Indeterminate vs. Undetermined — What's the Difference?

Indeterminate often describes situations, values, or problems in mathematics and science where the exact nature or value cannot be ascertained due to the problem's inherent complexity or limitations in the current understanding or methods. For example, an indeterminate form in calculus, like 0/0, arises not because the answer is unknown, but because it does not have a unique value. On the other hand, undetermined is used in contexts where a decision, conclusion, or resolution has not been reached, often due to a lack of effort, information, or necessity up to that point, rather than the inherent nature of the issue itself.

The term indeterminate is frequently used in the context of indeterminate forms in calculus, indeterminate equations in algebra, and indeterminate probabilities in statistics, highlighting scenarios where traditional mathematical operations or evaluations yield ambiguous or undefined results. Whereas, undetermined is more broadly applicable across various fields, indicating situations, outcomes, or quantities that have not been decided, discovered, or specified, such as undetermined causes of an event, undetermined variables in an experiment, or undetermined outcomes in a study.

In mathematics, indeterminate structures or problems challenge solvers to find innovative approaches or interpretations due to the nature of the problem itself being open to multiple valid solutions or interpretations. Conversely, undetermined elements in mathematical or scientific research often signify areas awaiting further investigation or decision-making, implying that additional data, analysis, or decision-making could resolve the ambiguity or uncertainty.

The distinction between indeterminate and undetermined also reflects the nature of inquiry or investigation into the unknown. Indeterminate problems or situations might require redefining the problem, developing new methodologies, or accepting multiple potential truths, indicating a qualitative aspect of uncertainty. In contrast, undetermined issues are typically resolved through the acquisition of more information, making decisions, or establishing consensus, highlighting a quantitative or procedural gap rather than a conceptual or foundational one.

Addressing indeterminate issues often necessitates a paradigm shift or a conceptual breakthrough because the uncertainty is rooted in the problem's nature. Meanwhile, resolving undetermined issues generally involves gathering more evidence, making choices, or applying existing knowledge, indicating that the uncertainty is procedural and, in principle, resolvable with additional information or effort.