The Calculus of AI Error Rates: Taylor’s Remainder Theorem and the Fallacy of Infinite Scaling By Sam C. Serey
The Calculus of AI Error Rates: Taylor’s Remainder Theorem and the Fallacy of Infinite Scaling By Sam C. Serey 1. Executive Framing: Mainstream Promises vs. Mathematical Reality As enterprise adoption of generative artificial intelligence accelerates across global sectors, corporate executive committees face a pivotal governance challenge. Senior leadership is routinely pressed to authorize multi-million-dollar capital allocations toward large-scale probabilistic models, driven by commercial vendor promises of impending zero-error reliability and human-level accuracy. However, making sound capital deployment and operational risk management decisions requires looking beyond marketing assertions and evaluating model reliability through the unyielding framework of continuous calculus. Evaluating AI error rates through foundational mathematics is a strategic imperative for organizations seeking to safeguard balance sheets and ensure long-term operational resilience. Commercial artificial i...