Formalteadused

Formalteadused, or formal sciences, refer to disciplines that study abstract structures and the rules for manipulating symbols rather than the natural world directly. They emphasize deduction, proof, modeling, and computation, with knowledge gained through rigorous reasoning and formal systems.

The core fields typically regarded as formal sciences include mathematics, logic, statistics, and theoretical computer science. Mathematics concerns the study of numbers, sets, functions, and shapes using axioms and proofs to establish truth. Logic analyzes the principles of valid inference and the structure of arguments, including proof theory, model theory, and foundational studies. Theoretical computer science examines algorithms, complexity, automata, formal languages, and computational models to understand what can be computed and how efficiently. Statistics provides the mathematical theory of uncertainty, probability, inference, and data modeling, often bridging theory with practical data analysis.

Formal sciences differ from empirical sciences in that they do not depend primarily on observation of the physical world; instead, they build and test models within formal systems. These disciplines underpin many areas of science and technology, offering foundations for software verification, cryptography, data analysis, and mathematical Modeling in the sciences.

Historically, formal sciences have developed through the refinement of axioms, logical principles, and abstract reasoning, with influential contributions from figures in logic, mathematics, and computer science. Today they remain essential for proving theorems, designing reliable algorithms, and formalizing theories across disciplines.