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Re: [math-fun] DeBranges claims proof of Riemann Hypothesis
by Daniel Asimov 10 Jun '04

10 Jun '04

Hi, Ed. << This has already been disproven via a counterexample. The paper is from last year, and was disproven last year. Why the news services are picking up on an old, known-wrong proof is a mystery. >> I remember hearing de Branges was working on a proof but not the upshot. In any case, could this "proof" respresent an attempt to fixw whatever was wrong with the one last year? Regards, Dan

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Re: [math-fun] Twin prime proof offered (annoyed review, delete before reading)
by Marc LeBrun 09 Jun '04

09 Jun '04

>=Mark D. Niemiec > One can always, in typical mathematical fashion, transform the concrete > into the theoretical, treating 'right-wing' and 'left-wing' as abstract > properties like 'red' and 'green', and then treat the concepts in the article > on their own merits, ignoring any inferred agenda. Yes, indeed one can. Equally if they were labeled "Jewish" and "Aryan". There is no doubting the power of the abstracted self: "The late Professor Jakow Trachtenberg was the founder of the Mathematical Institute in Zurich, Switzerland. After the Czar of Russia was overthrown, he escaped to Germany where he became very critical of Hitler. He was later imprisoned. Most fellow prisoners around him gave up hope and died even before being sent to their death. He realized that if he wanted to stay alive, he had to occupy his mind with something else rather than focus on the hopeless conditions surrounding them. He set his mind on developing methods to perform speed mathematics." (http://www.speed-math.com/) But my point is to question why, in supposedly civilized discourse, one should constantly be rudely required to perform such mental gymnastics just to read a simple account? Is it acceptable to acquiesce to what amounts to the nascent intellectual environment of the death camp without comment? The agenda in Devlin's essay isn't inferred, it's quite demonstrably explicit, unavoidably demanding of "treatment": "When it comes down to it, mathematics, for all that it appears to be the most right wing of disciplines, turns out in practice to be left wing to the core." He is a fine popularizer by a clumsy propagandist. As these meme wars escalate, there will be no non-combatants.

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[math-fun] DeBranges claims proof of Riemann Hypothesis
by Schroeppel, Richard 09 Jun '04

09 Jun '04

Louis DeBranges is claiming a proof of the Riemann Hypothesis. There's a news release from Purdue. His web page: http://www.math.purdue.edu/~branges/ The paper (124 pages) http://www.math.purdue.edu/ftp_pub/branges/riemannzeta.pdf There's also something called "Apology" which seems to be a mix of biography and overview. At least it's shorter. I've downloaded both, and skimmed the Apology. Frankly, it's not much of an apology. It's full of weighting functions and Hankel transforms. He hopes to use the prize to restore an ancestral residence in France. Old timers will recall that LDB presented an incorrect proof of the Bieberbach Conjecture in the 1970s, and then had incredible trouble getting a correct proof accepted in the early 1980s. (It was long, and noone would read it.) Another side of the "difficult proof" coin. Rich rcs(a)cs.arizona.edu

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Re: [math-fun] Twin prime proof offered (annoyed review, delete before reading)
by Mark D. Niemiec 09 Jun '04

09 Jun '04

Marc LeBrun <mlb(a)fxpt.com> wrote: > > Keith Devlin has a non-technical article describing how the error > > was found: http://www.maa.org/devlin/devlin_06_03.html . > > Math-funsters of more genteel sensibility should perhaps be advised that > the cited page is also yet another inflammatory political polemic disguised > as something else, in this case popular mathematical exposition. One can always, in typical mathematical fashion, transform the concrete into the theoretical, treating 'right-wing' and 'left-wing' as abstract properties like 'red' and 'green', and then treat the concepts in the article on their own merits, ignoring any inferred agenda. -- Mark D. Niemiec <mniemiec(a)interserv.com>

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[math-fun] Re: ... Permutation Probabilities
by Chris Landauer 09 Jun '04

09 Jun '04

109*108*...*92*91 126*124*122*120*...*92 Why would ----------------- = ----------------------- ? 127*125*... 93*91 127*126*125*124*...*110 cross multiply - then (127*126*125*124*...*110) * (109*108*...*92*91) = (127*125*... 93*91) * (126*124*122*120*...*92) since the LHS and RHS lines are both 127! / 90! (highs and then lows on the LHS, odds and then evens on the RHS) more later, cal

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RE: [math-fun] Re: ... Permutation Probabilities
by Daniel Asimov 09 Jun '04

09 Jun '04

Hi, Don. Thanks for the explanation. I'm probably missing something, but looking just at our distinct integer expressions for the same probability, it seems non-obvious that they are equal: 109*108*...*92*91 126*124*122*120*...* 92 Why would ----------------- = ----------------------- ? 127*125*... 93*91 127*126*125*124*...*110 --Dan

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[math-fun] Twin prime proof offered
by Richard Schroeppel 09 Jun '04

09 Jun '04

Title: There Are Infinitely Many Prime Twins Authors: R. F. Arenstorf http://arXiv.org/abs/math/0405509 http://www.math.vanderbilt.edu/faculty/Arenstorf.html Richard Arenstorf is a real mathematician, at Vanderbilt. I looked at the 38 page manuscript - it's a well presented bunch of analytic number theory. The proof requires a lot of multi-level series manipulations, and careful arguments about convergence. I'm way too rusty to check this, but it's clearly a serious attempt. He notes that he's been working on the problem intermittently for 20 years. A Google search turned up a few references to his other work. The author claims a bit more: That the expected asymptotic expression for the count is correct, including the twin-prime constant. My quick scan didn't show any reason the proof wouldn't adapt to more general {P,P+2k} twins, although "Twin" would have to be agnostic about the primality of the intermediate numbers between P+2 and P+2k-2 when k>2. Similar ideas might also show the infinity of Sophie Germain pairs P,Q=2P+1 with P and Q both prime; and a restriction to P=3(mod4) would show an infinity of Mersenne composites Mp. The more general problem of primes in arithmetic progressions (longer than 2 of course) was recently settled by a density argument. Arbitrary lengths exist. I'd welcome comments from someone who remembers more of their analytic number theory than I do. Rich rcs(a)cs.arizona.edu

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Re: [math-fun] Permuation Probabilities ... with apologies ...
by Daniel Asimov 09 Jun '04

09 Jun '04

Don reble wrote: << [Guy Haworth wrote: > In the 'knockout' first round involving 128 players and 64 matches, what > is the probability that none of 19 specific players are matched against > each other? 126*124*122*120*...*92 Could it be ---------------------- ~= .20822833 ? 127*126*125*124*...110 >> I wrote what amounts to << 109*108*107*...92*91 --------------------, 127*125*123*...93*91 >> which is ~= .20822833 also, so I presume Don's answer is another way to calculate the same probability. But I don't see why yet. Can someone please explain his method to me? --Dan

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[math-fun] Abramowitz & Stegun book in acrobat PDF,
by Simon Plouffe 08 Jun '04

08 Jun '04

Hello, apparently that book is widely distributed now these days. Unfortunately the copy we see in a couple of places is of poor quality. I made one myself a while ago with my own copy that I did cut and pass through the scanner. http://www.lacim.uqam.ca/%7Eplouffe/articles/Abramowitz&Stegun.pdf It is in the PDF format and of course I made the OCR on it. The result is not perfect but it is better than the one we see in other places. ps : I do not think that this is an infrigement of the copyright because the document is available in some place of the net, if ever it is I would remove it and of course the one I give away like this is NOT for sale, it is for research only. Simon Plouffe

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[math-fun] Permuation Probabilities ... with apologies ...
by Guy Haworth 07 Jun '04

07 Jun '04

.. for the dumb question, but I could use the answer faster than I can work it out (re the upcoming FIDE World Chess Championship). In the 'knockout' first round involving 128 players and 64 matches, what is the probability that none of 19 specific players are matched against each other? Not quite the 'birthday problem' but ... Guy

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