61. Russian Mathematician Announces Proof Of Celebrated Poincaré Conjecture russian mathematician announces proof of celebrated Poincaré Conjecture. By Alex Lefebvre 3 June 2003. http://www.wsws.org/articles/2003/jun2003/math-j03_prn.shtml

World Socialist Web Site www.wsws.org WSWS By Alex Lefebvre 3 June 2003 Back to screen version Send this link by email Email the author [In considering the following explanation, we advise readers to either locate actual ball and doughnut shapes to look at, or to use pencil and paper to draw them. This makes visualizing and grasping the content of this article easier.] The previous two examples give rise to a very important idea of equivalence. If one had a (very stretchy and malleable) beach ball and a lot of air, one could imagine inflating it, stretching it and pulling it so that it actually took on the shape of the surface of the earth. Mathematicians express this by saying that the surface of a beach ball and that of the earth are topologically equivalent Explaining precisely what a 3-dimensional sphere is to a lay audience presents some difficulties, as it is harder to visualize. Technically, one reasons by analogy. The fact that one traces out a 1-dimensional sphere (the edge of a circle) with a compass on a 2-dimensional plane indicates that a 1-dimensional sphere consists of the points in 2-dimensional space a fixed distance away from given point (the needle point of the compass). Similarly, the 2-dimensional sphere (the surface of a solid ball) consists of the points a fixed distance away from a given point in 3-dimensional space. So, the 3-dimensional sphere consists of the points a fixed distance away from a given point in 4-dimensional space. Notes: http://www.arxiv.org/abs/math.DG/0211159

62. Celebrated Math Problem Solved, Russian Reports By SARA ROBINSON. A russian mathematician is reporting that he has proved the Poincaré Conjecture, one of the most famous unsolved problems in mathematics. http://www2.polito.it/didattica/polymath/htmlS/Interventi/Articoli/Poincare/Repo

63. A Fate Of The Great Mathematical Discoveries When in 1826 the young russian mathematician Nikolay Lobatchevski from the Kazan University came to the new geometric system (Lobatchevski s geometry) his http://www.goldenmuseum.com/1103MathDiscover_engl.html

A fate of the great mathematical discoveries Nikolay Lobatchevski (1792 - 1856) Mikhail Ostrogradski (1801 - 1862) And during all his life Lobatchevski was subjected to ridicule on the part of the official Russian academic science of that period. Lobatchevski's recognition came from the West science due the genius mathematician Gauss who became the only mathematician who could access properly Lobatchevski's works in geometry. According to Gauss' proposal Lobatchevski was chosen by the Corresponding Member of the Gettingen scientific society. It was other example from the history of the French 19th century mathematics. The name of the French mathematician Evarist Galois is well-known in mathematics. His mathematical works gave the origin of modern algebra. However at his life Evarist Galois was well-known as revolutionary. For public speeches against royal regime he was twice in prison. In 1832 in the age of 21 he was killed on the duel organized by his enemies. His basic mathematical works named later by his name Evarist Galois obtained in the age of 16-18 when he studied in the Lyceum. Galois sent his works to the Paris Academy of Sciences. However even the greatest French mathematicians Cauchy and Fourier cannot understand Galois works. According to legend, academician Cauchy threw out all mathematical Galois' works to the garbage. Cauchy (1789 - 1857) Galois (1811-1832) Galois' works were read and published for 14 years later of his died. In 1870, that is for 38 years later of his died the famous French mathematician Jordan wrote the book on mathematical Galois' investigations and due this book Galois' theory became common property of the world.

64. A Short History Of Probability In 1933 a monograph by a russian mathematician A. Kolmogorov outlined an axiomatic approach that forms the basis for the modern theory. http://www.cc.gatech.edu/classes/cs6751_97_winter/Topics/stat-meas/probHist.html

A Short History of Probability From Calculus, Volume II by Tom M. Apostol nd The Dutch scientist Christian Huygens, a teacher of Leibniz, learned of this correspondence and shortly thereafter (in 1657) published the first book on probability; entitled De Ratiociniis in Ludo Aleae , it was a treatise on problems associated with gambling. Because of the inherent appeal of games of chance, probability theory soon became popular, and the subject developed rapidly during the 18th century. The major contributors during this period were Jakob Bernoulli (1654-1705) and Abraham de Moivre (1667-1754). In 1812 Pierre de Laplace (1749-1827) introduced a host of new ideas and mathematical techniques in his book, . Before Laplace, probability theory was solely concerned with developing a mathematical analysis of games of chance. Laplace applied probabilistic ideas to many scientific and practical problems. The theory of errors, actuarial mathematics, and statistical mechanics are examples of some of the important applications of probability theory developed in the l9th century. Like so many other branches of mathematics, the development of probability theory has been stimulated by the variety of its applications. Conversely, each advance in the theory has enlarged the scope of its influence. Mathematical statistics is one important branch of applied probability; other applications occur in such widely different fields as genetics, psychology, economics, and engineering. Many workers have contributed to the theory since Laplace's time; among the most important are Chebyshev, Markov, von Mises, and Kolmogorov.

65. TheWorldJournal.com News Forums - Powered By XMB 1.8 Partagium Final SP3 TheWorldJournal.com News Forums » Science » Celebrated Math Problem Solved, Says russian Mathematician, go to bottom. http://www.theworldjournal.com/forum/viewthread.php?tid=315

66. TheWorldJournal.com News Forums - Powered By XMB 1.8 Partagium Final SP3 A russian mathematician is reporting that he has proved the Poincaré Conjecture, one of the most famous unsolved problems in mathematics. http://www.theworldjournal.com/forum/post.php?action=reply&repquote=1352&tid=315

67. Links Journals (Free Access); russian Mathematical Journals (Free Access); Electronic journals math, phys, CERN list and scientific publishers http://wwwth.itep.ru/mathphys/links/links.htm

USEFUL LINKS World, Russian and Moscow News: Russian government Russian State map travel info and hotels Moscow general info mayor office travel guide maps ... map and weather [ infospace CNN YAHOO and ABC news Russia Today ; RFE/RL homepage news Russian News Service strana.ru gazeta ... Theater and TV [ rbc ] programs Business news Exchange rates MTS Embassies at Moscow ... MORE Russian/Moscow News and Links Computing and Net Navigators: Searching the net HotBot Alta Vista Yandex ... Moscow TEX Server Computer sites: Freeware.ru osp RIPN ITEP Links ITEP WWW server proxy.itep .ru ... .ru ITEP proxy servers MPG proxy server usage (details) ITEP PingER and Traceroute server. Lattice Group Physics Links Seminars in Moscow and Moscow Region Conference announcements from xxx.lanl.gov and CERN Moscow Independent University Russian Academy of Sciences [ Russian Foundation for Basic Research (RFFI), VINITI TST Landau Institute Chernogolovka Scientific Center ... Lebedev Institute (FIAN), Lebedev Center Theory Division HEP laboratories around the world Theory division of CERN APCTP (Asia Pacific Center for Theoretical Physics) Russian Library community Library for Natural Sciences RAS Journal Contents InfoMAG ... Russian Mathematical Journals (Free Access) Electronic journals [ math phys CERN list ] and scientific publishers American Physical Society Journal of High Energy Physics Elsevier Publishers Phys.Lett.B

68. References For Luzin Nauk 7 (2) (1952), 1730. LV Keldysh, The ideas of NN Luzin in descriptive set theory, russian Mathematical Surveys 29 (5) (1974), 179-193. http://www-gap.dcs.st-and.ac.uk/~history/References/Luzin.html

69. Gregori Aleksandrovich Margulis --  Encyclopædia Britannica born Feb. 24, 1946, Moscow, Russia, USSR russian mathematician who was awarded the Fields Medal in 1978 for his contributions to the theory of Lie groups. http://www.britannica.com/eb/article?eu=100135&tocid=0&query=margulis, lynn

70. Lobachevski, Nikolai --  Britannica Student Encyclopedia (1792–1856), russian mathematician, born in Nizhni Novgorod; cofounder, with Hungarian mathematician János Bolyai, of nonEuclidean geometry; entered Univ. http://www.britannica.com/ebi/article?eu=340149&query=bernhard riemann&ct=ebi

71. Biographies The russian mathematician Chebyshev established the inequality that gives an upper bound on the probability of a large deviation from the mean. 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.

72. References Men shov, DE, SB Stechkin and PL Ul yanov. Nina Karlovna BariObituary, russian Mathematical Surveys, 17(1) 1962, 119-127. Michalowicz, Karen Dee. http://www.agnesscott.edu/lriddle/women/biblio.htm

Biographies of Women Mathematicians , Agnes Scott College] References about Women Mathematicians Books and Articles Albers, Don. "Making Connections: A Profile of Fan Chung," Math Horizons, September 1995, 14-18. Albers, D. and G.L. Alexanderson. Mathematical People: Profiles and Interviews , Birkhauser, 1985. Contains interview with Olga Taussky-Todd. Albers, D., G.L. Alexanderson and C. Reid, More Mathematical People: Contemporary Conversations Contains conversations with Cathleen Morawetz, Julia Robinson, and Mary Ellen Rudin. The one of Julia Robinson is a reprint of the article by Constance Reid in the College Mathematics Journal with a correction to a mathematical misstatement and with better photos. Albers, D. and C. Reid. "An Interview with Mary Ellen Rudin," College Mathematics Journal, March 1988. Alic, Margaret. Hypatia's Heritage: A History of Women in Science from Antiquity throguh the NIneteenth Century, Beacon Press, Boston. [Agnesi, Chatelet, Germain, Lovelace, Kovalevsky] Anand, Kailash K. "Hanna Neumann: A great woman mathematician from down under," Association for Women in Mathematics Newsletter, 18(1) 1988, 10-13. Anand, Kailash K. "Cypra Cecilia Krieger and the Human Side of Mathematics," in

73. MSN Encarta - Print Preview - Calculus (mathematics) In the 18th century, the great Swissrussian mathematician Leonhard Euler, who had studied with Johann Bernoulli, wrote his Introduction to the Analysis of http://encarta.msn.com/text_761568582___5/Calculus_(mathematics).html

Print Preview Calculus (mathematics) Article View On the File menu, click Print to print the information. Calculus (mathematics) V. Development of Calculus 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 d c d . His proof extended the method of inscribed and circumscribed figures developed by the Greek astronomer and mathematician Eudoxus. Archimedes used the same technique for his other results on areas and volumes. Archimedes discovered his results by means of heuristic arguments involving parallel slices of the figures and the law of the lever. Unfortunately, his treatise The Method was only rediscovered in the 19th century, so later mathematicians believed that the Greeks deliberately concealed their secret methods. During the late middle ages in Europe, mathematicians studied translations of Archimedes’ treatises from Arabic. At the same time, philosophers were studying problems of change and the infinite, such as the addition of infinitely many quantities. Greek thinkers had seen only contradictions there, but medieval thinkers aided mathematics by making the infinite philosophically respectable.

74. A. A. Markov - Encyclopedia Article About A. A. Markov. Free Access, No Registra Pafnuty Lvovich Chebyshev ( ? ?) (May 4 1821 November 26 1894) was a russian mathematician. http://encyclopedia.thefreedictionary.com/A. A. Markov

Dictionaries: General Computing Medical Legal Encyclopedia A. A. Markov Word: Word Starts with Ends with Definition Andrei Andreevich Markov June 2 June 2 is the 153rd day of the year in the Gregorian calendar (154th in leap years), with 212 days remaining. Events 455 - The Vandals enter Rome, and plunder the city for two weeks. They depart with countless valuables, spoils of the Temple in Jerusalem brought to Rome by Titus, and the Empress Eudoxia and her daughters Eudocia and Placidia. 575 - Benedict I becomes Pope Click the link for more information. Centuries: 18th century - 19th century - 20th century Decades: 1800s 1810s 1820s 1830s 1840s - Years: 1851 1852 1853 1854 1855 - Events January 8 - Borax is discovered (John Veatch). January 29 - Queen Victoria institutes the Victoria Cross February 18 - The American Party (Know-Nothings) convene in Philadelphia, Pennsylvania to nominate their first Presidential candidate, former President Millard Fillmore. Click the link for more information. July 20 July 20 is the 201st day (202nd in leap years) of the year in the Gregorian Calendar, with 164 days remaining. Events 1304 - Fall of Stirling Castle: Edward I of England takes the last rebel stronghold in the Wars of Scottish Independence.

75. Department Of Probability Theory Gikhman II, Skorokhod AV, Yadrenko MI Probability theory and mathematical statistics, Vyshcha shkola, Kiev, 1979, 408 p. (russian). http://www.iamm.ac.donetsk.ua/english/math_sta.html

76. Lobachevsky, Nikolay Ivanovich 24 Feb. 12, OS, 1856, Kazan), russian mathematician who, with János Bolyai of Hungary, is considered the founder of nonEuclidean geometry. http://www.phy.bg.ac.yu/web_projects/giants/lobachevsky.html

Britannica CD Index Articles Dictionary Help Lobachevsky, Nikolay Ivanovich (b. Bolyai of Hungary, is considered the founder of non-Euclidean geometry. Lobachevsky was the son of an impecunious government official. His entire life centred around the University of Kazan, beginning at age 14, when he entered as a student. In 1811 he received the M.A. degree and then taught, from 1816 as extraordinary professor and from 1822 as ordinary professor. His administrative talents were soon recognized; in 1820 he became dean of the faculty of mathematics and physics, in 1825 university librarian, and in 1827 rector of the university, a position he held, with repeated reelections, until 1846. In all of his duties, he exercised remarkable organizing and educational skill in rescuing the university from the chaotic conditions into which it had drifted. The previous administration had reflected the spirit of the later years of Tsar Alexander I, who was distrustful of modern science and philosophy, particularly that of the German philosopher Immanuel Kant, as evil products of the French Revolution and a menace to orthodox religion. The results at Kazan during the years 1819-26 were factionalism, decay of academic standards, dismissals, and departure of some of the best professors, including Johann Martin Christian Bartels, friend of the German mathematician Carl Friedrich Gauss, and Lobachevsky's teacher of mathematics. In 1826 a more tolerant period was inaugurated with the accession of Tsar Nicholas I, and Lobachevsky became the leading innovator at the university, restoring academic standards and faculty harmony. He was active in saving lives during the cholera epidemic of 1830, in rebuilding several university buildings after a devastating fire in 1842, and in popularizing science and modernizing primary and secondary education in the region of Kazan. Although burdened with this work, in addition to a heavy administrative teaching load, he still found time for extensive mathematical research.

77. Math Digest article). These articles discuss reports that a russian mathematician, Grigory Perelman, has solved the Poincaré Conjecture. Long http://www.ams.org/new-in-math/mathdigest/200305-poincare.html

Mathematical Digest Short Summaries of Articles about Mathematics in the Popular Press "Celebrated Math Problem Solved, Russian Reports," by Sara Robinson. New York Times, 15 April 2003. Science, 18 April 2003. "A Mathematician's World of Doughnuts and Spheres," by George Johnson. New York Times, 20 April 2003. Nature , 24 April 2003. "Spheres in Disguise," by Erica Klarreich. Science News, 26 April 2003. New Scientist, 26 April 2003, page 8; "If it looks like a sphere...," by Erica Klarreich. Science News , 14 June 2003 (click here for a Math Digest of this article). Clay Mathematics Institute has offered a prize of $1 million. The news reports about Perelman's work have expressed cautious optimism. Experts in the field are still examining his work to see if all the details are right and whether the proof holds together. The New York Times article by Sara Robinson contains quotations of MIT mathematician Tomasz Mrowka that sum up the general feeling among mathematicians: "It's not certain, but we're taking it very seriously. [Perelman has] obviously thought about this stuff very hard for a long time, and it will be very hard to find any mistakes." The article also quotes Mrowka as saying: "This is one of those happy circumstances where it's going to be fun no matter what. Either he's done it or he's made some really significant progress, and we're going to learn from it." - Allyn Jackson

78. This Mathematical Month better economic opportunities. This exodus posed a serious threat to the vibrant russian mathematical tradition. The AMS formulated http://www.ams.org/ams/thismathmonth.html

This Mathematical Month: A Brief Look at Past Events and Episodes in the Mathematical Community Monthly postings of vignettes on people, publications, and mathematics to inform and entertain. June: June 1992: The Isaac Newton Institute celebrated its inauguration. Sir Michael Atiyah , founding director of the Newton Institute, said at the time: "I think the view is at the present time that a lot of the future development of mathematics will probably be to use more advanced mathematics in related fields and to bring problems from other fields into mathematics. So our aim is really to bridge the gap by bringing people together." Since then, it has become one of the world's main institutes for research in pure and applied mathematics. Visit the Newton Institute's web site June 1993: At a conference at the Isaac Newton Institute, Andrew Wiles gave his first ever lecture on his proof of Fermat's Last Theorem. The institute buzzed with rumors that his lecture would contain a big surprise, but few realized just how big it would be. Using a regular chalkboard, Wiles sketched his proof for the audience of experts, who burst into explosive applause when he came to the end and concluded that he had proved Fermat's Last Theorem. It was a few months later that a gap appeared in the proof, and it wasn't until sometime after that that the proof was finally complete. But many remember Wiles's historic lecture as a high point for mathematics. May: May 1923: Cathleen Synge Morawetz , the second woman to serve as President of the AMS, was born in Toronto, Canada. Her parents were both Irish and both trained in mathematics. Her father, John Lighton Synge, was on the faculty of the University of Toronto, and, after the family moved back to Ireland, he moved to Dublin University. Morawetz went to the Courant Institute at New York University as a doctoral student and finished her Ph.D. in 1951, under the direction of Kurt O. Friedrichs. She became part of the legendary group that, under the leadership of Richard Courant, made the Courant Institute the premier center for applied mathematics in the United States. She made fundamental contributions to partial differential equations related to shock waves and transonic flow. Her many honors include the National Medal of Science (1998) and the AMS Steele Prize (2003). Morawetz served as AMS President from 1995 to 1997. Read more about her in a

79. Russian Reports He Has Solved A Celebrated Math Problem By SARA ROBINSON. russian mathematician is reporting that he has proved the Poincaré Conjecture, one of the most famous unsolved problems in mathematics. http://www.math.uic.edu/~agol/blog/15MATH.html

April 15, 2003 Russian Reports He Has Solved a Celebrated Math Problem By SARA ROBINSON 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.

80. Type_Document_Title_here Department of Applied Mathematics is one of the leading russian centers in the field of mathematical physics, mathematical and computer modeling, and http://pm.miem.edu.ru/info_e.htm

FACULTY OF APPLIED MATHEMATICS Department "Applied Mathematics" Phone: +7(095)916-88-76. E-mail:pm@miem.edu.ru Head of the Department -laureate of State prize of the Russian Federation,Doctor of Science in Physics and Mathematics, Professor Karasev M.V. The graduates acquire the rank of engineers-mathematicians in speciality "Use of mathematical methods for solving engineering and economical problems" within the framework of speciality "Applied Mathematics". The term of study is 5 years. Department of Applied Mathematics is one of the leading Russian centers in the field of mathematical physics, mathematical and computer modeling, and information science. The first Head of the Department of Applied Mathematics was a prominent Russian mathematician and specialist in mechanics, academician Viktor Maslov. During the 30 years of the existence of the Department of Applied Mathematics, more than 30 monographs and manuals and more than 1000 scientific papers were published in central Russian and foreign Publishing houses. The studies of the members of the teaching and research staff and of postgraduate and graduate students were supported by numerous grants (Russian Foundation for Basic Research, Ministry of Education of the Russian Federation, the International Science Foundation, INTAS, and some others). Three professors of the Department were awarded stipends for prominent Russian scientists and two professors were awarded the title of Soros professor.

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