analytically

Analytically is an adverb derived from analytical. It describes performing an activity through analysis, systematic reasoning, or the decomposition of a complex whole into its parts in order to understand, explain, or solve it.

Derivation and usage: from late Latin analyticus, from Greek analytikos, from ana- “up, again” and lysis “a loosening or breaking.” In practice, analytically modifies verbs and adjectives to indicate the manner of investigation rather than the result. Usage spans mathematics, science, philosophy, and data analysis. Examples include: “The equation can be solved analytically,” “The team approached the data analytically,” and “Analytically derived expressions are common in symbolic computation.” In philosophy and logic, analytically true or analytically valid describes truths true by analysis of concepts or meanings.

Relation to other methods: analytically contrasts with empirically (based on observation) and numerically (based on approximation using numbers). It is also related to analytical approaches within disciplines such as analytical philosophy and analytical chemistry, where emphasis is placed on reasoning, symbolic manipulation, and rigorous deduction rather than experimentation alone.

Limitations and scope: not all problems admit a closed-form analytic solution; some require numerical methods, simulations, or empirical data to obtain usable results. The term emphasizes a theoretical or deductive route rather than a purely experimental or approximate one, and in practice many fields combine analytic and empirical methods.

See also: analytic, analysis, analytical reasoning, analytic philosophy.