answer:There are the Clay Institute Millennium Prize problems, with a cool $1M prize for solving. Of the 7 problems, 6 remain unsolved. (The Poincare conjecture was proved by Grigori Perelman, who refused the prize in 2010 and also refused the Fields Medal awarded in 2006.) 1 P versus NP 2 The Hodge conjecture 3 The Poincaré conjecture (proven) 4 The Riemann hypothesis 5 Yang–Mills existence and mass gap 6 Navier–Stokes existence and smoothness 7 The Birch and Swinnerton-Dyer conjecture Although I’m a fan of mathematics, I have only a dim notion of what some of these are about, and of others I am clueless. #1 is related to computer science, while 5 & 6 are related to physics. The others are “pure math” with seemingly no real-world applications, though history shows that these sometimes later turn up at the core of new physical theory.