas Salk , U.S. medical scientist, inventor of polio vaccine Israel Shahak , Polish-born Israeli chemistry professor, critic of Zionism Lina Stern , Soviet biochemist, inventor of "Soviet penicillin", the only female full member of the USSR Academy of Sciences George Waldbott , German-U.S. physician; allergy and fluoride research pioneer. Chaim Weizmann , Russian-born chemist, first president of the State of Israel edit Cognitive scientists and psychologists See Cognitive science and Psychology Alfred Adler , Austrian psychoanalyst Solomon Asch , U.S. social psychologist

69. Gaston Julia - Enpsychlopedia 1978) was a french mathematician who devised the formula for the Julia set.His works were popularised by french mathematician Benoit Mandelbrot, http://psychcentral.com/psypsych/Gaston_Julia

home resource directory disorders quizzes ... support forums Advertisement ( Gaston Julia Gaston Maurice Julia February 3 March 19 ) was a French mathematician who devised the formula for the Julia set . His works were popularised by French mathematician Benoit Mandelbrot , and the Julia and Mandelbrot fractals are closely related. Julia was born in the Algerian town of Sidi Bel Abbes , at the time under French rule. In his youth, he had an interest in mathematics and music. His studies were interrupted at the age of 20, when France got involved in World War I and he was called to serve in the army. In one attack on a cold, stormy night he suffered a severe injury, losing his nose. After many unsuccessful operations to remedy the situation, he resigned himself to wearing a leather strap around the area where his nose was for the rest of his life. Julia gained attention for his mathematical work after the war when a 199-page article he wrote was featured in the , a French mathematics journal. The article, which he published in at the age of 25, titled "

70. Fermat He also corresponded with french mathematician, Father Mersenne (pronouncedMerseen ) who was trying to increase discussion and the exchange of ideas among http://www.math.wichita.edu/history/men/fermat.html

Pierre de Fermat Pierre de Fermat (pronounced Fer-mah') was born in southwestern France in 1601. His father was a wealthy leather merchant who made it possible for Pierre to receive a monastery education and to attend the University of Toulouse. By the time he was 30, Pierre was a civil servant whose job was to act as a link between petitioners from Toulouse to the King of France and an enforcer of royal decrees from the King to the local people. Evidence suggests he was considerate and merciful in his duties. Since he was also required to act as an appeal judge in important local cases, he did everything he could to be impartial. To avoid socializing with those who might one day appear before him in court, he became involved in mathematics and spent as much free time as he could in its study. He was so skilled in the subject that he could be called a professional amateur. He was mostly isolated from other mathematicians, though he wrote regularly to two English mathematicians, Digby and Wallis. He also corresponded with French mathematician, Father Mersenne (pronounced Mer-seen') who was trying to increase discussion and the exchange of ideas among French mathematicians. One was Blaise Pascal who, with Fermat, established a new branch of math - probability theory. Fermat himself was secretive and, since he rarely wrote complete proofs or explanations of how he got his answers, was mischievously frustrating for others to understand. He loved to announce in letters that he had just solved a problem in math but then refused to disclose its solution, leaving it for others to figure out.

71. Mathematician - Definition Of Mathematician By The Free Online Dictionary, Thesa Fermat, Pierre de Fermat french mathematician who founded number theory; Evariste Galois, Galois - french mathematician who described the conditions http://www.thefreedictionary.com/mathematician

Domain='thefreedictionary.com' word='mathematician' Your help is needed: American Red Cross The Salvation Army join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia mathematician Also found in: Acronyms Wikipedia 0.01 sec. Page tools Printer friendly Cite / link Email Feedback math·e·ma·ti·cian (m th -m -t sh n) n. A person skilled or learned in mathematics. Thesaurus Legend: Synonyms Related Words Antonyms Noun mathematician - a person skilled in mathematics math mathematics maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement algebraist - a mathematician whose specialty is algebra arithmetician - someone who specializes in arithmetic geometer geometrician - a mathematician specializing in geometry number theorist - a mathematician specializing in number theory probability theorist - a mathematician who specializes in probability theory man of science scientist - a person with advanced knowledge of one of more sciences mathematical statistician statistician - a mathematician who specializes in statistics trigonometrician - a mathematician specializing in trigonometry Abel Niels Abel Niels Henrik Abel - Norwegian mathematician (1802-1829) Al-Hasan ibn al-Haytham al-Haytham Alhazen Ibn al-Haytham - an Egyptian polymath (born in Iraq) whose research in geometry and optics was influential into the 17th century; established experiments as the norm of proof in physics (died in 1040)

72. Re: How Does A Gramaphone Horn Amplify Sound? The french mathematician Marin Mersenne studied the vibration of stretched strings;the results of these studies were summarized in the three Mersenne s http://www.madsci.org/posts/archives/jul2001/996421645.Ph.r.html

MadSci Network : Physics Re: how does a gramaphone horn amplify sound? Date: Fri Jul 27 17:12:36 2001 Posted By: Jaime Valencia-Rodríguez, Guest Researcher, Chemical Science and Technology Lab, NIST. Area of science: Physics ID: 993560502.Ph Message: Dear Sunil: Thanks for your question. Lets begin with some definitions. In we find: Acoustics: the science concerned with the production, control, transmission, reception, and effects of sound. The term is derived from the Greek akoustos, meaning “hearing.” Beginning with its origins in the study of mechanical vibrations and the radiation of these vibrations through mechanical waves, acoustics has had important applications in almost every area of life. It has been fundamental to many developments in the arts—some of which, especially in the area of musical scales and instruments, took place after long experimentation by artists and were only much later explained as theory by scientists. For example, much of what is now known about architectural acoustics was actually learned by trial and error over centuries of experience and was only recently formalized into a science. Additionally, I found: http://webster .aip.org/radio/html/guitar_physics.html

73. Anecdotage.com - Mathematics Anecdotes. Anecdotes From Yeats To Gates The french mathematician and astronomer Pierre Laplace was so inspired by the me . Following the death of french mathematician Guillaume De L Hôpital in http://www.anecdotage.com/browse.php?term=Mathematics

74. MSN Encarta - Sound During the early 17th century, french mathematician Marin Mersenne determinedthe speed of sound by measuring the time of return of an echo. http://encarta.msn.com/encyclopedia_761560639_3/Sound.html

MSN Home My MSN Hotmail Shopping ... Sign In Web Search: Encarta Subscriber Sign In Help Home ... Upgrade your Encarta Experience Search Encarta Upgrade your Encarta Experience Spend less time searching and more time learning. Learn more Tasks Find in this article Print Preview Related Items Acoustics Decibel more... Further Reading Editors' picks for Sound Search for books and more related to Sound Encarta Search Search Encarta about Sound Editors' Picks Great books about your topic, Sound ... Click here Advertisement document.write(' Page 3 of 3 Sound Encyclopedia Article Multimedia 4 items Article Outline Introduction Physical Characteristics Sensations of Tone Historical Development A Three Important Types of Ordinary Sound In speech, music, and noise, pure tones are seldom heard. A musical note contains, in addition to a fundamental frequency, higher tones that are harmonics of the fundamental frequency. Speech contains a complex mixture of sounds, some (but not all) of which are in harmonic relation to one another. Noise consists of a mixture of many different frequencies within a certain range; it is thus comparable to white light, which consists of a mixture of light of all different colors. Different noises are distinguished by different distributions of energy in the various frequency ranges. When a musical tone containing some harmonics of a fundamental tone, but missing other harmonics or the fundamental itself, is transmitted to the ear, the ear forms various beats in the form of sum and difference frequencies, thus producing the missing harmonics or the fundamental not present in the original sound. These notes are also harmonics of the original fundamental note. This incorrect response of the ear may be valuable. Sound-reproducing equipment without a large speaker, for example, cannot generally produce sounds of pitch lower than two octaves below middle C; nonetheless, a human ear listening to such equipment can resupply the fundamental note by resolving beat frequencies from its harmonics. Another imperfection of the ear in the presence of ordinary sounds is the inability to hear high-frequency notes when low-frequency sound of considerable intensity is present. This phenomenon is called masking.

75. MSN Encarta - Calculus (mathematics) At about the same time, the french mathematician René Descartes’La A codiscovererof this analytic geometry was the french mathematician Pierre de http://encarta.msn.com/encyclopedia_761568582_2/Calculus_(mathematics).html

MSN Home My MSN Hotmail Shopping ... Sign In Web Search: Encarta Subscriber Sign In Help Home ... Upgrade your Encarta Experience Search Encarta Upgrade your Encarta Experience Spend less time searching and more time learning. Learn more Tasks Find in this article Print Preview Related Items definition and scope of study differential calculus more... Further Reading Editors' picks for Calculus (mathematics) Search for books and more related to Calculus (mathematics) Encarta Search Search Encarta about Calculus (mathematics) Editors' Picks Great books about your topic, Calculus (mathematics) ... Click here Advertisement document.write(' Page 2 of 2 Calculus (mathematics) Encyclopedia Article Multimedia 5 items Article Outline Introduction Differential Calculus Integral Calculus Differential Equations ... Development of Calculus V Development of Calculus Print Preview of Section The English and German mathematicians, respectively, Isaac Newton and Gottfried Wilhelm Leibniz invented calculus in the 17th century, but isolated results about its fundamental problems had been known for thousands of years. For example, the Egyptians discovered the rule for the volume of a pyramid as well as an approximation of the area of a circle. In ancient Greece, Archimedes proved that if c is the circumference and d the diameter of a circle, then 3

76. Joseph-Louis Lagrange COUNT (comte) DE L EMPIRE Click Here For April 10, 1813, Paris, Fr.), Italianfrench mathematician who made great In 1766, on the recommendation of Euler and the french mathematician Jean http://www.phy.bg.ac.yu/web_projects/giants/lagrange.html

Joseph-Louis Lagrange COUNT (comte) DE L'EMPIRE Click here for full size picture original Italian GIUSEPPE LUIGI LAGRANGIA (b. Jan. 25, 1736, Turin, Sardinia-Piedmont [Italy]d. April 10, 1813, Paris, Fr.), Italian-French mathematician who made great contributions to the theory of numbers and to analytic and celestial mechanics. His most important book is Mécanique analytique (1788; "Analytic Mechanics"), the textbook on which all later work in this field is based. Lagrange was from a well-to-do family of French origin on his father's side. His father was treasurer to the king of Sardinia and lost his fortune in speculation. Lagrange later said, "If I had been rich, I probably would not have devoted myself to mathematics." His interest in mathematics was aroused by the chance reading of a memoir by the English astronomer Edmond Halley. At 19 (some say 16) he was teaching mathematics at the artillery school of Turin. He was to be instrumental in founding the Turin Academy of Sciences. His early publications, on the propagation of sound and on the concept of maxima and minima, were well received; Leonhard Euler , in Berlin, praised Lagrange's version of his theory of variations. The young mathematician continued to surprise his contemporaries with his discoveries.

77. Biographies The french mathematician and scientist Cauchy contributed to just about everybranch of Laplace was a french mathematician, scientist, and statesman. http://www.fmi.uni-sofia.bg/vesta/Virtual_Labs/resources/resources3.html

Biographical Notes Bayes was a non-conformist minister in England. A version of what is now known as Bayes’ theorem was used in his paper "Essay towards solving a problem in the doctrine of chances," published in the Philosophical Transactions of the Royal Society of London in 1764. James Bernoulli was the first of the famous Bernoulli family of Swiss mathematicians. He wrote one of the early books devoted to probability, Ars Conjectandi , which was published after his death in 1713. Bernoulli formulated the version of the law of large numbers for independent trials, now called Bernoulli trials, and studied the binomial distribution. Buffon was the director of the Paris Jardin du Roi and was best known during his time for his thirty-six volume work on natural history. Buffon's famous coin and needle problems are considered to be among the first problems in geometric probability. Cardano, who lived in Italy, was a man of many interests: law, medicine, astrology, gambling, and mathematics. His book Liber de Ludo Aleae (The Book on Games of Chance), published after his death in 1663, contained perhaps the first mathematical analysis of gambling.

78. Fractal Geometry These derive from the work done by a french mathematician, Gaston Julia, on theiteration of nonlinear transformations in a complex plane. http://www.crystalinks.com/fractal.html

Fractal Geometry Reality is based on the patterns of sacred geometry which repeat in endless cycles. A fractal is a geometrical shape or pattern made up of identical parts, which are in turn identical to the overall pattern. The term "fractal" was coined by Benoit Mandelbrot about 1975 to describe a complex geometrical object that has a high degree of "self-similarity" and a fractional dimension that exceeds the normal, or "topological", dimension ( "D" ) for that type of object. The basic unit of the Koch snowflake , first constructed by the mathematician Helge von Koch (1870-1924), is the equilatorial triangle which can be built up into a much larger but still similar pattern. Any part of the snowflake is equally crinkly, whatever scale it is viewed at. Some of the most remarkable fractals are the Julia sets, devised by the French mathematician Gaston Julia (1893-1978). The Julia Sets are generated by applying an iterative non-linear process based on a very simple square-law function. F(z,C) = z2 + C where z is a point on the X-Y plane and C is a constant with both x and y components, Cx and Cy. The results were very surprising. No one expected that such a simple function could produce such complex images and be so difficult to analyze.

79. Evariste Galois: Literature Rothman postulated in his criticism about The french Mathematician One isleft feeling that a more effective strategy might have been to surround Galois http://www.galois-group.net/g/EN/literature.html

The Evariste Galois Archive This site in: German English French Italian ... Spanish Topics Introduction Translation Project Galois Theory Galois in Fiction ... What's New Evariste Galois Biography Preface Childhood School Days Strokes of Fate ... The Duel Other Biographies Paul Dupuy Biographical and Fictional Novels on Evariste Galois "In France, about 1830, a new star of unimaginable brightness appeared in the heavens of pure mathematics ... Evariste Galois." Felix Klein The French Mathematician. By Tom Petsinis Tony Rothman said about this book: "While reading Tom Petsinis's new novel about Evariste Galois, one wonders throughout whether Galois would be pleased with this portrait or would call his lawyer. Galois is not forthcoming. As his advocate I would be tempted to advise him to call not a lawyer, I think, but a book doctor. However, this case is one for the jury to decide." Galois Silence ( Galois Schweigen ) by Bernd Klein Galois wouldn't have any problems with this book, because the fictitious and known aspects are never intermingled in this novel. Rothman postulated in his criticism about "The French Mathematician": "One is left feeling that a more effective strategy might have been to surround Galois by a group of third-persons trying to make out this character." This is in a way the strategy Klein has chosen. The biographical or better factual basis of this novel is a biography by Bernard Bychan, which is cited in its main parts. Around this biography he has woven various plot strands which illuminate complementary and contrasting aspects of his life, which can't be directly deduced from historical facts. In this novel you also find an answer to the question, what might have happened to Galois in our times. After reading this entertaining book, you will be a lot closer to the real Galois.

80. Premium Archive Formulated by the french mathematician Henri Poincaré in 1904, the PoincaréConjecture is a central question in topology, the study of the geometrical http://www.msri.org/people/members/sara/articles/perlman.html

Welcome, arasr Today's News Past Week Past 30 Days Past 90 Days Past Year Since 1996 This page is print-ready, and this article will remain available for 90 days. Instructions for Saving About this Service Purchase History April 15, 2003, Tuesday SCIENCE DESK Russian Reports He Has Solved a Celebrated Math Problem By SARA ROBINSON (NYT) 1310 words A Russian mathematician is reporting that he has proved the Poincaré Conjecture, one of the most famous unsolved problems in mathematics. The mathematician, Dr. Grigori Perelman of the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, is describing his work in a series of papers, not yet completed. It will be months before the proof can be thoroughly checked. But if true, it will verify a statement about three-dimensional objects that has haunted mathematicians for nearly a century, and its consequences will reverberate through geometry and physics. If his proof is accepted for publication in a refereed research journal and survives two years of scrutiny, Dr. Perelman could be eligible for a $1 million prize sponsored by the Clay Mathematics Institute in Cambridge, Mass., for solving what the institute identifies as one of the seven most important unsolved mathematics problems of the millennium. Rumors about Dr. Perelman's work have been circulating since November, when he posted the first of his papers reporting the result on an Internet preprint server.

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