• Claimed Proof For Connection Between Prime Numbers.
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[quote] [h2]Proof claimed for deep connection between primes.[/h2] [B]If it is true, a solution to the abc conjecture about whole numbers would be an ‘astounding’ achievement.[/B] ==========================. The usually quiet world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved. Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers — a 'Diophantine' problem. The abc conjecture, proposed independently by David Masser and Joseph Oesterle in 1985, might not be as familiar to the wider world as Fermat’s Last Theorem, but in some ways it is more significant. “The abc conjecture, if proved true, at one stroke solves many famous Diophantine problems, including Fermat's Last Theorem,” says Dorian Goldfeld, a mathematician at Columbia University in New York. “If Mochizuki’s proof is correct, it will be one of the most astounding achievements of mathematics of the twenty-first century.” Like Fermat’s theorem, the abc conjecture refers to equations of the form a+b=c. It involves the concept of a square-free number: one that cannot be divided by the square of any number. Fifteen and 17 are square free-numbers, but 16 and 18 — being divisible by 42 and 32, respectively — are not. The 'square-free' part of a number n, sqp(n), is the largest square-free number that can be formed by multiplying the factors of n that are prime numbers. For instance, sqp(18)=2×3=6. If you’ve got that, then you should get the abc conjecture. It concerns a property of the product of the three integers axbxc, or abc — or more specifically, of the square-free part of this product, which involves their distinct prime factors. It states that for integers a+b=c, the ratio of sqp(abc)r/c always has some minimum value greater than zero for any value of r greater than 1. For example, if a=3 and b=125, so that c=128, then sqp(abc)=30 and sqp(abc)2/c = 900/128. In this case, in which r=2, sqp(abc)r/c is nearly always greater than 1, and always greater than zero. Deep connection It turns out that this conjecture encapsulates many other Diophantine problems, including Fermat’s Last Theorem (which states that an+bn=cn has no integer solutions if n>2). Like many Diophantine problems, it is all about the relationships between prime numbers. According to Brian Conrad of Stanford University in California, “it encodes a deep connection between the prime factors of a, b and a+b”. Many mathematicians have expended a great deal of effort trying to prove the conjecture. In 2007, French mathematician Lucien Szpiro, whose work in 1978 led to the abc conjecture in the first place claimed to have a proof of it, but it was soon found to be flawed. Like Szpiro, and also like British mathematician Andrew Wiles, who proved Fermat’s Last Theorem in 1994, Mochizuki has attacked the problem using the theory of elliptic curves — the smooth curves generated by algebraic relationships of the sort y2=x3+ax+b. There, however, the relationship of Mochizuki’s work to previous efforts stops. He has developed techniques that very few other mathematicians fully understand and that invoke new mathematical ‘objects’ — abstract entities analogous to more familiar examples such as geometric objects, sets, permutations, topologies and matrices. “At this point, he is probably the only one that knows it all,” says Goldfeld. Conrad says that the work “uses a huge number of insights that are going to take a long time to be digested by the community”. The proof is spread across four long papers1–4, each of which rests on earlier long papers. “It can require a huge investment of time to understand a long and sophisticated proof, so the willingness by others to do this rests not only on the importance of the announcement but also on the track record of the authors,” Conrad explains. Mochizuki’s track record certainly makes the effort worthwhile. “He has proved extremely deep theorems in the past, and is very thorough in his writing, so that provides a lot of confidence,” says Conrad. And he adds that the pay-off would be more than a matter of simply verifying the claim. “The exciting aspect is not just that the conjecture may have now been solved, but that the techniques and insights he must have had to introduce should be very powerful tools for solving future problems in number theory.” [B]Nature doi:10.1038/nature.2012.11378[/B] ========================== Source: [URL]http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378[/URL] [/quote] This is big news if his proof holds.. We've been at this problem for the better part of 2,500years.. [quote] EDIT: [URL="http://au.news.yahoo.com/world/a/-/world/14831400/mathematician-proof-prime-numbers/"]Yahoo[/URL] write a pretty good explanation. [/quote]
About time. People complain about Valve time, they should be thankful that it's not prime time.
[quote]If you’ve got that, then you should get the abc conjecture. It concerns a property of the product of the three integers axbxc, or abc — or more specifically, of the square-free part of this product, which involves their distinct prime factors. It states that for integers a+b=c, the ratio of sqp(abc)r/c always has some minimum value greater than zero for any value of r greater than 1. For example, if a=3 and b=125, so that c=128, then sqp(abc)=30 and sqp(abc)2/c = 900/128. In this case, in which r=2, sqp(abc)r/c is nearly always greater than 1, and always greater than zero.[/quote] I feel really unintelligent right now.
Fermats therom itself is hard enough to understand, now someone has taken that to another step? That's incredible. Fermats therom if anyone doesn't know was a 400 something year old math equation that a french mathematician claimed to have found and never left proof for. No one solved this until Andrew Wiles did in 1991, then not proven solved until 1995. It stated a(n)+b(n)=c(n) where n is never greater than 2, this was a massive find in mathematics. I really can't explain more than that because I can't explain the math behind any of it really. It's brilliant stuff. [url]http://en.wikipedia.org/wiki/Fermat's_Last_Theorem[/url] There's also a book called Fermats Last Theorem by Simon Singh that is an excellent read about this question and it's importance as well as the quest to solve it. Good enough just about anyone can get it.
Whenever I hear the name Fermat, I'm reminded of Fermat's Room.
I don't speak math.
[QUOTE=HumanAbyss;37639736]It stated a(n)+b(n)=c(n) where n is never greater than 2, this was a massive find in mathematics.[/QUOTE] Why did I read that and go "Oh that's easy, a1+b1=c2" then I remembered that (n) is an undefined variable so it can't be found out. Derp.
[QUOTE=HumanAbyss;37639736]Fermats therom itself is hard enough to understand, now someone has taken that to another step? That's incredible. Fermats therom if anyone doesn't know was a 400 something year old math equation that a french mathematician claimed to have found and never left proof for. No one solved this until Andrew Wiles did in 1991, then not proven solved until 1995. It stated a(n)+b(n)=c(n) where n is never greater than 2, this was a massive find in mathematics. I really can't explain more than that because I can't explain the math behind any of it really. It's brilliant stuff. [url]http://en.wikipedia.org/wiki/Fermat's_Last_Theorem[/url] There's also a book called Fermats Last Theorem by Simon Singh that is an excellent read about this question and it's importance as well as the quest to solve it. Good enough just about anyone can get it.[/QUOTE] It's [IMG]http://i.imgur.com/x84Uz.png[/IMG]
I will never be able to understand mathmaticians...
[QUOTE=Tarver;37639785]I don't speak math.[/QUOTE] Then you shouldn't use an avatar of Descartes, you liar!
what uses does this have
[QUOTE=DrBreen;37640010]what uses does this have[/QUOTE] Demonstrating another triumph in human intellectual accomplishment.. This will be spoken about for the rest of future history -- Just as we speak of Pythagoras' attempts to find the primes.
[QUOTE=DrBreen;37640010]what uses does this have[/QUOTE] Creates system in one of the few remaining places seemingly without. For someone like Einstein who's obsessed with explaining everything with simple equations it means the world.
[QUOTE=Sir Whoopsalot;37639739]Whenever I hear the name Fermat, I'm reminded of Fermat's Room.[/QUOTE] Whenever I hear Fermat, I remember my math teacher who named her cats after famous mathematicians. Her cats' names were Gauss, Pascal and Fermat.
wat
Thread music [MEDIA]http://www.youtube.com/watch?v=diu8i5UKTHc[/MEDIA]
The proof is 500-pages holy christ
[QUOTE=JohnnyMo1;37641625]The proof is 500-pages holy christ[/QUOTE] will you read this and give us a TLDR?
[QUOTE=marcin1337;37641695]will you read this and give us a TLDR?[/QUOTE] tl;dr an important conjecture in number theory and Diophantine analysis may just have been proven from which many important theorems and conjectures are a direct consequence. I can give you the mathematical formulation of the conjecture. It's not long or difficult to understand. I can't explain the consequences so well. I'm no number theorist. [editline]12th September 2012[/editline] Here's the conjecture for anyone interested: [B]For every ε > 0 there exist only finitely many triples (a,b,c) of positive coprime integers with a + b = c such that c > rad(abc)[sup]1+ε[/sup].[/B] Coprime means the numbers have no prime factors in common, and rad() means to multiply the [I]distinct[/I] prime factors of a, b, and c together i.e. rad(10) = 2*5 = 10, but rad(8) = rad(2[sup]3[/sup]) = 2. Basically what it says is that if you pick some positive number and raise rad(abc) to the 1 + that number power, that value will be bigger than c in almost every case.
[quote]Like Fermat’s theorem, the abc conjecture refers to equations of the form a+b=c. It involves the concept of a square-free number: one that cannot be divided by the square of any number. Fifteen and 17 are square free-numbers, but 16 and 18 — being divisible by 42 and 32, respectively — are not.[/quote] For anyone confused by this part, the article isn't talking about 42 or 32 but 4^2 = 16 and 3^2 = 9. The superscript seems to have been dropped between the OP and the original article.
[QUOTE=Killuah;37639796]It's [IMG]http://i.imgur.com/x84Uz.png[/IMG][/QUOTE] If I remember correctly... That only work if n is under 2
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