The Suppression of Nondual Mathematics: A Tragedy in Three Acts, Newcomb Greenleaf

Today’s mathematical orthodoxy is profoundly dual, visioning a timeless world of absolute truth, a world separate from our contingent, temporal lives. This “Platonist” view has ancient roots, but did not become mathematical orthodoxy until the Set Theory created by the German mathematician Georg Cantor was adopted as a “foundation” for all of math, over the period 1880 to 1900. There have been two significant challenges to this Platonist hegemony: first by the Dutch mathematician L. E. J. Brouwer from 1915 to 1930, and later by the American Errett Bishop from 1966 to 1973. Before exploring this history, we must ask how nondual math is different, and why non-mathematicians should care. How does nondual math shed a new light on such concepts as “existence”, “equality”, “truth”, and “infinity”? Nondual math by its human focus is naturally hospitable to ethnomathematics, and naturally sensitive to racism and sexism in math classrooms. We use our first two acts—Cantor’s sets and Brouwer’s logic—to provide context for an extended look at Bishop’s heroic, ill-fated, seven-year campaign for mathematics to embrace its nondual, constructed nature, a movement I saw from the inside. We will look closely at the methods of suppression, which were systemic rather than organized, and which achieved extreme marginalization rather than extermination. Why is nonduality so difficult for mathematicians to understand? Personally, I doubt that I would have replaced my Platonist faith and achieved a nondual vision without sustained mentoring from a good friend who was close to Bishop. As a student I had received a thorough indoctrination into Platonism, along with a belief that Brouwer had gone crazy. I note that even today, decades after Bishop showed that nondual math worked, math students are never given the choice of thinking nondually.

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