Phenomenology of Mathematical Understanding
We present the results of a phenomenological methodology that allowed for the investigation of the experience of understanding an abstract mathematical object as effectively lived by active mathematicians. Our method of analysis reveals the essential structure of such a phenomenon and, as a consequence, permits us to address the conditions of possibility for the occurrence of this particular phenomenon. We show that the different modalities of the experience of understanding an abstract mathematical object, as unearthed by the elucidation of the three phenomenological classes (parts and wholes, identity in a manifold, and presences and absences) reflect -- in addition to well-expected mathematical functional aspects -- what we call an embodiment of abstraction.
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