According to many, mathematical aptitude is an outcome of hard work and practice. You may have heard your teachers say : "Just try hard, and there is no problem on the earth that can not be solved." But the statement is far from reality. There are several problems in mathematics and physics that have puzzled the greatest of the mathematicians since centuries, and still continue to do so. Clay mathematics institute stated some such problems way back in 2000 and declare a prize of one million dollars to the one who correctly solves any one of the problem. Following the list of problems:
The "P vs NP" problem- a famous problem of computer science, proposed by Stephen Cook.
Hodge conjecture - a problem of algebra.
Poincare conjecture- a problem of topology. (proved by Grigori Yakovlevich Perelmann)
The Riemann Hypothesis (my favorite!!) - A proof or disproof of this would have far reaching implications in number theory, especially in distribution of prime numbers.
Yang-Mills existence and mass gap - A problem of electromagnetism
Navier-Stokes existence and smoothness- These equations describe the motion of fluids but still lack a rigorous mathematical version.
The Birch and Swinnerton-Dyer conjecture- A problem dealing with certain equations defining elliptical curves over rational numbers.
A more detailed discussion on the topic is welcome....!!!!