7 Math Problems Worth 1 Million Dollars

There are many problems in this world that require a solution. One of them will be the "Millenium Prize Problems" which consists of 7 mathematical problems that were chosen by Clay Mathematical Institute in the year 2000.

What's more interesting is that the parties from the Clay Mathematics Institute have promised a handsome reward of $1 million for a solution to every mathematical problem that has been stated.

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For that, $7 million in prize money is being offered to those who are worthy of solving all 7 mathematical questions on a very high level. To this day only one of the problems of the "Millenium Prize Problems" has been solved which was related to the "Poincaré Conjecture".

Clay Mathematics Institute awarded the sum of money to the Russian mathematician, Grigori Perelman in 2010. However, Grigori refused to accept the gift as he stated that a similar prize was not offered to Richard S. Hamilton who also took part in finding the answers used by Grigori Perelman to solve the question related to Poincaré Conjecture.

6 other questions still remain unsolved to this day which comprise Birch and Swinnerton-Dyer Conjecture, Hodge Conjecture, Navier-Stokes Equation, P vs NP, Riemann Hypothesis, and Quantum Yang-Mills Theory.

1. Poincaré Conjecture

In topology and geometry mathematics, conjecture or Poincaré conjecture is a theorem related to the characterization of 3 spheres which is a hypersphere that exceeds the ball units in a 4-dimensional space.

Originally, the assumption was made by Henri Poincaré in 1904. The theorem explains space that looks similar to ordinary 3-dimensional space but is also finite to an extent. The attempts to solve this theorem have spurred the development of topology and geometry in the 20th century.

2. Birch and Swinnerton-Dyer Conjecture

For these past few years, many mathematician experts have studied specifically the elliptic curve which is defined by a particular diophantine linear equation. This curve has crucial application in the number theories and cryptography as well as finding an even number solution or rationale to those that are their main field.

Birch and Swinnerton-Dyer stated a particular type of equation that defines the ellipse curve to a rational number. The guess is that there is an easier way to identify whether the equation has several rational solutions that are finite or infinite.

3. Hodge Conjecture

In the 20th century, we have witnessed the advancement in techniques to understand curvatures, surface, and hypersurface which happens to be the subjects of algebra geometry. A far complicated shape to imagine can easily be shaped by using sophisticated calculation techniques.

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The Hedge Conjecture suggests that a particular geometry structure has a very useful algebra friend that can be used to study and classify the shape much easier.

4. Navier Stokes Equation

The Navier-Stokes equation is a fluid dynamic version of the three laws of Newton's movements. This equation explains how the flow of liquid or gas will expand in various conditions.

Similar to the second law of Newton which explains how the flow of an object can change under an external influence while the Navier-Stokes equation explains how the flow of fluid will change under an internal influence such as pressure, and viscosity as well as external influence like gravity.

5. P vs NP

The real question for this case will be whether it is similar or not. All problems that involve algorithms can verify the solution at a fast pace (which is noted as polynomial-P), and algorithms can also find the solution to the problems quickly.

Due to the first statement stating that the class problems are stated as NP, whereas the second explains P, the question will be whether all problems in NP are also in P. In general, this question is considered the most crucial open question in mathematics and computer science if the answer can be proven.

6. Riemann Hypothesis

In mathematics, the Riemann Hypothesis is an assumption made by the mathematician, Bernhard Riemann that stated that all zero for Riemann zeta functions that are not identified as being trivial with real part half. Therefore, the equation ζ(s) = 0 where s is -2, -4, -6,.... is considered trivial.

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The Riemann Hypothesis is a non-trivial zero for the analysis continuity of the Riemann zeta function with the real part half. The result of the Riemann Hypothesis is related to a bunch of prime numbers. The proof or rejection of this theory will have great implications for the number theories, especially for the distribution of prime numbers.

7. Quantum Yang-Mills Theory

In the quantum field theory, the mass gap is the difference in energy between a vacuum and the next lowest energy state. The vacuum energy is zero-based on the definition and by assuming that all forms of energy are in the form of particles in a plane wave. The mass gap will be the lightest mass particles.

The Quantum Yang-Mills theory is the current fundamental for many application theories from thinking to reality as well as the potential of the reality of basic particle physics. This theory is the generalization of the Maxwell electromagnetism theory whereby the chromo-electromagnet field itself carries charges.

Source:

• Wikipedia

• Business Insider

Also read: Top 7 Strongest Material On Earth