The Epistemology of Mathematics: The Identity M = P + N

This essay proposes a radical revision of the nature of mathematical knowledge based on the triune identity M = P + N, where Mathematics appears not as a Platonic realm of ideal entities but as an emergent product of the synergy between Physics (primarily gravity as the universal structuring interaction) and Neurophysiology (the embodied biological processor that evolved to navigate this physical reality). The genesis of key mathematical concepts — number, the straight line, the limit, the logical law of identity — is traced back to sensorimotor and vestibular experience. Consequences are formulated for the foundations of mathematics, the philosophy of mind, and teaching methodology, and a program is outlined for building “Embodied Mathematics” as a synthetic discipline that erases the boundaries between pure and applied knowledge. Topology is reinterpreted as the mathematics of contact and containment — a formalization of basic, pre‑logical spatial intuitions born from bodily interaction with the physical world.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-26
DOI
https://doi.org/10.5281/zenodo.20900665
Primary Topic
Embodied and Extended Cognition
Type
article
Field-Weighted Citation Impact
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article

The Epistemology of Mathematics: The Identity M = P + N

Alexey (KAMAZ) Petrov
Zenodo (CERN European Organization for Nuclear Research)
Embodied and Extended Cognition
article

The Epistemology of Mathematics: The Identity M = P + N

Alexey (KAMAZ) Petrov
article en

Abstract

This essay proposes a radical revision of the nature of mathematical knowledge based on the triune identity M = P + N, where Mathematics appears not as a Platonic realm of ideal entities but as an emergent product of the synergy between Physics (primarily gravity as the universal structuring interaction) and Neurophysiology (the embodied biological processor that evolved to navigate this physical reality). The genesis of key mathematical concepts — number, the straight line, the limit, the logical law of identity — is traced back to sensorimotor and vestibular experience. Consequences are formulated for the foundations of mathematics, the philosophy of mind, and teaching methodology, and a program is outlined for building “Embodied Mathematics” as a synthetic discipline that erases the boundaries between pure and applied knowledge. Topology is reinterpreted as the mathematics of contact and containment — a formalization of basic, pre‑logical spatial intuitions born from bodily interaction with the physical world.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 6%
Embodied and Extended Cognition
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