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『素粒子論のランドスケープ』などを見ていると、21世紀の数学のキーワードは、dualityかなと

http://en.wikipedia.org/wiki/Duality
Duality (mathematics), a mathematical concept Dual (category theory), a formalization of mathematical duality
Duality (order theory), a concept regarding binary relations
Duality (projective geometry), general principle of projective geometry
S-duality (homotopy theory)
Duality (optimization)

List of dualities (Mathematics)
http://en.wikipedia.org/wiki/List_of_dualities#Mathematics