nonrigorous

Nonrigorous is an adjective used to describe reasoning, arguments, methods, or conclusions that do not meet the formal standards of rigor required by a field. In mathematics and related disciplines, rigor denotes precise statements with complete justification, leaving no logical gaps. Nonrigorous reasoning may rely on intuition, analogy, heuristic arguments, empirical evidence, or unstated assumptions.

In mathematics, nonrigorous arguments have historically preceded formal rigor; early calculus often used infinitesimals and manipulations that would not satisfy modern epsilon-delta criteria. Such approaches can lead to correct results but carry the risk of hidden gaps. In physics and engineering, nonrigorous models and approximations are common when exact solutions are intractable; they can provide useful predictions but are typically supplemented by experiments or later proof.

The term is often evaluative. Some contexts treat nonrigorous work as a preliminary stage toward rigor, while others view it as insufficient for publication as definitive mathematics. In rigorous communities, nonrigorous methods are scrutinized and gaps are closed; in applied settings, pragmatic success may be valued over formal proof.

Related concepts include heuristic, informal, and intuitive reasoning. While nonrigor can stimulate discovery and rapid progress, converting nonrigorous insight into rigorous justification remains a central goal in fields that prize formal correctness.