What is this millennium Problems?
Millennium problems in physics are the questions that put forward by the scientist which is not have been proved yet by any body till date. It is the Million Dollars question I can say. Why it is a Million Dollars because after the scientists left behind these unproved questions from various background of studying in Mathematical Physics, then Clay Mathematics Institute (CMI) collects these problems and set it to be a Million Dollars question as a package of Prize USD $1,000,000.
Any brilliant mind from all arround the world who can take a step of solving these question and give a perfect proof for the solution then he will be gaining a One Million Dollars ($ 1 million) Prizes.
This is really a big Prizes is not it?
Just consider you are staying at your laboratory doing research and trying to find the solutions of the problems, if you are more brilliant enough and luckily you unlock one of these question and I’m really sure you will become a millionaire without doing any contesting competition. Can you imagine it’s really such a big Prize of money isn’t it !! By the way you must try it once it might be a very interesting work for you right !!!
List of millennium Problems:
1. Yang–Mills and Mass Gap
Experiment and computer simulations suggest the existence of a “mass gap” in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known.
2. Riemann Hypothesis
The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann’s 1859 paper, it asserts that all the ‘non-obvious’ zeros of the zeta function are complex numbers with real part 1/2.
3. P vs NP Problem
If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily find a solution.
4. Navier–Stokes Equation
This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
5. Hodge Conjecture
The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown.
6. Poincaré Conjecture
In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston’s geometrization conjecture. Perelman’s proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries. It is already confirmed and proved by Grigori Perelman on the years of 2006, but he ignore the Prize.
7. Birch and Swinnerton-Dyer Conjecture
Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles’ proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three.
Among all these, hope you can do one from this list. The good news to say that Poincaré’s conjecture as I already mentioned above that it has been proved by the Russian Brilliant minded Grigori Perelman on the year 2006 it was confirmed that the problem has the solution existing which was accepted by many Mathematicians and Physicists of the world.