June 2004 - mathfun@mailman.xmission.com

[math-fun] Purdue press release about the Riemann Hypothesis
by Schroeppel, Richard 10 Jun '04

10 Jun '04

Here's a pointer to the Purdue press release about RH. http://news.uns.purdue.edu/UNS/html4ever/2004/040608.DeBranges.Riemann.html The department head is carefully noncommittal about the correctness of the proof, calling it important and saying it deserves to be carefully examined. The press release incorrectly gives the length as 23 pages, rather than 123. The contact information for DeBranges is in France. I paged through the proof. It makes a lot of the right noises, but I couldn't make out an overview of the argument; too many trees to make sense of the forest. Rich

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[math-fun] rightwing/leftwing *disproofs*
by Bernie Cosell 10 Jun '04

10 Jun '04

Ignoring Devlin's political bias, I suspect we understand the idea he was trying to outline [let me try: there's a spectrum for 'surety of proof' running from pure formal-symbol-manipulative rigor on one end, to largely unsubstantiated emotional handwaving at the other with many waystations of surety in between]. Anyhow, Keith was focusing on *proofs*. I got to wondering if there was the same sort of spectrum for *disproofs*. I had always generally thought that disproofs would all be at the for-sure, "rigorous", end of the spectrum [thinking about the usual approach: you find *one* case where the theorem fails and it's gone]... But with proofs getting a lot more complicated, subtle and LARGE I'm wondering if we'll have the same situation with disproofs as we see with proofs: of some mathematicians claiming that one part of a proof is flawed and others not being convinced, and no one being convinced one way or the other whether a proof is 'good' or not. /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--

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[math-fun] Ramanujan
by Jon Perry 10 Jun '04

10 Jun '04

I have formulated a Ramanujan-esque conjecture; http://www.users.globalnet.co.uk/~perry/maths/tworamanujan/tworamanujan.htm By simple I mean try and equate the numbers without invoking too difficult a function (1-1 correspondence would be great!). Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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

10 Jun '04

P.S. The current paper http://www.math.purdue.edu/ftp_pub/branges/riemannzeta.pdf by de Branges is dated May 24, 2004, so presumably it's an attempt to fix whatever was wrong with the previous paper. --Dan

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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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