In popular conception, mathematics is the ultimate resolvable discipline, immune to the epistemological murkiness that so bedevils other fields of knowledge in this relativistic age. Yet Philip Davis, emeritus professor of mathematics at Brown University, has pointed out recently that mathematics also is "a multi-semiotic enterprise" prone to ambiguity and definitional drift.
Yacht designers must also wrestle with these legendarily difficult equations. Over lunch, Davis told a story about yacht racing. He had recently talked to an applied mathematician who helped design a yacht that won the America's Cup. This yachtsman couldn't have cared less if the Navier-Stokes equations were solved; what mattered to him was that, practically speaking, he could model the equations on his computer and predict how water would flow around his hull. "Proofs," said Davis, "are just one of the tools that mathematicians now use."
We may never fully solve the Navier-Stokes equations, but according to Davis it will not matter. Like so many other fields, mathematics is becoming less about some Platonic ideal of ultimate answers, and more a functional project of computational simulation and communal negotiation. Dare we say it: Math is becoming postmodern.