Many people find math tough and its common to see students struggle to get good or even pass marks in exams. On the other hand, students who excel in math usually do better in their job or profession. Math is certainly not easy, as even the best mathematicians have not been able to solve all the known mathematical problems.
While there are numerous unsolved mathematical problems, there are the ones that are covered under the Millenium Prize Problems category. These are highly complex and remain unsolved till date. The Clay Mathematics Institute has pledged US$1 million to anyone who can solve these mathematical riddles. Out of the original 7 problems, six are yet to be solved. If you are confident about your mathematical abilities, here are 6 of the world’s toughest mathematical problems you can attempt to solve.
Birch and Swinnerton-Dyer conjecture – This mathematical riddle relates to the equations that could be used to define an elliptic curve. It is titled as such based on the names of mathematicians Bryan John Birch and Peter Swinnerton-Dyer. The duo had first developed the conjecture for this problem in 1960s. The problem is classified under number theory and till date, only a few special cases have been proven.
Hodge conjecture – This riddle is named after Scottish mathematician William Vallance Douglas Hodge, who had worked on the conjecture during 1930 to 1940. It comes under algebraic geometry and complex geometry. It essentially relates to the assertion that basic topological information of specific geometric spaces and complex algebraic varieties will be possible to unravel by analyzing the shapes sitting inside those spaces.
Navier–Stokes existence and smoothness – This mathematical puzzle relates to the mathematical characteristics of solutions provided to the Navier–Stokes equations. The latter is a collection of partial differential equations that are used to describe the motion of fluid in space. Solutions suggested till date end up including turbulence, which is the essence of the Navier–Stokes existence and smoothness problem.
P versus NP problem – Termed informally, the P versus NP problem is essentially asking the question if solutions that can be verified quickly can also be solved quickly. Here P refers to polynomial time whereas NP refers to nondeterministic polynomial time. It is estimated that the solution, if found, will result in significant advancements in the field of game theory, artificial intelligence, algorithm research, cryptography and economics.
Riemann hypothesis – Named after German mathematician Bernhard Riemann, the Riemann hypothesis asserts that the Riemann zeta function has the zeroes at only the negative even integers. Also, the zeroes are at the complex numbers with real part 1/2. Riemann hypothesis comes under number theory and has an important role to play in distribution of prime numbers.
Yang–Mills existence and mass gap – This is a non-abelian quantum field theory, which is considered similar to the Standard Model of particle physics. Solvers need to prove that the Yang–Mills theory exists. Also, that it should be in accordance to the rules of constructive quantum field theory. It also needs to be proven that mass of all particles that are part of the predicted force field are strictly positive.