If you are good at math and you are great for solving complex problems, you should consider giving these problems a shot. Not only will you be challenged mathematically, but you also put yourself at the top chance to win a million dollars for every problem you solve. These problems are called millennium problems, and they were originally 7 in total. However, only six remain to be solved currently. Here are the seven problems:
- Yang-Mills and Mass Gap
- Riemann Hypothesis
- P NP Problem
- Navier-Stokes Equation
- Poincare Conjecture – Solved
- Hodge Conjecture
- Birch and Swinnerton-Dyer Conjecture
The Poincare Conjecture
A Russian Mathematics genius called Grigori Perelman solved the Poincare Conjecture in 2003. His solution was not recognized until three years later. When he was handed the $1 million for solving the problem and the Fields Medal, he turned both down saying that his contribution was insignificant compared to other geniuses. He used the Ricci Flow by Hamilton to solve the problem and felt that he could not rightfully accept the award for solving the problem as others were more deserving of the prize.
The Remaining Six Problems
The other remaining problems are still up for takes by anyone who is brave enough and smart enough to solve them. From quantum mechanics, prime numbers, polynomial time, fluid dynamics, geometric interpretations, and elliptic curves, the problems cover a vast area of physics and mathematics that is still in the dark. Out of the lot, the toughest to explain is the Hodge Conjecture.
Yang-Mills and Mass Gap
The problem revolves around quantum mechanics is one of the theories that have been very successful in history. The theory has helped us understand how energy and matter behave in the atomic and sub-atomic levels. The theory is very important in mathematical structures and elementary particles theory.
One of the main areas of interest for any mathematician is prime numbers, and this hypothesis describes just that. The theory suggests that the frequency of the prime numbers are related to a function called the Riemann Zeta function. It goes on to show that any value in an equation that answers zero is on the same line.
P vs. NP Problem
The problem exists in the world of computer sciences. The questions behind the problem are to check if the problem is easy to solve if the answer can be checked. Solving large numbers using the problem is said never to exist. However, mathematicians believe that the proof of such a problem does not exist which is why this problem is one of the most significant ones in the list that related to recent times.
Most of fluid dynamics use Navier-Stokes equations of fluid movement. The flow of weather, ocean currents, air, etc. are calculated using the equations. The understanding of the Navier-Stokes equations is still very limited. The possible solutions to many of the unused NS Equations are the award-winning problem that deserves the prize.
Being the toughest one to explain, the Hodge Conjecture is based on geometrical shapes. In simple terms, the problem asks if complex shapes can be built using simple shapes in math. The problem has encouraged several mathematicians to investigate the possibilities of the shapes. However, over time they needed to include shapes that have no geometric value to complex the complex shapes. These are called as Hodge Conjectures.
Birch and Swinnerton-Dyer Conjecture
Rational solutions to define the elliptic curve is what the Birch and Swinnerton-Dyer Conjecture is all about. It is a challenging problem that remains to be solved. The problem is that the conjecture has too many rational solutions and the one that is true should be identified.