Axiomatic Narrative and Relations:

Result: The dynamics of AI integration across various sectors can be formalized through a system of nonlinear differential equations: dA/dt = α(I) - β(H)A + γ(S) dH/dt = δ(A)H - ε(I) dS/dt = ζ(A) + η(H) - θ(I)S Where: A = level of AI automation H = specialized human skills S = human-machine synergy I = rate of technological innovation t = time α, β, γ, δ, ε, ζ, η, θ = coefficients representing the interactions between the variables This system describes the interdependent evolution of AI automation (A), human skills (H), and human-machine synergy (S) over time, influenced by the rate of innovation (I). The equation of A shows how automation grows with innovation but is moderated by human skills. H evolves based on its interaction with A and the decline due to innovation. S increases with A and H but is limited by innovation that requires continuous adaptation. This mathematical formalization captures the complexity of relationships observed in data, highlighting the positive feedback between technological development and practical applications, as well as the dynamic tension between automation and human specialization.