A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. ... Conjectures must be proved for the mathematical observation to be fully accepted. When a conjecture is rigorously proved, it becomes a theorem. Share your favorite conjecture as a answer for this? let we know some beautiful unsolved statements in the field of science and Maths?
Dear Jack Son,
Goldbach's Conjecture:
Every even number n > 2 can be written as
n = Prime + prime or n = 1 + prime.
4 = 1 +3 ,
6= 1+5= 3+3
8= 1+7 = 3+5
10 = 7+ 3 = 5 + 5, etc.
It has very nice consequences in mathematics.
Do you know why? Because it is simple, popular,
school students can understand it's meaning.
It is a big challenge for human intelligence.
Not proved yet.
Best Wishes
@Issam
Just an idea about tools, but I couldn't prove:
an even number is of the form 2k the order of a dihedral group. The conjecture meant that the group contains orbits or classes of prime cardinals.
@ Hanifa,
Your claim:
Goldbach's Conjecture is equivalent to
[The conjecture meant that the group contains orbits or classes of prime cardinals.]
Interesting, can you explain the idea?
Best regards
This dosn't need any guess, The most important conjectures at mathematicians is : The Riemann Hypothesis ,the reason is the great contributions and best consequences of it in other science !!!!!
@ Rafik,
Could you please list some consequences in some science but not
number theory and mathematics.
Thank you in advance.
Best regards
The standard connection of RH to other science is Quantum mechanics and chaos theory and it's seems to me that all of your interest research occurs in matrix theory then one of the most important connection and consequence of RH is related also to Random matrxi (correlation of zeros ) , we have just to give the standard info as shown below :
As mathematicians have attacked the hypothesis from every angle, the problem has also migrated to physics. Since the 1940s, intriguing hints have arisen of a connection between the zeros of the zeta function and quantum mechanics. For instance, researchers found that the spacing of the zeros exhibits the same statistical pattern as the spectra of atomic energy levels. In 1999, the mathematical physicists Michael Berry and Jonathan Keating, building on an earlier conjecture of David Hilbert and George Pólya, conjectured that there exists a quantum system (that is, a system with a position and a momentum that are related by Heisenberg’s uncertainty principle) whose energy levels exactly correspond to the nontrivial zeros of the Riemann zeta function. Each of these energy levels, En, corresponds to a zero of the form Zn = ½ + iEn, which has a real part equal to ½ and an imaginary part formed by multiplying En by the imaginary number i.
If such a quantum system existed, this would automatically imply the Riemann hypothesis. The reason is that energy levels of quantum systems are always real numbers (as opposed to imaginary), since energy is a physically measurable quantity. And since the En’s are purely real, they become purely imaginary when multiplied by i in the formula for the corresponding Zn’s. There is never a case where an imaginary part of En is multiplied by i, canceling out its imaginary property and rendering it real, so that it then contributes to the real component of Zn and changes it from ½ to something else. Since energy levels are always real, the real parts of the zeros of the zeta function would always be ½, and the Riemann hypothesis would therefore be true.
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