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.

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  1. E

    Euler product and Goldbach conjecture

    In an anlaogy with the Euler product of the Riemann function we make: \prod_{p}(1+e^{-sp})=f(s) of course we have that: f(p1+p2+p3)=f(p1)f(p2)f(p3) f(x)=exp(-ax) if Goldbach Conjecture is true then p1+p2= even and p5+p6+p8=Odd for integer n>5? then this product should be equal to...
  2. R

    Triangular Number Conjecture: Recursive Series

    I have a new conjecture re triangular numbers that I think is fascinating. Conjecture For any two integers a and b such that ab is a triangular number, then there is an integer c such that a^2 + ac and b^2 + bc are both triangular numbers. Further, (6b-a+2c)*b and (6b-a+2c)*(6b-a+3c)...
  3. E

    HIlbert-Polya conjecture ¿proof or RH?

    My question is...could the Hilbert-Polya conjecture if true prove RH (Riemann Hypothesis) i mean let,s suppose we find an operator ( i found a Hamiltonian with a real potential that gave all the roots of \zeta(1/2+is) ) in the form: R=1/2+iH with H self-adjoint so all the "eigenvalues"...
  4. T

    Andrica's Conjecture Disproved: A Mathematical Mystery Solved

    Ok my thread seems to have gone into a black hole. The existence of such a number would disprove Andrica's conjecture.
  5. R

    Understanding the Poincare Conjecture: A Layman's Guide

    Could someone lay down, in layman's terms, The Poincare Conjecture? Lol, is this even possible?
  6. E

    A conjecture about the roots of real functions

    All the roots of a real function f(x) are real unless. 1.K(x) is a Polynomial of degree k 2.f(x)=exp(g(x)) where g(x) is different from ln of something 3.f(z) with z=u+iv is invariant under the transformation of v=-v with f(u+iv)=F(u-iv).. 4.the function f includes some of the functions...
  7. J

    Exploring Twin Primes Conjecture

    Bear with me. I'm new to forum and don't yet know all protocol. My question concerns twin primes. The previous thread on this topic seems to be closed. My question is this: When considering the Twin Primes Conjecture, has anyone researched the idea that (heuristically speaking) there is...
  8. V

    Exploring Beal Conjecture Solutions: Common Prime Factor Examples

    Where can I find examples, or a complete list, of computer generated (common prime factor) solutions to the Beal conjecture problem?
  9. E

    Are Riemann hypothesis and Goldbach conjecture related?

    this is a question i have i mean are RH and Goldbach conjecture related? i mean in the sense that proving RH would imply Goldbach conjecture and viceversa: RIemann hypothesis: (RH) \zeta(s)=0 then s=1/2+it Goldbach conjecture,let be n a positive integer then: 2n=p1+p2 ...
  10. K

    Proof of Golbach's conjecture and the twin prime conjecture

    I found this on arxiv...is this guy a loon or do the proofs seem reasonable? Proofs
  11. L

    Where to Find Original Manuscript of Proof of Taniyama Shimura Conjecture?

    Where to Find Original Manuscript of Proof of Taniyama Shimura Conjecture? Can anyone please tell me where i can find the proof of Proffessor Wiles?? I have scoured the web for it in vain. And since i am still not part of any institution, JSTOR have denied acess to me. Thanx for any help.
  12. S

    Extension of Thurston's Geometrization Conjecture to four dimensions?

    Hello all, I was wondering whether there might be anything similar to Thurston's Geometrization Conjecture, except for four manifolds instead of three manifolds. (Essentially, this conjecture (iiuc) states that it is always possible to take an arbitrary 3-manifold and break it up into...
  13. I

    Has the Poincaré Conjecture Been Proven? A Review of the Proposed Proof

    http://mathworld.wolfram.com/news/2003-04-15/poincare/ Is the proof considered valid? Did he claim the millennium prize? I can't find any recent news about it.
  14. M

    The Existence of The Book: Paul Erdos's Conjecture

    According to this paper, http://arxiv.org/abs/math.GM/0108201 Paul Erdos (of Erdos number fame) conjectured the existence of The Book, a book that contains all the smallest proofs of mathematics arranged in lexical order. What are your thoughts on it, do you believe in the existence of such book?
  15. V

    Brane Worlds, the Subanthropic Principle and the Undetectability Conjecture

    http://www.arxiv.org/abs/physics/0308078 Could we belong to a non-aggressive advanced civilization, which protects earth? And does the general population suffer from the crown of creation syndrome?
  16. R

    Exploring the Prime Factorial Conjecture

    Here is a tentative conjecture that needs to be tested. [P! + P]/P^2 = INTEGER if and only if P is a prime number P! is P factorial, e.g. 3*2*1 , 5*4*3*2*1 , 7*6*5*4*3*2*1, etc...
  17. S

    The Poincare Conjecture *Kinda long*

    Are there any updates on this? I don't know how old this is, but I am curious. I thought it was pretty interesting stuff. -------The Poincare Conjecture, one of the most famous math problems solved A Russian mathematician claims to have proved the Poincare Conjecture, one of...
  18. MathematicalPhysicist

    A partial solution to the Goldbach Conjecture

    im not trying to be a crank and give you a solution to it but I am looking for the proof of Ivan Vinogradov "that every sufficiently large odd integer can be expressed as the sum of three odd primes"( quoted from here:http://primes.utm.edu/glossary/page.php?sort=Vinogradov), the original proof...
  19. S

    Has the Poincare Conjecture Finally Been Solved?

    Mathematicians are now saying that Grigory Perelman has really solved the conjecture and the proof will be in a paper he will post in the near future. His previous papers on this subject are in the arxiv specal topic Differential Geometry (under mathematics). Keep your eyes on this space!
  20. O

    Is the Aleph0-1 Conjecture Correct?

    An edited post: Please can you show a proof that contradicts my conjecture, saying: "By using base^power representation method we can represent a list of rational numbers (repetitions over scales, for example: 0.123123123...) where the missing rational number is based on the diagonal...
  21. U

    A Conjecture : can anyone find a counter-example or otherwise disprove ?

    Hi, I have a conjecture and I am not sure whether it is true. I can't construct a counter example but perhaps someone more mathemetically resourceful than myself can do so (or perhaps even offer a direct proof or disproof). Here's the conjecture. Let X_n = r_1 \, r_2 \, r_3 \, ... \, r_n...
  22. M

    Maldacena Conjecture: 55-min RealPlayer Lecture

    "Maldacena conjecture" Does somebody here believe that the Maldacena conjecture is true? Here's a lecture of 55 minutes in RealPlayer explaining the conjecture: http://www.wlap.org/umich/mctp/workshops/2003/may/20030508-03/
  23. D

    Difficulty with the Erdos-Straus Conjecture

    The Erdos-Straus Conjecture proposes that: For n >= 1, 4/n = 1/a + 1/b + 1/c, has postive integer solutions. n = 2k (evens) n = 4k+3 (odds) n = 4k+1 (odds) For 2k I have found the pattern --> if k >= 1, 4/2k = 1/2k + 1/2k + 1/k. This is simple, I know. I am having difficulty...
  24. R

    Goldbach Conjecture: Proving the Theory

    GOLDBACH CONJECTURE Goldbach conjecture: ”Each even number greater than six, could be written as sum of two primes” This conjecture is almost experimentally proven on computer , but we still miss theoretical proof. I’ll try to reach it by the method showed below. Let...
  25. MathematicalPhysicist

    Has the Erdos-Strauss Conjecture Been Proven?

    did someone proove this conjecture or is still just a conjecture?
  26. marcus

    The Marcus Conjecture: Exploring the Relationship Between CMB & Dark Energy

    I have chosen to honor PF by publishing my conjecture first here :smile:. The Marcus Conjecture, which I formulated a few days ago on one of the cosmological redshift threads, is that the energy lost from the CMB by expansion has gone into the form of dark energy. I shall now show...
  27. MathematicalPhysicist

    What is the Double Bubble Conjecture and its Proof?

    what is it and how was it prooved?
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