tag:blogger.com,1999:blog-8666091.post7693455284347644663..comments2019-08-16T18:26:26.975+02:00Comments on The Reference Frame: Japanese guy may have proved the \(abc\) conjectureLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-8666091.post-4835287001949313772012-09-17T04:15:50.761+02:002012-09-17T04:15:50.761+02:00lanvin Made within a trademark materials seeing th...<a href="http://www.lanvinbagonline.com/" rel="nofollow">lanvin</a> Made within a trademark materials seeing that tasteful the way it is usually sturdy, in addition to complete having some sort of effortless external jean pocket together with a changeable crossbody secure, that silhouette is usually a favourite intended for weekends, errands in addition to traveling. <a href="http://www.lanvinbagonline.com/" rel="nofollow">lanvin bag</a> case Purses interior in addition to available hold particular objects sorted in addition to safeguarded. Interior multifunction purses. <a href="http://www.lanvinbagonline.com/" rel="nofollow">http://www.lanvinbagonline.com/</a>lanvinnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-53407199209629562332012-09-16T15:16:16.942+02:002012-09-16T15:16:16.942+02:00Again, Tobias, I just want to make you sure that w...Again, Tobias, I just want to make you sure that when one is ready to be *completely* accurate, and I am arguably more strict than you are right now ;-), what you considered a mistake isn't a mistake. <br /><br /><br />The equation doesn't use the term "prime factors". It involves a product over all primes - which are positive numbers 2,3,5... - that are divisors of abc. And they're the same primes regardless of the sign of abc by the most common definition of "divisors". <br /><br /><br />Whether "prime factors" are only defined for positive integers or all integers is irrelevant because the equation doesn't use the phrase "prime factors", neither verbally nor in notation.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-3898797714209281472012-09-16T15:09:07.172+02:002012-09-16T15:09:07.172+02:00Yes, Lubos, you are basically right, of course. Ex...Yes, Lubos, you are basically right, of course. Except that the textbooks are usually careful to define prime factors only for positive integers, see also here: <br />http://en.wikipedia.org/wiki/Prime_factor <br />I already regret my admittedly useless comment. I just got excited about the beautiful equation so I looked at every detail of it... ;-) Tobias Sandernoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-42302936494028092362012-09-16T14:47:14.683+02:002012-09-16T14:47:14.683+02:00No, Tobias, the absolute value you mention is not ...No, Tobias, the absolute value you mention is not necessary because the divisors of abc and -abc are exactly the same.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-9925842751306997732012-09-16T14:42:56.711+02:002012-09-16T14:42:56.711+02:00Yes, so the product should run over the prime fact...Yes, so the product should run over the prime factors of the magitude of abc as well. (Sorry for the unimportant nitpick.)<br />Very interesting developments, thanks for writing about them.Tobias Sandernoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-46017383911168063332012-09-15T20:58:26.148+02:002012-09-15T20:58:26.148+02:00Is there a part of maths that can be proved to be ...Is there a part of maths that can be proved to be useless for physics?AntiWignernoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-4761234559869671982012-09-15T01:05:49.022+02:002012-09-15T01:05:49.022+02:00well, maybe, but I'm with Gauss, although the ...well, maybe, but I'm with Gauss, although the famous bad judgement he made was that roots of quintics weren't worth pursuing (led to group theory)). But he was right otherwise, ie Mathematics has become a ridiculously complicated game that no one but the players or unfortunate conscripts (because they're semi-autistic) care aboutJames Gallagherhttp://jbg.f2s.com/quantum2.txtnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-80351526119548403642012-09-15T00:40:22.950+02:002012-09-15T00:40:22.950+02:00Oh, please, The axiom of choice is a perfectly cro...Oh, please, The axiom of choice is a perfectly cromulent axiom.Jasonhttp://elnaschiewatch.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-88407590959597104782012-09-15T00:18:11.581+02:002012-09-15T00:18:11.581+02:00Glorying in the "sophistication" of the ...Glorying in the "sophistication" of the proof, is pretty shit modern thing (supports my academic field etc etc,) I hope this proof proves wrong, and I hope some-one comes up with a "proof" (convincing to humans) not involving the axiom of choice ala Wiles for these numerical odditiesJames Gallagherhttp://jbg.f2s.com/quantum2.txtnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-30459561186808610342012-09-14T22:32:18.456+02:002012-09-14T22:32:18.456+02:00I wonder if Hodge theatres will be a standard stri...I wonder if Hodge theatres will be a standard string theory calculation tool in 20 years.David Natafnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-85083711145444509152012-09-14T19:44:11.190+02:002012-09-14T19:44:11.190+02:00They use a more symmetric convention in which each...They use a more symmetric convention in which each a,b,c may be either positive or negative.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-34711657218751682812012-09-14T19:14:12.051+02:002012-09-14T19:14:12.051+02:00If A+B=C, what's the point of the MAX function...If A+B=C, what's the point of the MAX function?MikeNnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-4429300395751640982012-09-14T16:20:26.473+02:002012-09-14T16:20:26.473+02:00"Square free" can mean fermions: http://..."Square free" can mean fermions: http://en.wikipedia.org/wiki/M%C3%B6bius_function#Physics<br /><br />How long until we have "Mochizuki for physicists"? :-)Mitchell Porternoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-65359167167501580012012-09-14T14:09:47.677+02:002012-09-14T14:09:47.677+02:00This proof is the most arcane and forbidding I'...This proof is the most arcane and forbidding I've ever seen. Only a handful of mathematicians could begin to understand it for now (and most of them no doubt are trying to). There is no way any non-specialist could verify the proof, at least without so many years of study that it would have been verified (or, perhaps, debunked) long before.tlssnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-36909457333085127762012-09-14T09:34:00.685+02:002012-09-14T09:34:00.685+02:00Hi Luboš, regarding the minimum size of the expone...Hi Luboš, regarding the minimum size of the exponent implicit in the statement of Goldfeld's theorem. I don't have an answer for you but pages 16 through 19 of this 1995 PDF by Barry Mazur of your old alma mater are closely related to your question. It says that under certain circumstances that seem very lax (but unfortunately nonetheless are unproven), ABC implies Fermat for exponents greater than 5.<br /><br />http://www.math.harvard.edu/~mazur/papers/scanQuest.pdfJasonhttp://elnaschiewatch.blogspot.com/noreply@blogger.com