Date: Wed, 19 Jun 2002 21:36:09 -0400 (EDT) From: "Keith F. Lynch" <kfl at keithlynch.net> To: WSFAlist at keithlynch.net Subject: [WSFA] Re: Goldbach's Conecture proven? Reply-To: WSFA members <WSFAlist at keithlynch.net> >> ... http://front.math.ucdavis.edu/math.GM/0206033 ... ronkean at juno.com wrote: > I don't know if 1 is strictly prime, ... 1 is not considered prime since if it were considered prime, integers would no longer have a unique prime factorization. 15 would not just be 3 * 5 but also 1 * 3 * 5 and 1 * 1 * 3 * 5, etc. And unique prime factorization is too important to give up. > so it looks like Goldbach's Conjecture is true for the even numbers > up to 20. Computers have tested it up to a few trillion. Which proves nothing, except that if there are any counterexamples they are all larger than that. > But, since a computer could never count to infinity (in a finite > time), Nor even in an infinite time, unless it also had infinite memory, which would require an infinite amount of matter in an infinite amount of space. You'd also need infinite energy to power this computer for an infinite amount of time. And it would generate infinite waste heat and infinite entropy. And don't get me started on the maintenance costs. > it seems that it would be impossible for a computer to prove the > conjecture for all even numbers. Not by proceeding that way, anyhow. > But, a human has allegedly done so. Not by proceeding that way. If someone asserts that every even number is the sum of two odd numbers, is it necessary to test them all? Or is there an easy way to prove that this must be true? If someone claims they found an odd number which is the sum of two odd numbers, only a fool would write a computer program to start rapidly adding successive odd numbers to see if they can find this wondrous number. "Eric Jablow" <erjablow at netacc.net> wrote: > Someone announced a proof of the Poincare Conjecture earlier this > year [one of the two great unproved conjectures in mathematics]. > He was wrong. I assume the Reimann conjecture is the other one you're thinking of? It's true that the Goldbach conjecture isn't considered as significant. But it does have the virtue of being easy to understand. Anyhow, I think P=NP is more important than any of them. > In fact, I just looked at the paper--it has the whiff of crank-hood. That was in part of the "Mathematics ArXiv," which I thought was peer reviewed (i.e. approved by several randomly chosen experts in the field). If it's not peer reviewed, why isn't that website overrun with obvious crackpots as the sci.math and sci.physics newsgroups are? > I'm not going to get my hopes up. I have mixed feelings. It's kind of fun having unexplored territory so close at hand. Knowing for certain whether Fermat, Goldbach, Reimann, Poincare, etc, are true is like seeing the results from the first interplanetary probes. It's nice to *know*, but suddenly there is no more room for canals and ancient wise beings on Mars, or for primordial swamps on Venus. Similarly, DNA analysis has made untenable all those wonderful stories about how our species is a recent immigrant from another solar system, and didn't evolve here on earth. Besides, I like having Goldbach as an example of something which most probably is true but unprovable. If you choose odd numbers at random with a frequency like that of primes, if the first few even numbers happen to be the sum of two numbers in this set, probably all of them will, since the odds of one *not* being such a sum drop so rapidly. Very likely Goldbach is true only for this purely stochastic reason, in which case no proof can exist. Which means we can never no for certain that it's true, even though it is. Goedel proved that there must be true but unprovable conjectures. ronkean at juno.com wrote: > There is some garbled grammar on page 2, which is not a good sign, > and it's surprising considering that page 1 reads smoothly. Actually, there is a glaring error in the single page abstract (which is all I've seen, since I can't do PDF, DVI, or PS). Can you find it? It's not a grammatical or spelling error. > If mathematicians have been working on this without success since > 1742, it seems unlikely that a valid proof would be compact enough > to fit on 11 pages. Not necessarily. > Mathematicians have presumably also been working since 1742 to > disprove the conjecture, including using fast computers to look > for an arithmetic counterexample. True, even though probably nobody thinks it's false, so the search for a disproof is a half-hearted effort. "Strong, Lee" <StrongL at MTMC.ARMY.MIL> wrote: > Ghod, but I love the sensation of listening to people with triple > digit I.Q.'s! I doubt there are any WSFAns without triple digit IQs. People with 2 digit IQs would be bored in our meetings. So would people with 4 digit IQs. Ted White <tedwhite at compusnet.com> wrote: > So are you saying that "the average IQ at a WSFA meeting" equates to > all WSFAns averaging in the top two percentiles of IQ? Actually, Mensa accepts anyone scoring on the top two percent of any of several tests (not just IQ tests but also SATs, etc), on any of several occasions. Since tests don't correlate perfectly with each other, much more than two percent of the population qualifies for Mensa. Since practice on IQ tests, like practice on anything else, improves one's performance, and since IQ is pretty much bogus anyhow, I think more than half the population could qualify for Mensa membership if they really wanted to. Which I don't. -- Keith F. Lynch - kfl at keithlynch.net - http://keithlynch.net/ I always welcome replies to my e-mail, postings, and web pages, but unsolicited bulk e-mail (spam) is not acceptable. Please do not send me HTML, "rich text," or attachments, as all such email is discarded unread.