$1 Million Millennium Problem #7
The Hodge Conjecture
The final Millennium #7 is another "missing piece" problem from topology. The Hodge conjecture deals with the technicalities of how mathematicians classify certain kinds of abstract objects called projective algebraic varieties into combinations of geometric pieces called algebraic order. Devlin describes it as "the one the layperson will have the most trouble understanding."
See Keith Devlin's The Millennium Problems: The Seven Greatest Unsolved Puzzles of Our Time, Basic Books, 2002.