What is Conjecture: Definition and 227 Discussions

In mathematics, a conjecture is a conclusion or a proposition which is suspected to be true due to preliminary supporting evidence, but for which no proof or disproof has yet been found. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

View More On Wikipedia.org
Recent contents Top users
  1. T

    Our Old Friend, the Twin Primes Conjecture

    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...
  2. 2

    Final state conjecture in general relativity?

    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...
  3. F

    Collatz Conjecture Progress

    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...
  4. caffeinemachine

    MHB Curve Selection Conjecture.

    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) $g([0,1])\cap f([0,1])=\{(0,0)\}$...
  5. mathbalarka

    MHB Twin Prime Conjecture : A Brief History of the Present

    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...
  6. mathbalarka

    MHB Generalized Erdos-Moser conjecture

    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 +...
  7. Greg Bernhardt

    Evidence that Maldacena’s hologram conjecture is true

    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
  8. A

    Beal Conjecture - Demonstration

    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...
  9. DreamWeaver

    MHB A conjecture on a Generalized Barnes' function - can anyone help?

    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...
  10. E

    A conjecture on Greek-based biology before 1800 C.E.

    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...
  11. G

    Why is Goldbach conjecture that every even = a prime + a prime becomes

    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...
  12. caffeinemachine

    MHB A Conjecture About Polynomials in Two Variables

    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...
  13. S

    MHB Explore Beal's Conjecture: A Number Theory Challenge

    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...
  14. 5

    Make a conjecture about y = ax+b

    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...
  15. F

    Method for proving the collatz conjecture, would this work?

    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)...
  16. A

    What are the effects of the Goldbach 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?
  17. R

    Where's the flaw in this proof of the Collatz Conjecture?

    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...
  18. T

    Twice the Preceding Root Number: Proving a Conjecture

    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...
  19. S

    Proof of the twin primes conjecture

    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...
  20. Mandelbroth

    Proving a conjecture in complex analysis

    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...
  21. S

    Beale Conjecture Reduced to Practicality?

    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...
  22. qspeechc

    Claimed Proof of ABC Conjecture in Number Theory

    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...
  23. M

    Why is the Twin Primes Conjecture still relevant to mathematicians today?

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

    MHB Breaking news about twin prime conjecture.

    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
  25. M

    Cosmic censorship conjecture - status?

    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...
  26. E

    Is the Goldbach Conjecture Finally Proven? New Proof on arXiv Sparks Debate

    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
  27. J

    Some ideas concerning the Goldbach conjecture

    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...
  28. V

    A Conjecture on the Collatz Conjecture

    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...
  29. D

    Proving/Creating a conjecture on the roots of complex numbers

    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...
  30. M

    Conjecture: There exists no number k s.t. k^2+2 is a multiple of 7

    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)...
  31. D

    Is Goldbach's Conjecture Finally Solved?

    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...
  32. Jameson

    MHB ABC Conjecture Proof: News, 500-Page Claim | ScienceMag

    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...
  33. D

    Is the ABC Conjecture Solved? New Proof Claims Deep Connection to Prime Numbers

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

    Conjecture Regarding rotation of a set by a sequence of rational angles.

    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}...
  35. MathematicalPhysicist

    Conjecture regarding perfect numbers.

    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...
  36. R

    Question about Beals conjecture

    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...
  37. R

    Schiff conjecture and LQG or m-theory?

    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...
  38. F

    A Question About Prime Numbers and Goldbach's Conjecture

    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...
  39. B

    Inscribed sphere - Kepler Conjecture

    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...
  40. P

    Poincare Conjecture: Explaining Lower Dimension Equivalent

    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...
  41. P

    Goldbach Conjecture: Relationship to Even Numbers

    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 >...
  42. M

    Solutions to Polignac's and Twin Prime's Conjecture

    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...
  43. H

    Solution for Goldbach Conjecture

    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...
  44. Math Amateur

    Area of a Triangle and Elliptic Curves - Birch and Swinnerton Dyer Conjecture

    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...
  45. T

    What mathematics did Perelman use to prove Poicare's conjecture? Do

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

    Erdos conjecture on arithmetic progression

    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...
  47. S

    An algebraic proof of Fermat's conjecture

    I'm sure there are mistakes here so criticism is welcome. In the unlikely event someone would like to sponsor my article for ArXiv, please let me know. http://www.non-ducor.com/fj/Algebraic_proof_of_Fermats_conjecture_001.png...
  48. Y

    Prove the number theory conjecture

    Homework Statement prove or disprove the following conjecture: If n is a positive integar, then n^2 - n +41 is a prime number Homework Equations no, just prove or disprove The Attempt at a Solution I think one possible answer may be there is no factorization for this except...
  49. G

    An approach to the Twin Prime Conjecture

    The prime numbers are the multiplicative building blocks of the integers. Even so, their distribution escapes all methods of rationalization. As with building a pyramid, the primes are most densely distributed near zero, the point of origin, and as we move towards larger numbers the primes are...
  50. C

    Challenge to the community, Squaring of polynomials conjecture

    Given polynomials of degree n > 2, such that they have the form of p(x) \ = \ x^n \ + \ a_1x^{n - 1} \ + \ a_2x^{n - 2} \ + \ a_3x^{n - 3} \ + \ ... \ + \ a_{n - 2}x^2 \ + \ a_{n - 1}x \ + \ a_n. And \ \ all \ \ of \ \ the \ \ a_i \ \ are \ nonzero \ integers \ (which...
Back
Top