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.
Earlier this year, Davis gave a lecture to the mathematics department at USC titled “How Do We Know When a Problem Is Solved?” Often, he told the audience, we cannot tell, for “the formulation and solution of problems change throughout history, throughout our own lifetimes, and even through our rereadings of texts.”
Part of the difficulty resides in the notion of what we mean by a solution, or as Davis put it: “What kind of answer will you accept?” — Margaret Wertheim —Definitional Drift: Math Goes Postmodern (LA Times)
Interesting… the author saved “Dare we say it: Math is becoming postmodern” for the very end of her essay, but the headline writer gave it all away up front. Because I went into this article expecting to read about mathematics as a postmodern phenomenon, I was disappointed to find that claim only hinted at, not fully supported.
This isn’t a criticism of the essay, but rather an observation of the different rhetorics of newspaper headlines (which are designed to grab the reader) and the classical essay (which is designed to build slowly to a conclusion that rewards the committed reader).