81. John Quiggin » Blog Archive » Riemann Hypothesis Proved ? I bought a book on the riemann hypothesis a few months ago “The Riemann Are teams engineers waiting for the final word on the riemann hypothesis before http://johnquiggin.com/index.php/archives/2004/06/11/riemann-hypothesis-proved/

John Quiggin A real bargain Darfur and the G8 Riemann hypothesis proved ? According to this report It is also, I think, the last of the big and well-known unsolved problems in mathematics, and its nice to see the search ending in success. Some of the other big problems have been closed, rather than solved. The classic problems of the Greeks such as squaring the circle were shown to be insoluble in the 19th century, and the Hilbert program of formalisation was shown by Godel to be infeasible. And the four-colour problem (not a really important problem, but a big one because it was easily described, interesting and very tough) was dealt with by a brute-force computer enumeration. Almost instant update Commenter Eric points to Mathworld This entry was posted on Friday, June 11th, 2004 at 1:48 pm and is filed under Philosophy . You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed. Eric Says: June 11th, 2004 at 2:06 pm

82. *Concerns Of Young Mathematicians* || Louis De Branges Proves The Riemann Hypoth De Branges has often claimed to have proved the riemann hypothesis before. Louis De Branges proves the riemann hypothesis again 0 comments (0 http://concerns.youngmath.net/story/2004/6/10/17438/3407

The Young Mathematicians' Network Serving the Community of Young Mathematicians Sections: Front Page News Grad Life Undergrad Life ... All Louis De Branges proves the Riemann Hypothesis ... again Research By overconvergent Posted Thu Jun 10th, 2004 at 17:43:08 PDT This seems to be the time of year for attempted solutions to very hard problems. Unfortunately, Arenstorf has withdrawn his paper which claimed to prove the Twin Prime conjecture , but the BBC is reporting that Louis De Branges has claimed to have proved the Riemann hypothesis. Post a Comment The professional mathematicans on sci.math are slightly sceptical about this: The same [proof]? or a new one? De Branges has often claimed to have proved the Riemann hypothesis before. However, he did play an important role in the proof of the Bieberbach conjecture, so there is at least the possibility that this is a correct proof. I am not completely convinced that it is useful for the mainstream (non-mathematical) media to report such things so credulously. It is quite likely that De Branges is wrong, and therefore it might have been better to hold the story until other mathematicians had actually read his new preprints.

83. The Riemann Hypothesis: The Most Important Unsolved Problem In Mathematics The Mathematical Explorer allows us to understand some of the functions relatedto the Riemann function and to examine some of the evidence for the truth of http://www.wolfram.com/products/explorer/topics/riemann.html

PreloadImages('/common/images2003/btn_products_over.gif','/common/images2003/btn_purchasing_over.gif','/common/images2003/btn_services_over.gif','/common/images2003/btn_new_over.gif','/common/images2003/btn_company_over.gif','/common/images2003/btn_webresource_over.gif'); Products The Mathematical Explorer What Is The Mathematical Explorer ... Give us feedback Sign up for our newsletter: Part of the glamour, mystery, and excitement of mathematics involves finding solutions to famous problems. The Four-Color Problem and Fermat's Last Theorem have been solved in the past 30 years to great public acclaim. Both of these long-standing problems are easy to state even though their solutions baffled the best minds in mathematics for centuries. There is general agreement in the mathematical community that the most important unsolved problem of mathematics now is the Riemann Hypothesis. This hypothesis involves concepts of advanced mathematics but connects to elementary notions such as prime numbers. A proper understanding of the Riemann Hypothesis requires some advanced mathematics, but you will see how The Mathematical Explorer allows us to understand some of the functions related to the Riemann function and to examine some of the evidence for the truth of the Riemann Hypothesis.

84. Foreign Dispatches: Reasons To Doubt The Riemann Hypothesis http://foreigndispatches.typepad.com/dispatches/2005/06/reasons_to_doub.html

Foreign Dispatches Random Remarks on Current Affairs Advertising Periodicals Asahi (English) Daily Star (Lebanon) Der Spiegel Die Zeit ... Yomiuri (English) Math/IT ACM AMS Acta Arithmetica Annals of Mathematics ... PARC - User Interfaces References Classic Works of Japanese Literature Government Accountability Office International Monetary Fund MIT OpenCourseWare ... World Bank Politics American Enterprise Institute Brookings Institution Cato Institute Centre for the New Europe Blogs A Different Opinion A Fistful of Euros Adam Smith Institute AdamSmithee ... Winds of Change Sitemeter var site="s12fgndisp" Math Books K. F. Ireland and M. Rosen: A Classical Introduction to Modern Number Theory Herbert B. Enderton: A Mathematical Introduction to Logic Robin Hartshorne: Algebraic Geometry G. H. Hardy, E.M. Wright: An Introduction to the Theory of Numbers ... Main June 09, 2005 Reasons to Doubt the Riemann Hypothesis I found this while looking up all citations of Odlyzko and Riele's paper disproving Mertens' Conjecture . Although I'm 99% convinced that the Riemann Hypothesis is true, if anyone is in a position to know why it might be false, it's Aleksandar Ivic , who's literally written the book (or at least, one of the books) on the Riemann zeta function.

85. Noscope | Riemann Hypothesis This entry is entitled riemann hypothesis , and is filed under Sidenotes.It was published June 12th, 2004. Subscribe To This Entry. Email. Comments (XML) http://www.noscope.com/journal/2004/06/riemann-hypothesis

Noscope Index Journal Archives ... Colophon Search Fahrenheit Posters Home Google: FutureSplash June ... Riemann Hypothesis [Riemann hypothesis] Filed in Sidenotes Leave a Comment Name (required) E-mail (required) Website Formatting your comment Close Formatting Your Comment The following XHTML tags are available for use: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <code> <em> <i> <strike> <strong> URLs are automatically converted to hyperlinks. Textile Textile is a method that uses simple symbols to quickly write rich text markup. These are the most common: *strong* -deleted text- "link text":http://link.url bq. quoted content @short code snippet@ Back to Top Larger Smaller Your Comment Notify me of followup comments via e-mail Preview: Anonymous says: Posted on September 17th, 2005, 01:44 This Entry Riemann Hypothesis " was written June 12th, 2004 and filed under Sidenotes There are no responses. Jump to comments or follow responses via XML Subscribe without commenting E-Mail: Ongoing Discussions ZenPhoto 0.8 Released!

86. [Prime] Riemann Hypothesis : Proof? Prime riemann hypothesis Proof? Yann Forget yann at forgetme.net Sat Sep 18083816 PDT 2004. Previous message Prime riemann hypothesis Proof? http://hogranch.com/pipermail/prime/2004-September/000201.html

[Prime] Riemann hypothesis : Proof? Yann Forget yann at forget-me.net Sat Sep 18 08:38:16 PDT 2004 Previous message: [Prime] Riemann hypothesis : Proof? Next message: [Prime] cgi-bin/primenet_user.pl not working? Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] An article relating to primes and the Riemann hypothesis. Someone claims to have a proof - which, of course, isn't provided in the article. (The proof would, I'm sure, be over my head anyway.) http://www.guardian.co.uk/uk_news/story/0,3604,1298728,00.html I thought some of you might find it interesting. Anyway, yes, interesting reading. Thanks. Yann http://www.non-violence.org/ http://www.forget-me.net/ http://fr.wikipedia.org/ http://www.forget-me.net/pro/ Previous message: [Prime] Riemann hypothesis : Proof? Next message: [Prime] cgi-bin/primenet_user.pl not working? Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the Prime mailing list

87. [Prime] Riemann Hypothesis : Proof? Prime riemann hypothesis Proof? Stephen Whitis gimps at whitis.com An article relating to primes and the riemann hypothesis. http://hogranch.com/pipermail/prime/2004-September/000200.html

[Prime] Riemann hypothesis : Proof? Stephen Whitis gimps at whitis.com Sat Sep 18 06:31:13 PDT 2004 Previous message: [Prime] Counting Number of Digits of a^n Next message: [Prime] Riemann hypothesis : Proof? Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] An article relating to primes and the Riemann hypothesis. Someone claims to have a proof - which, of course, isn't provided in the article. (The proof would, I'm sure, be over my head anyway.) http://www.guardian.co.uk/uk_news/story/0,3604,1298728,00.html I thought some of you might find it interesting. Previous message: [Prime] Counting Number of Digits of a^n Next message: [Prime] Riemann hypothesis : Proof? Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the Prime mailing list

88. Could Solution To Riemann Hypothesis Endanger Internet Security? :: Ephilosopher Philosophy News, Research and Philosophical Discussion. http://www.ephilosopher.com/article871.html

@import url("themes/PostNukeBlue2/style/style.css"); E P H I L O S O P H E R Sep 16, 2005 - 07:06 PM Hey You! Want to join? or Login Search advanced web Menu Home Site Map Academic Jobs Fun Stuff Philosophy ... Community Special Sections Feeds Help Archives Notices The Dialectical Biologist Bunge's Treatise, vol. 5 Bunge's Treatise, vol. 6 Philosophy Tutor in London ... More... Quotables Can one be a saint if God does not exist? That is the only concrete problem I know of today. - The Plague Albert Camus EP Newsletter You are currently not logged in , but you can still subscribe to our newsletter. Links Books Harry Potter and the Half-Blood Prince Could Solution to Riemann Hypothesis Endanger Internet Security? Posted by: adimantis on Monday, September 06, 2004 - 06:37 PM Related: Reclusive Russian May Have Made Maths Breakthrough , reuters.com , Big Maths Solution "looks good" , BBC Guardian.co.uk: "Mathematicians could be on the verge of solving two separate million dollar problems. If they are right - still a big if - and somebody really has cracked the so-called Riemann hypothesis, financial disaster might follow. Suddenly all cryptic codes could be breakable. No internet transaction would be safe. On the other hand, if somebody has already sorted out the so-called Poincaré conjecture, then scientists will understand something profound about the nature of spacetime, experts told the

89. Riemann S Zeta Function This conjecture, known as the riemann hypothesis, has never been proved or The riemann hypothesis makes the zeta function so famous, and numerical http://numbers.computation.free.fr/Constants/Miscellaneous/zeta.html

The Riemann Zeta-function z (s) (pdf version : pdf ; (postscript version : ps The Riemann Zeta-function is defined as z (s) = n=1 n s for complex values of s. While converging only for complex numbers s with z n=1 n but it was Riemann who, in the 1850's, generalized its use and showed that the distribution of primes is related to the location of the zeros of z (s). Riemann conjectured that the non trivial zeros of z (s) are located on the critical line (s)=1/2. This conjecture, known as the Riemann hypothesis , has never been proved or disproved, and is probably the most important unsolved problem in mathematics. The Riemann hypothesis makes the zeta function so famous, and numerical computation have been made to check it for various sets of zeros. We expose here the most classical results about the zeta-function, together with some computational aspects. Our presentation is divided into several parts that are listed here : The Riemann Zeta-function z (s) : generalities Numerical evaluation of the Riemann Zeta-function ... Computation of zeros of the Zeta function . Contains announcement and details of the latest record about Riemann Hypothesis numerical verification (on the first 10 zeros), and about zeros computation at very large height.

90. Riemann Hypothesis From ALL; Date May 7, 2005; Subject riemann hypothesis. Hi,. Can someone giveme a simple definition to the riemann hypothesis. http://at.yorku.ca/cgi-bin/bbqa?forum=ask_an_algebraist_2005;task=show_msg;msg=1

91. Holtzbrinck Academic Marketing In The riemann hypothesis, acclaimed author Karl Sabbagh interviews some of The riemann hypothesis provides ample handholding for anyone who pales at http://www.holtzbrinckpublishers.com/academic/book/BookDisplay.asp?BookKey=15662

92. Riemann Hypothesis And Primes - Physics Help And Math Help - Physics Forums Physics Forums is a science and physics community. http://www.physicsforums.com/showthread.php?goto=lastpost&t=80292

93. Slashdot | Riemann Hypothesis Proved? riemann hypothesis Proved? article related to Encryption, Education, and Science. http://science.slashdot.org/article.pl?sid=03/03/03/1224243&mode=thread&tid=93&t

94. Foreign Dispatches: Has The Riemann Hypothesis Been Proven? Has the riemann hypothesis been Proven? From this press report, it would appearthat Louis de Branges, of Bieberbach Conjecture fame, is claiming a proof of http://reti.blogspot.com/2004/06/has-riemann-hypothesis-been-proven.html

Foreign Dispatches Random remarks on current affairs. Thursday, June 10, 2004 Has the Riemann Hypothesis been Proven? From this press report , it would appear that Louis de Branges, of Bieberbach Conjecture fame, is claiming a proof of the Riemann Hypothesis This, if true, would be the single greatest mathematical result of the decade, and maybe even of the last 100 years, depending on one's viewpoint; as such, I shall refuse to accept that the Riemann Hypothesis has fallen until de Branges' proof goes through the normal process of peer review several times. The strangest thing about this purported proof is the rambling style of the " apology ", which touches on, amongst many other things, de Branges' early life, his mathematical education and even his ancestral backround, including how he intends to use the million-dollar Clay prize to rehabilitate his ancestral seat; the real meat and potatoes are saved for a 124-page paper innocuously titled Riemann Zeta Functions . Now, it may be that the guy's always been an oddball, but there's just something about the way he's chosen to announce his results (why a press release, instead of via ArXiv ?) that tells me that the old boy's gone completely nuts, a known occupational hazard of the mathematician's profession.

95. Riemann's Hypothesis And Tests For Primality The second upper bound is dependent on the Extended riemann hypothesis (ERH)assuming Jacques Vélu, Tests for primality under the riemann hypothesis, http://portal.acm.org/citation.cfm?id=803773

96. Riemann Hypothesis riemann hypothesis. Ronn!Blankenship ronn.blankenship at att.net Thu Jun 10163658 PDT 2004. Previous message riemann hypothesis; Next message Riemann http://www.mccmedia.com/pipermail/brin-l/Week-of-Mon-20040607/004526.html

Riemann hypothesis Ronn!Blankenship ronn.blankenship at att.net Thu Jun 10 16:36:58 PDT 2004 Previous message: Riemann hypothesis Next message: Riemann hypothesis Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] "Ronn!Blankenship" wrote: http://zdnet.com.com/2100-1104_2-5229702.html?tag=zdfd.newsfeed http://www.math.purdue.edu/ftp_pub/branges/apology.pdf I have not read the paper. I found out about it and figured that I should share now, rather than waiting however long it might take for me to get the time to get through the paper. :) Julia with someone screaming at me even as I type That would indeed make it difficult to concentrate on mathematical reasoning of any sort, as having forgotten your functional analysis would be an impediment to reading that particular paper. (I, too, passed it along to others, including at least one who ought to be able to make some intelligent comments, presuming he finds the time to do so . . . ) Ronn! :) Previous message: Riemann hypothesis Next message: Riemann hypothesis Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the Brin-l mailing list

97. Riemann Hypothesis riemann hypothesis. Ronn!Blankenship ronn.blankenship at att.net Wed Jun 9 220514PDT 2004. Previous message riemann hypothesis; Next message Riemann http://www.mccmedia.com/pipermail/brin-l/Week-of-Mon-20040607/004507.html

Riemann hypothesis Ronn!Blankenship ronn.blankenship at att.net Wed Jun 9 22:05:14 PDT 2004 Previous message: Riemann hypothesis Next message: Riemann hypothesis Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Louis de Branges de Bourcia of Purdue University claims to have proven the Riemann Hypothesis. It still has to be peer-reviewed. Article at http://zdnet.com.com/2100-1104_2-5229702.html?tag=zdfd.newsfeed Paper in PDF format at http://www.math.purdue.edu/ftp_pub/branges/apology.pdf So, presuming you have read the paper, what do you think? Can he tell us, do you truly confess? Ronn! :) Previous message: Riemann hypothesis Next message: Riemann hypothesis Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the Brin-l mailing list

98. Riemann Hypothesis Proved? CNET News.com riemann hypothesis proved? With eyes on $1 million prize, Purdue Universityprofessor publishes proof for cult math problem. http://news.com.com/Riemann hypothesis proven?/2100-7348_3-5229702.html

99. Inside ISPCON: Cracked Riemann Hypothesis Would Spell Massive Crypto Disaster Cracked riemann hypothesis would spell massive crypto disaster. Whoa, someonemay have cracked the socalled riemann hypothesis, which would spell financial http://ispcon.blogs.com/ispcon/2004/09/cracked_riemann.html

Inside ISPCON Views from the Inside of ISPCON About IM Me ICQ: 236155890 Yahoo: jon_t_price AIM: goldengroupie Sign up for the Fall show! September 2005 Sun Mon Tue Wed Thu Fri Sat Googaliciousness (wanna help me pay Typepad?) Recent Comments Satish Bhardwaj on GoogLink - GoogleNet=Cogent Frank Muto on Martin + Bush 2007 BB Goal Roger on Now THAT'S churn Renee Johnson on Photos from Spring ISPCON SATISH BHARDWAJ on AOL says their spam is down 75% SATISH BHARDWAJ on Stalker Software and Ciphertrust Session SATISH BHARDWAJ on Eyes on IPTV moves, AOL's in particular SATISH BHARDWAJ on SBC moves closer to that 20,000 hotspot target Peter Radizeski on Consumer Advisory Committee Meeting tell on SBC does 19.95/mo DSL Fall 04 Session Audio Photo Albums ABEOC EC Expo INBOX East INBOX West 2004 ... Main Cracked Riemann hypothesis would spell massive crypto disaster Whoa, someone may have cracked the so-called Riemann hypothesis, which would spell financial disaster for electronic commerce. Suddenly all cryptic codes could be breakable. No internet transaction would be safe. The Riemann hypothesis would explain the apparently random pattern of prime numbers - numbers such as 3, 17 and 31, for instance, are all prime numbers: they are divisible only by themselves and one. Prime numbers are the atoms of arithmetic. They are also the key to internet cryptography: in effect they keep banks safe and credit cards secure.

100. Mathematics Magazine: Purdue Mathematician Claims Proof For Riemann Hypothesis Boutin, Chad, Purdue mathematician claims proof for riemann hypothesis, PurdueNews (8 June 2004), http//news.uns.purdue.edu/UNS/html4ever/2004/040608. http://www.findarticles.com/p/articles/mi_qa3789/is_200410/ai_n9458576

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Home Advanced Search IN free articles only all articles this publication Automotive Sports FindArticles Mathematics Magazine Oct 2004 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Featured Titles for ASA News ASEE Prism Academe African American Review ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports Purdue mathematician claims proof for Riemann hypothesis Mathematics Magazine Oct 2004 by Campbell, Paul J Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. Boutin, Chad, Purdue mathematician claims proof for Riemann hypothesis, Purdue News (8 June 2004), http://news.uns.purdue.edu/UNS/html4ever/2004/040608.DeBranges.Riemann.html. Hogan, Jenny, Mathematicians sceptical over claimed breakthrough, New Scientist (11 June 2004), http://www.newscientist.com/news/news.jsp?id=ns99995104 . de Branges de Bourcia, Louis, Apology for the proof of the Riemann hypothesis, and Riemann zeta functions, both available at http://www.math.purdue.edu/~branges/. Conrey, J.B., and Xian-Jin Li. A note on some positivity conditions related to zeta and L-functions. International Mathematics Research Notices 2000 (18) 929-940 http://arxiv.org/abs/math.NT/9812166. Louis de Branges de Bourcia (Purdue) has announced a proof of the Riemann hypothesis, one of the Clay Foundation's Millennium Million-Dollar Prize Problems, following a research program that he announced in 1986. However, Conrey and Li "indicate the difficulty of approaching the Riemann hypothesis by using de Branges' positivity conditions," a result that suggests that de Branges's approach can't work. (Of course, unless there's an easy proof that everybody missed, any approach will be difficult.) Nevertheless, in 1985 de Branges proved the Bieberbach conjecture, a famous unsolved problem open since 1916, about coefficients of power series of conformai maps of the unit disk.

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