- Birch and Swinnerton-Dyer Conjecture
- Hodge Conjecture
- Navier-Strokes Equations
- P vs NP
- Poincare Conjecture (seems to have already been solved)
- Riemann Hypothesis
- Yang-Mills Theory
Its a pretty good book- the math and mathematicians are spot-on. Its a good airplane book, say the kind of book you can read on the airplane on your way to Conf on Computational Complexity 2008.