81. Prime Numbers Get Hitched § SEEDMAGAZINE.COM Mar 27, 2006 For 150 years many have been too frightened to tackle the Riemann Hypothesis. The prospect that we might finally have the tools to http://seedmagazine.com/content/article/prime_numbers_get_hitched/

var activeTags = new Array( "geometry", "limits", "math", "structure", "theory" ); Seed Magazine about SEEDMAGAZINE.COM October 31, 2010 Prime Numbers Get Hitched Incubator / by Marcus du Sautoy / March 27, 2006 In their search for patterns, mathematicians have uncovered unlikely connections between prime numbers and quantum physics. Will the subatomic world help reveal the elusive nature of the primes? Print In 1972 It is striking that Dyson should have written about scientific ships passing in the night. Shortly after he published the piece, he was responsible for an abrupt collision between physics and mathematics that produced one of the most remarkable scientific ideas of the last half century: that quantum physics and prime numbers are inextricably linked. This unexpected connection with physics has given us a glimpse of the mathematics that might, ultimately, reveal the secret of these enigmatic numbers. At first the link seemed rather tenuous. But the important role played by the number 42 has recently persuaded even the deepest skeptics that the subatomic world might hold the key to one of the greatest unsolved problems in mathematics. Prime numbers

82. Science Fair Projects - Riemann Hypothesis The Ultimate Science Fair Projects Encyclopedia Riemann hypothesis http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/RH

All Science Fair Projects Science Fair Project Encyclopedia for Schools! Search Browse Forum Coach ... Dictionary Science Fair Project Encyclopedia For information on any area of science that interests you, enter a keyword (eg. scientific method, molecule, cloud, carbohydrate etc.). Or else, you can start by choosing any of the categories below. Science Fair Project Encyclopedia Contents Page Categories Analytic number theory Zeta functions ... Conjectures Riemann hypothesis (Redirected from RH RH directs here. RH is also the common abbreviation for the soap opera Ryan's Hope In mathematics , the Riemann hypothesis , first formulated by Bernhard Riemann in , is one of the most famous of all unsolved problems. It has been an open question for well over a century, despite attracting concentrated efforts from many outstanding mathematicians. Unlike some other celebrated problems, it is more attractive to professionals in the field than to amateurs. The Riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function s ). The Riemann zeta function is defined for all

83. Riemann Hypothesis | Facebook Welcome to the Facebook Community Page about Riemann hypothesis, a collection of shared knowledge concerning Riemann hypothesis. http://www.facebook.com/pages/Riemann-hypothesis/109579369061011

Riemann hypothesis 226 people like this. to connect with Wall Info Fan Photos Riemann hypothesis + Others Riemann hypothesis Just Others Riemann hypothesis changed their Description October 25 at 12:07pm Riemann hypothesis changed their Description October 24 at 9:10am Riemann hypothesis joined Facebook. March 26 at 11:06pm See More Posts English (US) Español More… Download a Facebook bookmark for your phone. Login Facebook ©2010

84. A Whirlpool Of Numbers | Plus.maths.org The conjecture has become known as the Riemann Hypothesis and it is the key to understanding the distribution of the primes. Recent computerbased calculations have shown that at http://plus.maths.org/issue25/features/whirlpool/index.html

Skip to Navigation about Plus support Plus Plus sponsors ... subscribe to Plus Search this site: A whirlpool of numbers by Nick Mee Issue 25 Submitted by plusadmin on April 30, 2003 in Arthur C Clarke cryptography Fundamental theorem of arithmetic number theory ... zeta function May 2003 Jeserac sat motionless within a whirlpool of numbers. The first thousand primes, expressed in the binary scale that had been used for all arithmetical operations since electronic computers were invented, marched in order before him. Endless ranks of 1's and 0's paraded past, bringing before Jeserac's eyes the complete sequences of all those numbers that possessed no factors except themselves and unity. There was a mystery about the primes that had always fascinated Man, and they held his imagination still. Jeserac was no mathematician, though sometimes he liked to believe he was. All he could do was to search among the infinite array of primes for special relationships and rules which more talented men might incorporate in general laws. He could find how numbers behaved, but he could not explain why. It was his pleasure to hack his way through the arithmetical jungle and sometimes he discovered wonders that more skilful explorers had missed. He set up the matrix of all possible integers, and started his computer stringing the primes across its surface as beads might be arranged at the intersections of a mesh. Jeserac had done this a hundred times before and it had never taught him anything. But he was fascinated by the way in which the numbers he was studying were scattered, apparently according to no laws, across the spectrum of the integers. He knew the laws of distribution that had already been discovered, but always hoped to discover more.

85. The Believer - The Last Great Problem I ll say here that the Riemann Hypothesis (RH, among pros) concerns the The Riemann Hypothesis is safe only for those people who know enough math to http://www.believermag.com/issues/200311/?read=article_ellenberg

86. Teacher Package: Prime Numbers | Plus.maths.org Dec 1, 2008 The prime number lottery — The first of a two part exploration of the Riemann Hypothesis by Marcus du Sautoy. We find out how the German http://plus.maths.org/content/teacher-package-prime-numbers

Skip to Navigation about Plus support Plus Plus sponsors ... subscribe to Plus Search this site: Teacher package: Prime numbers Issue 49 Submitted by plusadmin on December 1, 2008 in teacher package December 2008 The Plus teacher packages are designed to give teachers (and students) easy access to Plus content on a particular subject area. Most Plus articles go far beyond the explicit maths taught at school, while still being accessible to someone doing A level maths. They put classroom maths in context by explaining the bigger picture — they explore applications in the real world, find maths in unusual places, and delve into mathematical history and philosophy. We therefore hope that our teacher packages provide an ideal resource for students working on projects and teachers wanting to offer their students a deeper insight into the world of maths. Prime numbers This teacher package brings together all Plus articles on prime numbers. In addition to the Plus articles, the try it yourself section provides links to related problems on our sister site NRICH We've grouped the articles into four categories: Hunting primes — We've known since ancient times that there are infinitely many primes, but how do you find them all? This category looks at prime number algorithms and new discoveries of largest primes;

87. Documents For Exponential Sums Course (FS 2010) Sep 20, 2010 These are notes (from 1998/1999) of three lectures trying to explain Deligne s first proof of the Riemann Hypothesis over finite fields, http://www.math.ethz.ch/~kowalski/exp-sums.html

Exponential sums over finite fields, I and II (ETHZ FS 2010, HS 2010) This page contains links and documents relevant to the first part of the course, which ran in the Spring Semester 2010, as well as the second part, which is running in Fall Semester 2010. : First almost complete draft of the lecture notes of part I are available. : Information concerning the second part of the course added. Here is the abstract in the catalogue for the first part: This course will introduce exponential sums over finite fields. It will first discuss basic examples (Gauss sums, Kloosterman sums, etc) and motivations for their study, coming from various problems of number theory, such as counting integral solutions of certain diophantine equations using the circle method. We will then develop some of the existing techniques that can be used to obtain interesting bounds for such sums, concentrating on elementary methods which do not involve deep algebraic geometry, such as the Stepanov method (leading to the Riemann Hypothesis for one-variable exponential sums, proved first by Weil) and the more recent methods based on additive combinatorics, introduced by Bourgain. It is expected that the course will be followed by another one in Winter Semester 2010 which will present the methods and results coming from more advanced algebraic geometry (work of Grothendieck, Deligne, Katz and others) and their applications. And here is the abstract for the second part: This course will present the modern techniques, based on algebraic geometry, that are used to study exponential sums over finite fields. Because of the large amount of material involved, a number of important facts will be taken as "black boxes", including Deligne's statement of the general form of the Riemann Hypothesis over finite fields. However, the way to use this formalism will be explained in detail, with a particular emphasis on Deligne's Equidistribution Theorem. Various applications will be given, including bounds for multi-variable character sums, families of exponential sums, and certain sieve problems.

88. BARRY MAZUR 1. - NUMBER THEORY AS GADFLY - BARRY MAZUR 1. Comments File Format PDF/Adobe Acrobat Quick View http://tan.epfl.ch/~rhoades/Notes/mazur-NTasGadfly.pdf

89. The Riemann Hypothesis For Elliptic Curves File Format PDF/Adobe Acrobat Quick View http://www.math.ucdavis.edu/~osserman/math/riemann-elliptic.pdf

90. Distinguished Lecture Series Jul 30, 2010 The Riemann Hypothesis has, for more than a century and a half, to a friend declaring that he had proved the Riemann Hypothesis. http://maa.org/news/072810Conrey.html

MAA Distinguished Lecture Series Past Lectures From Primes to Zeros, Brian Conrey Tours the Riemann Hypothesis at MAA Distinguished Lecture July 30, 2010 The Riemann Hypothesis has, for more than a century and a half, resisted every attempt at proof or disproof. Along the way, this key question about the distribution of prime numbers has developed a mystique among the many mathematicians obsessed with the problem. At an MAA Distinguished Lecture on July 28, Brian Conrey , executive director of the American Institute of Mathematics In the 1930s, when G.H. Hardy once embarked on what promised to be a stormy sea voyage, he wrote a postcard to a friend declaring that he had proved the Riemann Hypothesis. He reasoned that God would not allow him credit for such a great honor, so would keep the boat from sinking. Thomas Jan Stieltjes claimed in 1885 to have proved a statement that implied the Riemann Hypothesis, and he was widely believed. He never wrote down the proof. In a 1997 email message that was forwarded around the world, Enrico Bombieri Conrey presents his Distinguished Lecture in MAA's Carriage House Conrey began with primes: numbers evenly divisible by only themselves and 1. The first few prime numbers are 2, 3, 5, 7, 11, and 13, but the list continues forever. There is no largest prime number.

91. JSTOR: An Error Occurred Setting Your User Cookie Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.jstor.org/stable/2000378

Skip to main content Login Help Contact Us Trusted archives for scholarship Search Basic Advanced Citation Locator ... Profile An Error Occurred Setting Your User Cookie The JSTOR site requires that your browser allows JSTOR ( http://www.jstor.org ) to set and modify cookies. JSTOR uses cookies to maintain information that will enable access to the archive and improve the response time and performance of the system. Any personal information, other than what is voluntarily submitted, is not extracted in this process, and we do not use cookies to identify what other websites or pages you have visited. JSTOR is part of ITHAKA, a not-for-profit organization helping the academic community use digital technologies to preserve the scholarly record and to advance research and teaching in sustainable ways. Terms and Conditions Accessibility

92. DE GRUYTER - Mathematics - Casimir Force, Casimir Operators And The Riemann Hypo This volume contains the proceedings of the conference Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry http://www.degruyter.de/cont/fb/ma/detailEn.cfm?isbn=978-3-11-022613-3

93. On Robin S Criterion For The Riemann Hypothesis File Format PDF/Adobe Acrobat Quick View http://www.emis.de/journals/JTNB/2007-2/article03.pdf

94. Abundant Numbers And The Riemann Hypothesis File Format PDF/Adobe Acrobat Quick View http://www.expmath.org/expmath/volumes/15/15.2/Briggs.pdf

95. A Sequential Riesz-like Criterion For The Riemann Hypothesis by B Luis 1900 http://www.hindawi.com/journals/ijmms/2005/141565.abs.html

96. Some Observations On The Riemann Hypothesis The Riemann hypothesis1, 2 remains the most challenging unsolved problem in mathematics at the beginning of the third millennium. The other two problems http://www.dhushara.com/DarkHeart/RH2/RH.htm

Experimental Observations on the Riemann Hypothesis, and the Collatz Conjecture Chris King Mathematics Department, University of Auckland PDF (with full size equations) Abstract: This paper seeks to explore whether the Riemann hypothesis falls into a class of putatively unprovable mathematical conjectures, which arise as a result of unpredictable irregularity. It also seeks to provide an experimental basis to discover some of the mathematical enigmas surrounding these conjectures, by providing Matlab and C programs which the reader can use to explore and better understand these systems (see appendix 6 Fig 1: The Riemann functions and : absolute value in red, angle in green. The pole at z = 1 and the non-trivial zeros on x as a peak and dimples. The trivial zeros are at the angle shifts at even integers on the negative real axis. The corresponding zeros of show in the central foci of angle shift with the absolute value and angle reflecting the functionÕs symmetry between z and 1 - z . If there is an analytic reason why the zeros are on x Mac XCode High performance RZ Viewer Source Code Flight manual This gives excellent high performance rendition of zeta and related functions and their Mandelbrot and Julia sets . It has been developed and tested on both Tiger and Snow Leopard. For companion complex function viewers see Dark Heart Matlab toolbox - Full Matlab and XCode download PDF version of the article with full size equations Introduction The Riemann hypothesis and the Zeta Function The Quantum Chaos Connection Julia and Mandelbrot sets of the Riemann Zeta Function ... References Introduction:

97. Chance News 2 - ChanceWiki Sep 26, 2005 1 Dan Rockmore s book Stalking the Riemann Hypothesis He chose as his topic The Riemann Hypothesis This is generally considered the http://www.causeweb.org/wiki/chance/index.php/Chance_News_2

Chance News 2 From ChanceWiki June 1 2005 to June 30 2005 Table of contents showTocToggle("show","hide") 1 Dan Rockmore's book: Stalking the Riemann Hypothesis 2 The powerball lottery suspects fraud, but it's the Fortune Cookies 3 Red enhances human performance in contests 4 Mix math and medicine and create confusion ... edit Dan Rockmore's book: Stalking the Riemann Hypothesis Stalking the Riemann Hypothesis http://www.amazon.com/exec/obidos/ASIN/037542136X/qid%3D1111091478/sr%3D2-1/ref%3Dpd%5Fbbs%5Fb%5F2%5F1/103-9738865-3722248 Pantheon Books, New York, 2005 Dan Rockmore The Proof: an interview with Dan Rockmore http://nhpr.org/view_content/8573/ New Hampshire Public April 12. 2005 John Walters As the stakes increase, Prime-Number theory Moves Closer to Proof http://www.cs.dartmouth.edu/~rockmore/WSJ.pdf Wall Street Journal, Science Journal, April 8. 2005 Sharon Begley Math Monster http://www.cs.dartmouth.edu/~rockmore/telegraph.html The Telegraph (Calcutta, India), April 8, 2005 Pathik Guha In 1998 the Mathematical Sciences Research Institute in Berkeley, California http://www.msri.org had a three-day conference on "Mathematics and the Media". The purpose of this conference was to bring together science writers and mathematicians to discuss ways to better inform the public about mathematics and new discoveries in mathematics. As part of the conference, they asked Peter Sarnak, from Princeton University, to talk about new results in mathematics that he felt the science writers might like to write about. He chose as his topic "The Riemann Hypothesis" This is generally considered the most famous unsolved problem in mathematics and is the major focus of Sarnak's research.

98. Riemann Hypothesis That this is the case is the Riemann Hypothesis. This mystery is so important for the mathematicians that the one who strictly proves that all nontrivial http://www.math-it.org/Mathematik/Riemann/Riemannia.html

Home About math IT Mathematics Quantum Computation e-mail The Mystery of the Land of Riemannia Somewhere, far behind one of the infinite dimensions of Hilbert space, there is the Land of Riemannia. It was discovered in 1859 by Bernhard Riemann (1826-1866), and so it bears his name. Riemann was a mathematician, and also the few pioneers who entered this land were mathematicians. This might frighten some of you, but let me nonetheless some tell me remarkable facts about it. Certainly, one of the most astonishing things about this land is that you can shoot two distinct photographs of the same lanscape: the landscape is four-dimensional! Figure 1: Three perspectives of Riemannia. These are the graphs of the real part, , of the imaginary part, , and of the absolute value of the Riemann zeta function. ( .) You recognize the wide plane in the East ( x s = 1 and y = 0, and the wild mountains in the West. Figs. from: http://mathworld.wolfram.com/RiemannZetaFunction.html The mathematicians call the ``landscape'' the graph of the Riemann Zeta function , in symbols , where s is a so-called complex number. Complex numbers contain the square roots of negative numbers, especially the number

99. THE PURSUIT OF THE RIEMANN HYPOTHESIS John Derbyshire, Prime File Format PDF/Adobe Acrobat Quick View http://homepage.mac.com/mcolyvan/papers/Derbyshire.pdf

Page 5     81-99 of 99    Back | 1  | 2  | 3  | 4  | 5