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. C

    Collatz Conjecture: Plotting Integer Steps with Joe

    Hello there everyone! I've written a lovely little program to go through the tedious process of testing numbers in the "If odd 3n+1; If even n/2; Repeat." scenario. It then saves all of the numbers, starting with the integer being tested, and ending with "1" in a file of the form...
  2. E

    Conjecture on superposition: simple concept, complex math

    I have conjectured that two different waves in the same region, will not exactly result in the superposition, or addition of both waves independently. The logic: Every point in a region which a wave propagates has a position, and an acceleration which partially, if not totally, depends on the...
  3. O

    Riemann Hypothesis and Goldbach Conjecture Proof?

    Hey guys, I saw these just showed up on arXiv, published by some unknown who claims to have invented his own number system and is not affiliated with any academic institutions. What do you make of this? http://arxiv.org/abs/1110.3465 http://arxiv.org/abs/1110.2952
  4. D

    A conjecture about the rationallity of a definite integral

    Is it true that \int_0^1 f(x) dx \in \mathbb{Q} \Rightarrow \int_0^1 x f(x) dx \in \mathbb{Q} ? (Suppose f(x) integrable as needed) I thought of this conjecture yesterday and still couldn't prove it, I tried using integration by parts to relate it to the original, but didn't...
  5. P

    Collatz Conjecture - Bouncing Ideas

    Hey, this is my first post, so... Hello everybody! I've been looking into the Collatz conjecture, and like most mathematically minded people, been completely absorbed by it. I'm looking to bounce some ideas off other people, kind of a peer review of a couple things if you will. I'll be the...
  6. K

    The Epsilon Conjecture In Fermat's Last Theorem

    By supposing there is a solution to Fermat's Last Theorem then according to Frye you can create an elliptic curve that isn't modular. Taniyama-Shimura says that all elliptic curves are modular, so in proving that that Frye curve is not modular which was done by Ribet don't you disprove the...
  7. S

    In short, I don't know if there is a clear answer to your question at this time.

    Hi there PF My question here is: Is the Bagger-Lambert-Gustavsson action (http://en.wikipedia.org/wiki/Bagger%E2%80%93Lambert%E2%80%93Gustavsson_action) a way of proving the "M-theory as a matrix model: a conjecture" (http://arxiv.org/abs/hep-th/9610043) or is it a different approach? And how...
  8. Q

    New Sieving Method, Goldbach's Conjecture

    Hi all, I've developed a new sieving method that I believe provides a tight lower bound for the counting of certain kinds of primes. I'm 99% sure my solution works, and if so, it would allow the solution of many kinds of problems in additive number theory. The sieving method came out of...
  9. J

    Binomial coefficients sum conjecture about exponential

    Fix some constant 0<\alpha \leq 1, and denote the floor function by x\mapsto [x]. The conjecture is that there exists a constant \beta > 1 such that \beta^{-n} \sum_{k=0}^{[\alpha\cdot n]} \binom{n}{k} \underset{n\to\infty}{\nrightarrow} 0 Consider this conjecture as a challenge. I don't...
  10. R

    Conjecture: Prime Divisibility & First Differences of Stirling & Eulerian Triangles

    CONJECTURE: Subtract the Absolute Values of the Stirling Triangle (of the first kind) from those of the Eulerian Triangle. When row number is equal to one less than a prime number, then all entries in that row are divisible by that prime number. Take for instance, row 6 (see below). The...
  11. bcrowell

    Conjecture about parallel and series circuits

    If we have n (possibly unequal) resistors, we can combine them in various ways to produce a device with two terminals. In many cases, the equivalent resistance of this device can be found by repeatedly breaking the circuit down into parallel and series parts. Conjecture: n=5 is the lowest for...
  12. D

    What is the significance of k being a multiple of 2 or 3?

    Let p,q be two different primes from 5 onwards (not 2 or 3). Let p be the biggest of the two. The difference of squares p^2 - q^2, since p,q are both odd, is always a multiple of 8 (easy to prove). So take the integer k = (p^2 - q^2) / 8. It turns out that k seems to be (says friend computer)...
  13. M

    (Not a Proof of) Goldbach's Conjecture

    I was doing some thinking about good old Goldbach and noticed that every pair of primes was the same distance away from half of the even number. For example, 3 + 5 = 8 and |4 - 3| = 1 = |4 - 5| 3 + 13 = 16 and |8 - 3| = 5 = |8 - 13| 7 + 17 = 24 and |12 - 7| = 5 = |12 - 17| 19 + 23 = 42...
  14. R

    Conjecture: Sophie Germain Triangles & x | 2y^2 + 2y - 3 = z^2

    Limiting ourselves to N... Conjecture: (sqrt (16x + 9) - 1)/2 = y | 2y^2 + 2y - 3 = z^2 for x = a Sophie Germain Triangular Number, which is recursively defined as: a(n)=34a(n-2)-a(n-4)+11 First 11 values (I have not checked further as I would be very surprised if this equivalency...
  15. J

    Possible conjecture relating to factors and powers of 12

    I have read in the past that having a base 12 number system is superior to a decimal system because of the number of factors that 12 has. For instance we essentially use base 12 for time, it's better to have a 60 minute hour than a 100 minute hour as there are more 'convenient chunks' or factors...
  16. FeDeX_LaTeX

    Proving Conjecture: No Real Solutions Greater than 2 for Polynomial Equation

    Hello; I don't know how to prove this conjecture I've made; For the polynomial equation -\sum_{n=0}^{\infty}k^{n}=0 there exist no real solutions greater than 2, no matter how large the value of n. How do I show that this is true? If it's a little unclear, what I mean is, for example, if...
  17. F

    Elliott-Halberstam conjecture and the Riemann Hypothesis

    I was wondering if one of the consequences of the Elliott-Halberstam conjecture would imply the Riemann Hypothesis (RH) or the Generalized Riemann Hypothesis (GRH)? Or at least if there is a connection between the Elliott-Halberstam conjecture and RH or GRH? I ask because the...
  18. C

    Does the poincare conjecture disprove the shape of strings in string theory

    Considering that the smallest particles in nature are supposed to be strings, which are donut and line shapes. And the poincare conjecture says the simplest shape in nature is a sphere. wouldn't it make sense that the true fundamental particles are sphere shaped and that if they combine to form...
  19. M

    Simple Proof of Fermat's Last Theorem and Beal's Conjecture

    Attached is the proof.
  20. P

    Any tips on how to conjecture formulas for Induction?

    What are usual tips in conjecturing formulas for math induction if I am given a certain sum of sequence? Thank you.
  21. B

    Questions of Conjecture in Physics.

    Hey, I am a junior in physics at penn state and am currently in a philosophy class. We have an assignment to argue a question of conjecture(my professor specified he wanted a problem of the "did/does anything actually happen") in our fields(majors). I am kind of struggling to find a good topic...
  22. marcus

    Why spin is quantized one-dimensionally (spon. dim. red. conjecture)

    Spin behaves as if it is one dimensional, along any axis you select. This behavior would be just what one expected from a vector which, owing to spontaneous dimensional reduction, lived in a one-dimensional world. But according to several approaches to QG, very small "things" or degrees of...
  23. F

    Odd Party Conjecture: Can You Prove or Disprove?

    Conjecture: Consider any group with an even number of people where each member is connected to any other through some chain of people. Then the original group can be split into groups where each member knows an odd number of people directly. Note: If the party is such that each member knows an...
  24. C

    Very simple (Dis)proof of Riemann hypothesis, Goldbach, Polignac, Legendre conjecture

    (Dis)proof of Riemann hypothesis,Goldbach,Polignac,Legendre conjecture I'm just an amateur and not goot at english ^^;
  25. Z

    A CONJECTURE (could someone help ? )

    i have the following conjecture about infinite power series let be a function f(x) analytic so it can be expanded into a power series f(x)= \sum_{n=0}^{\infty} a_{2n}(-1)^{n} x^{2n} with a_{2n} = \int_{-c}^{c}dx w(x)x^{2n} w(x) \ge 0 and w(x)=w(-x) on the whole interval (-c,c) in case...
  26. M

    Revised Simple Proof of the Beal's Conjecture

    SIMPLE PROOF OF BEAL’S CONJECTURE (THE $100 000 PRIZE ANSWER) Beal’s Conjecture Beal’s conjecture states that if A^x + B^y = C^z 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. Examples...
  27. M

    Simple Proof of Beal's Conjecture

    SIMPLE PROOF OF BEAL’S CONJECTURE (THE $100 000 PRIZE ANSWER) Beal’s Conjecture Beal’s conjecture states that if A^x + B^y = C^z 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. Examples...
  28. R

    Is the Goldbach Conjecture part of a larger pattern?

    I wonder if the Goldbach Conjecture could be extended, so that the even number halfway between two primes that differ by 4n + 2 can be written as the sum of two primes from pairs that differ by 4n + 2? This conjecture often fails for the first few numbers, but then seems to begin working. For...
  29. M

    Is the Twin Prime Conjecture Finally Proven? A Scientist's Perspective

    Here is my proof of the 'Twin Prime Conjecture'.
  30. M

    Proof of the Twin Prime Conjecture

    I believe I have proved that there are an infinitude of twin primes using elementary algebra and a straightforward thought experiment. My proof will be sent shortly.
  31. E

    Introduction to Dirac's Conjecture

    Hey there! I want to make myself familiar with Dirac's conjeture. Does anyone know a good source for it? I don't want to read his paper form the 50ies and hope there is a more pedagogical introduction of the topic... :) Thanks!
  32. R

    Conjecture: Solving 32n^2 + 3n = 0 mod P for odd P

    Conjecture: If P is odd, then there is one and only one number n in the set {1,2,3,...(P-1)} which satisfies the equation (32*n^2 + 3n) = 0 mod P an this number. Can anyone help me with a proof of this? If by chance this is a trival matter. I have gone further and determined 4 equations for...
  33. D

    Conjecture about the nth derivative of the function f(x)=e^(ax)

    Make a conjecture about the nth derivative of the function f(x)=e^(ax). This conjecture should be written as a self contained proposition including an appropriate quantifier. What is the last sentence saying to do. I know what a conjecture is but I am confused on what the book wants here.
  34. M

    Poincare Conjecture: Understanding & Appreciating the Proof

    hello! i would like to be able to understand and appreciate the proof of the poincare conjecture. i have some idea of where to begin, and my supervisor is going to help me out (i'm starting a master's in pure math and my supervisor does geometric analysis), but i was wondering if anyone here...
  35. M

    Are There Exceptions to the Goldbach Conjecture for Even Numbers of the Form 2p?

    4=2+2, 6=3+3. Are there any other cases where an even number of the form 2p, where p is a prime, cannot be represented as the sum of two different primes?
  36. N

    Is There a Topological or Geometrical Approach to the Riemann Hypothesis?

    Hello dear forum members I wanted to know where are the research on the Riemann hypothesis , the latest advances ,who are the currently leading experts and is now known that mathematics it requires for its resolution
  37. A

    Goldbach's Conjecture - Proof (better link)

    Hi. I might just have something here. Please let me know if you have any questions or comments. Thanks. Andy Lee. leeaj@shaw.ca See proof at http://www.facebook.com/pages/Goldbachs-Conjecture-Proof/237054761999
  38. R

    A Single String Conjecture ? -Feynman revisited

    a "Single String Conjecture"? -Feynman revisited Do we all remember Feynman's "Single Electron Conjecture" that states, basically, that a single electron moving back and forth in time could "fill in the gaps" on every electron ring around every atom in the universe? Well, assuming Superstring...
  39. M

    Proving the Goldbach Conjecture with G{N}

    Homework Statement The Goldbach Conjecture: Every even number greater than 2 is the sum of 2 primes Consider P(n) = (n is congruent to 3mod4) Then g(n) ={0 if n = 1 or 2n is a sum of 2 primes 1 if 2n is not a sum of 2 primes and P(n) is true...
  40. Z

    A conjecture about Xi function

    i've got the following conjecture about XI function, the following determinant p_n(x) = \det\left[ \begin{matrix} \mu_0 & \mu_1 & \mu_2 & \cdots & \mu_n \\ \mu_1 & \mu_2 & \mu_3 & \cdots & \mu_{n+1} \\ \mu_2 & \mu_3 & \mu_4 & \cdots & \mu_{n+2} \\ \vdots & \vdots & \vdots & & \vdots \\...
  41. F

    Approximating the reals by rationals (Littlewood's Conjecture)

    Hi all, Tim Gowers has a list of possible Polymath projects up, where he mentions the Littlewood Conjecture: This states, informally, that all reals can be approximated reasonably well, in the sense that if we let the denominator of an approximation \frac{u}{v} grow, the error term becomes...
  42. M

    Has anyone read Ken Conrow's Collatz Conjecture website?

    http://www-personal.ksu.edu/~kconrow/" I mean really read it, to where they understand it, not just to the point where their eyes glaze over? I see his site cited quite frequently, but I don't know if I've ever seen any critique. I admit, I was intimiitaded by his site at first. But...
  43. camilus

    Why doesnt Bertrand's postulate imply Legendre's conjecture?

    I mean, according to my knowledge, Bertrand's postulate has already been proved, I've already read and understood one, but Paul Erdos, and a few other mathematicians have proved it using various methods. I just finished reading Ramanujan's proof. Its amazingly advanced, and really short. The...
  44. J

    Can the No Win Random Walk Conjecture Be Proven Using Martingales?

    A random walk can be defined by the following recurrence relation, X_{t+1} = X_t + \Delta X where \Delta X \sim \mathcal{N}(0, \sigma^2). At any time t1 \geq 0 a strategist may enter, and at any time t2 > t1 a strategist may exit. The resulting profit p is given by: p(t1,t2) = X_{t2}...
  45. Loren Booda

    Conjecture for prime pairs of difference two

    Can it be proven that the number of prime pairs with a difference of two (that is, primes separated by only one even number) approaches infinity?
  46. Loren Booda

    A conjecture about sums of uniquely valued primes

    "Of the numbers N>1, only 4 and 6 cannot be expressed as a sum of prime numbers with unique values."
  47. C

    Trouble creating a conjecture, relating to graphs and complex functions

    Need to investgate the ratio of the areas formed when y=xn is graphed between two arbirary parameters x=a and x=b such that a<b 1. Given the funtion y=x2, consider the region formed by this function from x=0 to x=1 and the x-axis. Label this area B. Label the region form y=0 to y=1 and the...
  48. Z

    Conjecture on primes (not mine=)

    i saw this conjecture on the web but do not know if is true the number of primes between the expressions x^2 and (x+1)^2 for every x or at least for x bigger than 100 is equal to the Number of primes less than 2x+1 (the x are the same)
  49. D

    An Elementary Proof Of Both The Beal Conjecture And Fermat's Last Theorem.

    An Elementary Proof Of The Beal Conjecture And Fermat's Last Theorem. By: Don Blazys. The Beal Conjecture can be stated as follows: For positive integers a,b,c,x,y,z, if a^x+b^y=c^z, and a,b,c are co-prime, then x,y,z are not all greater than 2. Proof: Letting all variables...
  50. Jim Kata

    I have a conjecture/ possibly already a theorem

    I am not very well read so this may already exist as a theorem. If not, try to prove it, or disprove it. Let G be a compact group over the reals, then the maximally compact subgroup of the complexification of G is just G over the reals. That is the maximally compact subgroup of...
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