Conjecture Definition and 231 Threads

Urs Schreiber submitted a new PF Insights post It Was 20 Years Ago Today -- the M-theory Conjecture Continue reading the Original PF Insights Post.

The following popped into my head and I am curious whether it is already a known relationship and whether it has an utility in math/physics. It is a follows: Where x and y are consecutive, whole numbers, the following is true: x + y = y2 - x2

Does the Poincaré's conjecture for a three dimensional manifold involves only simple connectedness or is it meant that the first and second homotopy groups are trivial ? Since in the first case the conjecture seems to me wrong whereas in the second true. Thanks.

I was fooling around with the Prime Zeta Function just recently. Prime Zeta Function, P(s), is defined as Σ1/(p^s), where p is each successive prime. When inputting various positive integer values for (s) on wolfram alpha, I noticed a pattern. Well, an approximate pattern, I should say. My...

I have to be honest--- I am not sure exactly the right tone to strike here. I find that if one comes in cocksure proclaiming "I have a proof of the twin primes conjecture! SOLVED! QED, BAY-BAY!" then one achieves a great deal of annoyance, and rightly so. On the other hand, it also seems...

Hi all, I am really curious about the final state conjecture in general relativity, but I don't really understand it... There seems to be a really good explanation provided by Willie Wong here: http://math.stackexchange.com/questions/50521/open-problems-in-general-relativity however it is...

From what I can tell off of Wikipedia and Wolfram, it doesn't look like this is currently known. Regrettably, I live in a social vacuum of mathematical pursuits, so I've come here in the hopes that someone can tell me if this is really new information or simply a retread. Brief Collatz...

Hello MHB, I have the following conjecture which I cannot seem to settle either way: Let $f:[0,1]\to\mathbb R^2$ be a differentiable function such that $f(0)=(0,0)$. Then there exists a continuous function $g:[0,1]\to\mathbb R^2$ such that: 1) $g(0)=(0,0)$ 2) $g([0,1])\cap f([0,1])=\{(0,0)\}$...

I don't know if such thread has been created, all I can find out is one mentioning Zhang's initial bound of $7 \times 10^7$. This has been greatly improved by now so I thought it is worthwhile to post it here as well as the resources which I somehow collected from here and there. History; a...

I have been researching on a generalization of Erdos-Moser, which asks for ordered tuple of consecutive integers with first $n-1$ integers, summed and exponentiation by $n$, equals the $n$-th power of the last and the greatest. The generalization can be observed as $$3^2 + 4^2 = 5^2$$ $$3^3 +...

Simulations back up theory that Universe is a hologram http://www.nature.com/news/simulations-back-up-theory-that-universe-is-a-hologram-1.14328

Good morning, my name is Alberto and I'm from Peru (South America); and this is my first post on this forum. My Question is: A few hours ago I just discover an equation to obtain the values of the Beal Conjecture: A^x + B^y = C^z A, B, C has a common factor and x, y, z are coprimes, all of...

This is NOT a tutorial, so any and all contributions are very much welcome... :DI've recently been working on the Barnes' function - see tutorial in Math Notes board - and been trying to generalize some of my results to higher order Barnes' functions (intimately connected with the Multiple Gamma...

This conjecture does not include Descartes (1596 C.E.-1650 C.E.), Carolus Linnaeus (1707 C.E.-1778 C.E.), and others who preceded 1800 C.E. evolutionary biologists. I have often wondered how the history of biology might have turned out differently without the contributions of the Darwin...

more and more likely to be true the bigger the even? Primes become more rare, so it seems to me this notion is counter intuitive. :confused: A few recent papers all point to that Goldbach becomes more and more likely the higher up you go. A very large even can be the sum of two large odds or...

Let $p(x,y)$ and $q(x,y)$ be two polynomials with coefficients in $\mathbb R$. Define $P=\{(a,b)\in\mathbb R^2 : p(a,b)=0\}$ and $Q=\{(a,b)\in \mathbb R^2:q(a,b)=0\}$. Now assume that there is a sequence of points $(x_n,y_n)$ in $\mathbb R^2$ such that: 1. $(x_n,y_n)\to (0,0)$. 2. $(x_n,y_n)\in...

I’m a number theory lover but not an expert in the area. Recently, motivated by the report of Peter Norvig, Director of Research at Google, I’m interested in searching for counterexamples of Beal’s conjecture. Billionaire banker Andrew Beal formulated this conjecture in 1993. For a proof or...

Homework Statement I have to make a conjecture about y = ax+b in terms of the ratio of the x coordinate in regards to the y-coordinate of the function. Homework Equations y = ax + b The Attempt at a Solution So I need to investigate the function like this: y = ax + b...

Would it be possible to prove the collatz conjecture indirectly by demonstrating rules that apply to 'Collatz-like' conjectures? (I call anything where you simply change the values in the 3n+1 part of the conjecture to other values, holding everything else the same a Collatz-like conjecture)...

The question in the title really says it all... I was wondering, what relies on the Goldbach conjecture being true? What would happen if it was proven correct?

The conjecture states that: Given a positive integer n, If n is even then divide by 2. If n is odd then multiply by 3 and add 1 Conjecture: by repeating these operations you will eventually reach 1. Proof: Let n be the smallest positive integer that is a counterexample...

I don't know if this is the proper thing to call it, but I haven't used any mathematical terminology in a while so I think I will try :P The number of imperfect roots between any two consecutive perfect roots will always be twice the preceding root number. for example there is 2 imperfect...

I have just found links to a few articles discussing the proof of the twin prime conjecture by Yitang Zhang, a once obscure mathematician working as a lecturer at the University of New Hampshire, and who according to reports had difficulty finding academic work and worked as an accountant and a...

How would I go about proving that, for a curve in the complex plane ##\alpha## and a real number ##\beta##, $$\exists\alpha,\beta: \frac{x}{2\pi i}\int\limits_\alpha \frac{\Gamma(z+\frac{1}{2})\Gamma(-z)x^{\beta z}}{\Gamma(\frac{3}{2}-z)}\, dz = \arctan{x}?$$ The poles of the integrand are...

What is the easiest way to explain the Beale Conjecture to someone who isn't math literate? BEAL'S CONJECTURE: If Ax + By = Cz, where A, B, C, x, y and z are positive integers and x, y and z are all greater than 2, then A, B and C must have a common prime factor. What exactly is...

I'm sorry if this has been posted already, but here's the article. I don't know much about number theory, but it seems like many of the biggest problems in number theory are quite simple to state, like this one, even a school child could understand it. Sounds like some really exciting...

Proof towards Twin Primes Conjecture! http://www.wired.com/wiredscience/2013/05/twin-primes/

I don't know if this has already been posted. This article is about a possible proof of the twin prime conjecture. This is a breakthrough in the field of Number Theory. First proof that infinitely many prime numbers come in pairs : Nature News & Comment

What is the current status of the conjecture? I am interested in all possible aspects, counterexamples, attempts to formulate it in a mathematically rigorous way, proves in special cases, opinions, expectations and so on. Of course I have been trying to find information and have seen some things...

Hi, I found this proof on arxiv just yesterday, though it was published on March 18. I don't know if it is right, but can you guys check it? Is it right? http://arxiv.org/abs/1303.4649

Video illustration Hello, Me and a friend, David Barrack, are non-mathematicians but we've been having fun lately with the Goldbach conjecture. I thought I'd share some of our tools with you guys, some of you might be interested in helping us to progress on this problem - that would be greatly...

I have created a program in javascript that has tested integers on the collatz conjecture. Recall that the collatz conjecture says given any natural number n you must divide n by 2 if it is divisible by 2 and multiply n by 3 and add 1 if it is not divisible by 2. Repeat this process and you...

Homework Statement Formulate a conjecture for the equation (z^3)-1=0, (z^4)-1=0 (z^5)-1=0 and prove it. Homework Equations r^n(cosnθ + isinnθ) The Attempt at a Solution Well my conjecture is that 2pi/n and 2pi/n + pi are possible values. I'm a bit iffy on how to word it. don't...

Hey everyone, I was doing a problem in my Discrete Mathematics book and it called for finding an infinite number of counterexamples to the statement "7n+2" is a perfect square (which fails for n=3 at least). In my search for such an infinite counterexample, I tried to find A, n=n(k,A)...

http://timesofindia.indiatimes.com/city/guwahati/Mathematician-solves-270-year-old-conjecture/articleshow/16635760.cms This came up on my twitter feed. Can someone verify this? I am in a state of disbelief. India is always coming up with articles about people starting fires with their minds...

Did you guys hear about this? Sudharaka was kind of enough to let me know about this potential proof. http://news.sciencemag.org/sciencenow/2012/09/abc-conjecture.html?ref=hp an article about it. Apparently the proof is around 500 pages long so obviously the claim hasn't been confirmed yet and...

http://www.scientificamerican.com/article.cfm?id=proof-claimed-for-deep-connection-between-prime-numbers

Conjecture Regarding Rotation of a Set by a Sequence of Angles. Consider the following sequence, where the elements are rational numbers mulriplied by \pi: (\alpha_{i}) = \hspace{2 mm}\pi/4,\hspace{2 mm} 3\pi/8,\hspace{2 mm} \pi/4,\hspace{2 mm} 3\pi/16,\hspace{2 mm} \pi/4,\hspace{2 mm}...

From taking breaks from preparing for a talk I have in geometry, I started toying a little bit with perfect numbers. We all know that 3^3+4^3+5^3=216=6^3 This and the well known pythogrean triplet 3^2+4^2=5^2. So I thought of toying a little bit with powers of three and two, and I found...

Dear all, yesterday I ve read something about Beals conjecture on Wikipedia, But today I've said I will go through some of fake proofs with few lines. The majority of this so called proofs is based on the false logic that Fermats theorem and Beals conjecture are linked directly. By directly I...

Recently heard about the Schiff conjecture saying that any reasonable theory of gravitation should adhere to the ideas of EEP and UFF. I realize that this isn't a "strong" idea (only a conjecture after all), but to anyones understanding, does either loop quantum gravity or m-theory appear to...

I know that one of Goldbach's conjectures is that every even number is the sum of 2 primes. So, I was wondering if there was a definite, largest prime number ever possible. I know that as a number gets larger, there are more numbers that can be tried to divide it (At least I think so), and I...

Newbie to the forum here. Hoping y'all can help with something that's been bugging me for a while now. I would like to know the relationship between two characteristic radii in a close packing of equal spheres. The first radius of interest is that of the equal sphere's themselves (r1). The...

I've been doing a project on Henri Poincare and I am attempting to explain his conjecture to my Calculus class so I am using the common lower dimensional equivalent to do so. If a rubber band is wrapped around an object and becomes smaller and smaller until it is a point than that object is...

I found the following relationship concerning goldbach's conjecture; viz that every even number is the sum of two primes. If goldbach's conjecture is true then the following must hold for all 2N \sum^{2N-1}_{l=0} ( \sum^{p < 2N-1}_{ p odd primes=3} cos (2πpl/2N) ])2 >...

I know that there is likely an error somewhere in my solutions to these problems, so I won't be audacious and claim that I have 'the' proof; however, I have been able to convince myself and a few other people with graduate level training in mathematics that this solution is true. I have...

Can anyone find any stupid mistake in this? Also, can I get some professor names to send solutions for unsolved math problems? I have the solutions for Goldbach Conjecture, Polignac's Conjecture, Hadwiger Conjecture, Ringel-Kotzig Conjecture, Collatz Conjecture, Erdős conjecture on arithmetic...

In the book by Keith Devlin on the Millenium Problems - in Chapter 6 on the Birch and Swinnerton-Dyer Conjecture we find the following text: "It is a fairly straightforward piece of algebraic reasoning to show that there is a right triangle with rational sides having an area d if and only if...

What mathematics did Perelman use to prove Poicare's conjecture? Do you know any guide or any book?

I read this through wikipedia and some other sources and find it to be unsolved. Erdos offer a prize of $5000 to prove it. A mathematician at UW has looked at it and verify them to be correct. However, i still have some doubt about it because the proof i give is pretty simple. Can anyone take a...