Back in 2000, the Clay Mathematics Institute in the US announced the Millennium Prize problems, a compilation of seven math problems that are unsolved. The institute had also kept a huge cash prize for anyone who solves them. These problems were selected by a scientific advisory board. According to the board, these equations have “resisted solutions for many years”. Needless to say, these problems are ridiculously hard and they have been chosen precisely for this reason. But this does not mean that these equations cannot be solved.
One of them, the Poincare Conjecture, was solved in 2006 by mathematician Grigori Perelman. However, there are still six others lying unsolved. Researchers and mathematicians are optimistic that someone will eventually solve the remaining equations and win the prize money. Cracking each problem can fetch you $1 million (Rs 7.4 crore). The only caveat is that the solution must be peer-reviewed and rigorous.
If you too are certifiable genius or see yourself as a bit of a maths whizz, you too can try your hand at these puzzles and could land with a million-dollar reward.
Let’s take a look at the six unsolved math equations that are worth the huge cash sum.
- The Navier-Stokes equations: This equation governs the flow of fluids such as water and air. While there is no proof of an equation for questions like “do solutions exist?” and “are they unique?”, mathematics and physicists believe that an explanation can be found for the turbulence in a modern jet if one understands the Navier-Stokes equations.
- Yang-Mills and Mass Gap: Many experiments and computer simulations in the past have suggested the existence of mass gap. Physicists discovered that even though the classic waves travel at light speed, the quantum particles do have positive masses. However, till now this property has not been understood from a theoretical point of view.
- The Riemann Hypothesis: This unsolved number equation implies results about the distribution of prime numbers.
- The Birch and Swinnerton-Dyer Conjecture: It is recognised as one of the most difficult mathematics problems to solve. It is related to number theory.
- The Hodge Conjecture: This problem is related to algebraic geometry that relates to algebraic topology of a non-singular complex algebraic variety.
- P vs NP: This equation is related to computer science and goes by the rule that if the solution to a problem is easy to check for correctness so the problem should be easy to solve. While P is a set of relatively easy problems and NP is a set of very hard equations, then P=NP would mean that hard problems will have relatively simple solutions.