We've computationally verified that Peano arithmetic emerges naturally from just two operators: Δ (distinction/branching) and Σ (connection/composition).

This isn't just coding — it's evidence for the Δ–Σ Turing Completeness Theorem: a system is Turing-complete iff it can be represented through Δ and Σ.

Code implements the proofs: https://github.com/muskin88/delta-sigma-peano/blob/main/Peano_from_deltasigma.py
Formal statement: https://zenodo.org/records/17895986
(Theorem 3)

The implications are ontological: these operators appear inevitable for any non-trivial reality. The framework unites computation, mathematics, and fundamental ontology.

#CategoryTheory #FoundationsOfMath #Computation #Ontology #FormalMethods #TypeTheory #PeanoArithmetic #TuringCompleteness #MathematicalPhilosophy

Tenure-track opening @ U. Colorado Boulder Dept. of Math!

Esp. (but not only) looking for:
algebraic geometry
homotopy theory
foundations
functional analysis
number theory
interdisciplinary collab. b/w math & computer science or the math of quantum physics

https://www.mathjobs.org/jobs/list/27231

Please help spread the word!

#AlgebraicGeometry #HomotopyTheory #AlgebraicTopology #FoundationsOfMath #FunctionalAnalysis #NumberTheory #ComputerScience #Quantum #Math