Proving the Riemann conjecture.
Goldbach's conjecture states that every even integer which is greater than 2 can be expressed as the sum of two prime numbers.
There is not "the" conjecture: there are several. The oldest and probably best known unsolved conjecture in number theory is the Goldbach conjecture. According to it every even integer greater than two can be expressed as the sum of two prime numbers.
Hypothesis
Because mathematics is a axiomatic system so that every new statement remains a conjecture until it is proved.
It is a proposition or a belief that has not yet been proven.
The Collatz conjecture
Proving the Riemann conjecture.
Goldbach's conjecture states that every even integer which is greater than 2 can be expressed as the sum of two prime numbers.
There is not "the" conjecture: there are several. The oldest and probably best known unsolved conjecture in number theory is the Goldbach conjecture. According to it every even integer greater than two can be expressed as the sum of two prime numbers.
Hypothesis
When you say "hartest", I assume you mean "hardest". There are a total of 7 Millenium problems, which one of them has been solved by Gregori Perelman. These problems are so intense that, whoever gives a correct answer (or proof) will be awarded 1 million USD. The topics are: P versus NP The Hodge Conjecture Yang-Mills Theory The Poincare Conjecture Riemman Hypothesis Navier-Stokes Birch and Swinnerton-Dyer Conjecture
The future tense of "conjecture" is "will conjecture."
Because mathematics is a axiomatic system so that every new statement remains a conjecture until it is proved.
Perhaps you mean "conjectural" which means based on supposition, conjecture, or just plain guesswork.
famous ones include the classification of finite simple groups, the poincare conjecture, fermat's last theorem
What does length mean in math