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. R

    Stronger Goldbach-related conjecture

    For any positive integer n>1, define gap(n) as gap(n) = |n-p| = |n-q| for p,q the two primes closest to n such that p+q = 2n. The Goldbach Conjecture is equivalent to the existence of p and q, and thus the existence of gap(n), for all n>1. (Or all n>2 if p and q are required to be odd...
  2. S

    Exploring Gilbreath's Conjecture: A Guide to Research and Collaboration

    Has anyone ever heard of it, or better yet, done any research involving it? I'm doing some work with the conjecture, and I'm wondering if anyone could help me out.
  3. P

    Collatz Conjecture Paper: Check it Out & Give Opinion

    The paper at this site "http://uts.awardspace.info" looked interesting to me, but would anyone else familiar with this problem, it's been around since the 30's, check it out and give an opinion.
  4. M

    Empirical proof of a conjecture

    can a conjecture be proved by 'empirical' means (observation) ?? i mean let us suppose that exists some functions named f_{i} (x) so \sum _{n=0}^{\infty} = \sum _{p} f(p) then an 'empirical' method would be to calculate the 2 sums and compare the error , let us suppose that the...
  5. C

    Proof of Ira Gessel's Lattice Path Conjecture

    http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/gessel.html"
  6. P

    Is the Goldbach Conjecture Finally Proven?

    is there a proof for the goldbach's conjecture? that the every number can be written as the sum of three primes... or, every even integer can be written as the sum of two primes??
  7. D

    Proving Conjectures About the Binet Formula for Q(\sqrt{k})

    Let Q(\sqrt{k}), for some positive integer k, be the extension of the field of rationals with basis (1, \sqrt{k}). For example, in Q(\sqrt{5}) the element ({1 \over 2}, {1 \over 2}) is the golden ratio = {1 \over 2} + {1 \over 2}\sqrt{5}. Given an extension Q(\sqrt{k}), let B(n) denote the...
  8. K

    Simplest the AdS/CFT correspondence is a conjecture

    Does anyone have a simple explanation for this?
  9. L

    Goldbach’s Conjecture and the 2-Way Sieve

    Detail attached Goldbach’s Conjecture and the 2-Way Sieve Intro: Mr. Hui Sai Chuen is an amateur mathematician born in May 1937 in the Canton province of China. After graduating with an engineering and construction degree, he proceeded to do research on architecture and material science...
  10. R

    Conjecture re Fibonacci numbers

    Given A_1 = 3 \texttt{ and } A_n = A_{n-1}^{2} -2; is there a way to prove the following: \prod_{i=1}^{n}A_{i} = F_{2^{n+1}} or if someone has already proven this, can you give the reference?
  11. E

    Solved Poincaré Conjecture: Find Perelman's Proof Here

    [SOLVED] poincare conjecture http://en.wikipedia.org/wiki/Solution_of_the_Poincar%C3%A9_conjecture The links to Perelman's original proof do not work. Can someone fix them please?
  12. S

    You are subscribed to this thread Proving conjecture for recursive function

    Hi, Homework Statement Just having some troubles with a proof i have been asked to do, (sorry for not knowing the math code) basically, f(1)=0, f(2)=1/3 and f(n)= ((n-1)/(n+1))*f(n-2) and I've come up with the conjecture that f(n) = 0 when n is odd, and = 1/(n+1) when n is even...
  13. S

    Artin's Conjecture on Primitive Roots: Perfect Squares

    If a is a perfect square then a is not a primitive root modulo p (p is an odd prime). (from Artin's conjecture on primitive roots) http://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots This is what I know: suppose a = b^2 a is a primitive root mod p when , a^(p-1) congruent to 1...
  14. M

    What is the Set Cardinality Conjecture?

    Well, it's a conjecture to me because I don't know (yet) if it's true or false. Let |A|=n, where n is an infinite cardinal. Let B be the collection of all subsets of A with cardinality less than n. Then |B|=n. Is it true first of all? And will the proof be short or long?
  15. O

    New Mersenne numbers conjecture

    Hi everyone! Is anyone able to find the demonstration of the following Mersenne conjecture? for j=3, d=2*p*j+1=6*p+1 divide M(p)=2^p-1 if and only if d is prime and mod(d,8)=7 and p prime and there exists integer n and i such that: d=4*n^2 + 3*(3+6*i)^2 This conjecture has...
  16. P

    Open Subsets of a Union: A Conjecture

    Homework Statement Conjecture: If K=a union of subsets of G with K open then each subset in the union is open The Attempt at a Solution Can't really see the proof. In fact it's false as any non discrete topology have open sets which are a union of subsets whch may not be open.
  17. K

    Explaining the Hodge Conjecture in Simple Terms

    Can Anyone explain the hodge conjecture in simple terms?
  18. R

    Conjecture re form x^2 + Mxy + y^2

    Conjecture: If x and y are coprime and M <> 2 then x^2 + Mxy +y^2 = p^2 has integral solutions only for p = a prime or for products of such primes. Also if M is positive then both x and y are partial solutions for X^2 -MXY + Y^2 = p^2. Thus 3*3 +3*5 +5*5 = 49 and 9 - 3*8 + 8*8 and 25 - 5*8 +...
  19. vincentm

    Solving of the Poincare' Conjecture

    Ok first i'd like to note that I'm not good at mathematics and have a vague understanding of the conjecture. What i'd like to know though is what comes now that this has been solved by Perelman? What implications does this have?
  20. H

    Logical Systems+new Principles+attempt To Solve Collatz Conjecture

    LOGICAL SYSTEMS+NEW PRINCIPLES+ATTEMPT TO SOLVE COLLATZ CONJECTURE. First i would like to say that am honoured to share my thought with great people in here who always provide help.I will not say iam right or wrong.I hope this post will be aspark to good mindes. I have viewed the laws of...
  21. H

    Logical System+new Principles+attempt To Solve Collatz Conjecture

    LOGICAL SYSTEMS+NEW PRINCIPLES+ATTEMPT TO SOLVE COLLATZ CONJECTURE. First i would like to say that am honoured to share my thought with great people in here who always provide help.I will not say iam right or wrong.I hope this post will be aspark to good mindes. I have viewed the laws of...
  22. M

    Conjecture about Dirichlet series.

    Hi, i hope it is not a crack theory i had the idea when reading Ramanujan resummation, i believe that for a Dirichlet series which converges for Re (s) > a , with a a positive real number then we can obtain a regularized sum of the divergent series in the form: \sum_{n >1}a_{n}n^{-s}-...
  23. S

    Goldbach's Conjecture (Theorem?)

    Goldbach's Conjecture (Theorem??) Hi guys, I just need to know if Goldbach's Conjecture has been demonstrated or not! Thx! :D
  24. R

    Conjecture on triangular numbers T(n)

    Let a triangular number T(n) = n*(n+1)/2 be factored into the product A*B with A less or equal to B. Let gcd(x,y) be the greatest common divisor of x and y For each of pair (A,B) define C,D,E,F as follows C = (gcd(A,n+1))^2, D = 2*(gcd(B,n))^2, E = 2*(gcd(A,n))^2, F = (gcd(B,n+1))^2...
  25. Evo

    Conjecture and dangling prospects

    I know I've commented before about some of the amazing things that my co-workers have come up with like "Is Germany its own country?" The guy that believes dinosaurs are faked by Darwinists because "you can make anything you want out of a pile of bones", was talking about the tv show "Are you...
  26. A

    I made the following conjecture

    Every prime number > 3 could be written as a sum of a prime number and a power of two. p,q are primes, n is positive whole number ==> p = q + 2^n 5 = 3 + 2^1 7 = 5 + 2^1 = 3 + 2^2 11 = 7 + 2^2 13 = 5 + 2^3 17 = 13 + 2^2 19 = 3 + 2^4 23 = 7 + 2^4 29 = 13 + 2^4 31 = 23 + 2^3 37 = 29...
  27. A

    Can This Conjecture Predict Prime Numbers?

    Now that we've all warmed up a bit... Let's try this little gem of a conjecture... Instead of 2^x - 3^y or 3^y - 2^x, which together can be represented as abs( 2^x - 3^y ) since all we care about are the positive solutions, where abs( ) is absolute value, instead of that, let's try...
  28. A

    Is Jacobian Conjecture still open?

    Is Jacobian Conjecture still open for general case? who knows the recent progress on this problem, especially in the approach of Feyman graph? 3x.
  29. P

    Poincare Conjecture: Fundamental Group of V Explained

    Does the Poincare conjecture say: Consider a compact 3-dimensional manifold V without boundary. Poincare conjectured that The fundamental group of V is trivial => V is homeomorphic to the 3-dimensional sphere? It has been proved for all manifolds except 3. However Perelman completed a proof...
  30. J

    HIlbert-Polya conjecture proof of RH through Quantum mechanics

    The main idea to prove RH through the HIlbert Polya conjecture , is finding a Hamiltonian H=p^2 V(x) (QM) , so its energies are precisely the imaginary parts of the Non-trivial zeros. Using the Von Mangoldt formula for the Chebyshev function, differentiating respect to x , and setting...
  31. K

    Poincaré conjecture - singularities - quantum cohomology

    In 2006, the mathematically rigorous proof of the Poincaré conjecture was completely excepted. The Poincaré conjecture was put forward by Henri Poincaré in the early 1900's. It is a theorem about the characterization of the 3D sphere amongst 3D manifolds. It was considered one of the most...
  32. K

    Impact of Poincaré conjecture on mathematics?

    In 2006, the mathematically rigorous proof of the Poincaré conjecture was completely excepted. The Poincaré conjecture was put forward by Henri Poincaré in the early 1900's. It is a theorem about the characterization of the 3D sphere amongst 3D manifolds. It was considered one of the most...
  33. L

    Mathematica How many reflections before absorption on a perfect rectangular mirror?

    I have a mathematical conjecture. It has to do with physics, but I call it a mathematical conjecture because the cases I which I generalized into a conjecture were done purely mathematically, with no actual physical experimentation. Consider a perfect rectangular mirror which obeys the law...
  34. quasar987

    Conjecture Connecting All Branches of Math

    I'm looking for the name of the optimistic conjecture that, if I remember correctly, conjectures the existence of a certain kind of connection between every branch of mathematics. I read about it in Singh's book on Fermat's last theorem. Fueled by the enthusiasm following the discovery of a...
  35. K

    A conjecture on Cesaro summation and primes.

    After studying Cesaro and Borel summation i think that sum \sum_{p} p^{k} extended over all primes is summable Cesaro C(n,k+1+\epsilon) and the series \sum_{n=0}^{\infty} M(n) and \sum_{n=0}^{\infty} \Psi (n)-n are Cesaro-summable C(n,3/2+\epsilon) for any positive epsilon...
  36. F

    Is Tripling Odd Numbers Necessary in the Collatz Conjecture?

    Hey, i was reading about the Collatz conjecture, where, if you take a integer, divide it by 2 if its even and triple it then add one if it's odd, and do it over and over again, the result would be one. I was thinking, "wouldnt it have the same effect if you didnt triple odd numbers?" am i wrong?
  37. T

    A conjecture about Dirichlet series.

    if g(s)= \sum_{n=1}^{\infty} a(n) n^{-s} Where g(s) has a single pole at s=1 with residue C, then my question/conjecture is if for s >0 (real part of s bigger than 0) we can write g(s)= C(\frac{1}{s-1}+1)-s\int_{0}^{\infty}dx(Cx-A(x))x^{-s-1} of course A(x)=\sum_{n \le x}a(n)...
  38. S

    Exploring Goldbach's Conjecture: Three Papers Analyzed

    I was under the impression that Goldbach's Conjecture is still an open question in mathematics. Then what is it that the following three papers claim to do? (http://arxiv.org/ftp/math/papers/0609/0609486.pdf" ) Thanks for clearing up my confusion.
  39. R

    Poincare Conjecture Explained: Layman's Terms

    What is the poincare conjecture in layman's terms?
  40. C

    Pointcare Conjecture - Grigory Perelman's Proof

    Greetings, I'm far from a skilled mathematician and I was wondering what greater minds than mine thought of Perelman's proof of the Pointcare conjecture. Also, if you could offer a brief explanation of the conjecture it would be very much appreciated. Here is a link to a bried article on...
  41. marcus

    Vilenkin claims to have refuted the CNS conjecture

    http://arxiv.org/abs/hep-th/0610051 On cosmic natural selection Alexander Vilenkin 4 pages "The rate of black hole formation can be increased by increasing the value of the cosmological constant. This falsifies Smolin's conjecture that the values of all constants of nature are adjusted to...
  42. M

    Make a conjecture about the sum? Confused on what they want exactly

    Hello everyone, I'm confused on the directions. It says, Evalute the sum, for n = 1, 2, 3, 4, and 5. Make a conjecture about a formula for this sume for general n, and prove your conjecture by mathematical induction. This is the sum and my work...
  43. M

    Can the Poincare Conjecture Simplify 3D Objects for Mathematical Calculations?

    After reading the article on Poincare's conjecture in the Economist, I became curious about simplified 3-dimensional objects. Excerpt: Let's take a cube and simplify it into a circle. Could we then use equations ment for circles for the simplified shape, ie calculate the cube's surface...
  44. C

    Legendre's Conjecture: Exploring the Search for Primes Between n^2 and (n+1)^2

    Is anything more known about Legendre's conjecture that there is a prime between n^2 and (n+1)^2 for positive integers n than what appears on MathWorld? MW says that a prime or semiprime always satisfies this, and that there is always a prime between n and n^{23/42} (21/42 would be equivilent...
  45. P

    Parameter Within A Linear Equation Conjecture

    HELLO, IN A LINEAR EQUATION OF THE FORM, X2 + Y2 + Z2 + D = 0 CAN THE PARAMETER BE -D WHERE t = parameter = -D and V = direction vector and Vt = <at, bt, ct> It seems as if it is...but I can't seem to prove it. HELP HELP HELP HELP
  46. Clausius2

    Perelman, Poincare Conjecture solved now?

    Perelman, Poincare Conjecture solved now?? Seems that this guy has solved the Poincaré Conjecture: http://en.wikipedia.org/wiki/Grigori_Perelman He is supposed to get the Fields Medal in Madrid this year, in the next international congress of mathematics. But it is likely that he won't...
  47. E

    Question Regarding Goldbach's Conjecture

    1*1 1*3 2*2 3*1 1*5 2*4 3*3 4*2 5*1 1*7 2*6 3*5 4*4 5*3 6*2 7*1 * * * etc. If we go on constructing the pattern of numbers above, will each row contain atleast 1 product of two odd...
  48. D

    Grimm's Conjecture: Origin & Sources

    Can someone tell me when Grimm's conjecture (http://mathworld.wolfram.com/GrimmsConjecture.html) was formulated? I can't find any sources on that, and I don't have Guy's book.
  49. S

    Complete Solution of Poincare Conjecture

    Announced in http://www.intlpress.com/AJM/p/2006/10_2/AJM-10-2-165-492.pdf" . Differential Geometry meets Geometric Surgery on three-manifolds; Perelman clarified and (perhaps) corrected. A COMPLETE PROOF OF THE POINCAR´E AND GEOMETRIZATION CONJECTURES – APPLICATION OF THE...
  50. E

    Is the Berry Operator the Key to Solving the Zeta Function?

    Is "Berry Operator"... H=-i\hbar(x\frac{d}{dx}+1/2) the operator which give all the solutions of \zeta(1/2+iE_{n})=0 ?..it seems too easy to be true...:eek: :eek:
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