
Celebrated mathematician Stewart explains why mathematical problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole.Great problems --Prime territory : Goldbach Conjecture --The puzzle of pi : squaring the circle --Mapmaking mysteries : Four Color theorem --Sphereful symmetry : Kepler Conjecture --New solutions for old : Mordell Conjecture --Inadequate margins : Fermat's Last Theorem --Orbital chaos : Three-body problem --Patterns in prime : Riemann Hypothesis --What shape is a sphere? : Poincaré Conjecture --They can't all be easy : P/NP problem --Fluid thinking : Navier-Stokes Equation --Quantum conundrum : Mass Gap Hypothesis --Diophantine dreams : Birch-Swinnerton-Dyer Conjecture --Complex cycles : Hodge Conjecture --Where next? --Twelve for the future.