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[math-fun] RH and thoughts on 'proof'
by Guy Haworth 12 Jun '04

12 Jun '04

The latest stirrings about a claimed proof of the RH hypothesis prompt the following thoughts from this 'amateur': a) someone (Lakatos?) said "proof is a social process" http://www.math.tau.ac.il/~yahave/talks/3 is relevant b) do we now consider the social process sufficiently quorate on: '4 Colours Suffice' and on Fermat's Last 'Theorem'? c) the finality of a proof was part of the attraction of maths for me "you know when you're done" (at least before the 'social' bit) d) I hear that trainee maths teachers can qualify successfully now ... ... without knowing what the concept of 'proof' is. Call me old-fashioned but ... :-( ! e) there seem to be good steps to computerise the proof process http://metamath.org/ is the most comprehensive approach I've seen Are there others of note? How far 'up' can this process go? Cambridge (UK) is doing something on maths, proof and computers (?) ... don't know what though. f) I look forward to those with the appropriate heavy toolkit getting in there and sorting out the DeBranges forest. Guy

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[math-fun] # of words
by Thane Plambeck 11 Jun '04

11 Jun '04

>From the Guardian, in a perhaps already suspect article about a dog with a large vocabulary: http://www.guardian.co.uk/uk_news/story/0,3604,1236272,00.html "From the age of two, children start to pick up 10 words a day: a teenager typically knows 60,000 words." * * * * This seemed at bit high, at 60,000 Opening a 1500 page dictionary to a random page, I counted 25 main entries. Of these, I didn't know "feer" (to draw the first furrow in ploughing) "feis" (an ancient Irish assembly) "feldsher" (in Russia and parts of Eastern Europe, a partly trained person who practices medicine) "Felibre" (a member of Provencal literary brotherhood) and I was proud to already know "feldgrau" (field-gray, the color of German military uniforms) as well as one naughty word that happened to appear on the same page. Some more random experiments yielded similar results. I don't think many teenagers know that many words Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.plambeck.org

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[math-fun] Invariant numbers
by Jon Perry 11 Jun '04

11 Jun '04

Anyone seen this before? http://www.users.globalnet.co.uk/~perry/maths/morerecentstuff/morerecentstuf f.htm An invariant number, p ---------------------- If we define p as an invariant number, we can find solutions to equations. An invariant number is one that has the following properties: p=-1 p+k=p p^k=p for all k (real or complex or invariant) This, for example, provides roots to 1+x+x^2+x^3+..., and more generally for P(x), the generating function of the partition numbers. Let x=p/2^(1/k), so for k=1, x=p/2 and for k=2, x=p/sqrt(2), etc... Then 1+x+x^2+x^3 = 1 + p/2 + p^2/4 + p^3/8 + ... = 1-1/2-1/4-1/8-... = 0. And 1+x^2+x^4+x^6+... is zero for the k=2 case, and so on. 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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[math-fun] rand() and the random number generator in excel
by Simon Plouffe 10 Jun '04

10 Jun '04

good evening, According to microsoft the rand() uses (probably?) the formula given on their website, a quick test showed that the function looks normaly random, I generated 260000 entries and they seem correct. The tool I mentioned earlier is the one in the Data Analysis package that comes with excel. You can access it with Tools:Data Analysis:Random Number Generator, choose between [0,1] for 30000 entries and 1 variable. That is the faulty one not the rand() function that one can call within a cell in excel. Why is Microsoft using 2 different from which 1 is faulty , that's a good question. Simon Plouffe

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Re: [math-fun] Microsoft Excel : really bad random number generator
by Daniel Asimov 10 Jun '04

10 Jun '04

If this RNG is as bad as it sounds, then it reminds me of the old IBM generator RANDU, alive and well in 1980. As I recall, it picked an integer in the range [0,32767]. When used to create successive coordinates of points in 3-space, one after the other (when output was divided by 32767.0), all of the points ended up on something like only 20 different planes in the unit cube. And on each plane, the points lay on only a small number of lines. --Dan

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[math-fun] Microsoft Excel : really bad random number generator
by Simon Plouffe 10 Jun '04

10 Jun '04

Hello, I am conducting some tests with the built-in random number generator of Excel. I asked 4 runs of 30,000 random numbers between 0 and 1. It has some limitations of course since a column can hardly have more rows anyway, if you ask for 1 million entries the program is too dumb to figure out to spread the results on many columns, so you have to split the thing in many parts. In principle this works since it apparently make a different run each time BUT...! There is a little surprise with this. Actually it does not look really a good random number generator because of this. - There are 120,000 entries but only 3037 are different, in other words it did pick up the same number up to 15 times! - The precision is suppossedly of 15 digits but according to the choice of different values I bet one could find the generator by doing a reverse engineering on it, ;-) - It did pick up the number 1 , 2 times. I think that this is BAD, how a random number generator can pick up the same values so many times at a precision of 16 digits : this is impossible. Did someone ever tested this particular bad program and if so, does anybody has any idea what is the formula or algorithm they (Bill Gates and Co.) use? I suspected that Excel and Microsoft are not so advanced , I had no idea it was so bad! I use the latest version of Excel with Windows XP, service pack 1 and Office XP. If you want to do a simulation and you use Excel? : bad idea. ps: I should send this to D.E. Knuth! Simon Plouffe

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[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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