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date: 09 December 2019

Abstract and Keywords

The extent to which practicing mathematicians of a conventional tendency are already intuitionists is reassuring. Today's mathematicians treat mathematical claims much as Brouwer once did: as independently meaningful efforts to record mathematical facts which are, when true, demonstrable from proofs rooted in basic assumptions or principles. Until they are proven, those assumptions rest upon intuitions: illuminating, at times fallible, insights into the dynamical behaviors of numbers, sets, functions, and operations on them.

Keywords: intuitionism, Brouwer, mathematical claims, mathematics, mathematical facts, intuitions, numbers

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