The chapter discusses the problem of hidden variables in quantum mechanics, a controversial topic that has persisted for four decades. While most physicists view the classical reinterpretation of quantum mechanics as unlikely or irrelevant, a minority continues to explore it. The paper aims to provide a proof of the nonexistence of hidden variables by establishing a precise necessary condition for their existence. This condition involves the algebraic structure of quantum mechanical observables, specifically the concept of a partial algebra. The authors show that a finite partial algebra of quantum mechanical observables cannot be embedded in a commutative algebra, which is a requirement for a classical reinterpretation. They also discuss the logical differences between quantum and classical logic, proving that there exists a classical tautology that is false for some meaningful substitutions of quantum mechanical propositions. The proof is compared with von Neumann's well-known proof, which is based on the non-existence of a real-valued function that can consistently assign probabilities to all possible outcomes of measurements.The chapter discusses the problem of hidden variables in quantum mechanics, a controversial topic that has persisted for four decades. While most physicists view the classical reinterpretation of quantum mechanics as unlikely or irrelevant, a minority continues to explore it. The paper aims to provide a proof of the nonexistence of hidden variables by establishing a precise necessary condition for their existence. This condition involves the algebraic structure of quantum mechanical observables, specifically the concept of a partial algebra. The authors show that a finite partial algebra of quantum mechanical observables cannot be embedded in a commutative algebra, which is a requirement for a classical reinterpretation. They also discuss the logical differences between quantum and classical logic, proving that there exists a classical tautology that is false for some meaningful substitutions of quantum mechanical propositions. The proof is compared with von Neumann's well-known proof, which is based on the non-existence of a real-valued function that can consistently assign probabilities to all possible outcomes of measurements.