How Mathematics Sparked the Rise of Modern Linguistics and NLP

French mathematician J. Hadamard famously called linguistics a bridge between mathematics and the humanities, anticipating the discipline’s mathematical turn. In the mid‑19th century scholars such as V. Bulyakovsky proposed probabilistic approaches to grammar, while Saussure (1894) argued that linguistic quantities could be expressed by regular formulas, and later works by Baudouin de Courtenay and L. Bloomfield reinforced the view that mathematics could elevate linguistic study.

After the first electronic computer appeared in 1946, researchers began assigning tasks like translation, summarization, and document retrieval to machines, prompting the development of mathematical language models, formal syntax and semantics, and the construction of linguistic databases suitable for computational processing.

The surge in machine translation and automatic information retrieval spurred morphological research, where discrete mathematics—especially finite‑automaton theory—was employed to design models for word segmentation. Soviet mathematician O. Kulagina applied set‑theoretic methods to define linguistic concepts, providing the theoretical basis for early French‑Russian machine translation systems.

Overall, the advent of computers acted as a catalyst, integrating mathematics into morphology, syntax, lexicology, semantics, and other linguistic subfields, giving rise to mathematical linguistics. This interdisciplinary blend links language to statistics, information theory, set theory, recursion, graph theory, fuzzy mathematics, and formal logic, underscoring the modern scientific character of linguistics.

Source: Shen Wenxuan & Yang Qingtiao, "Mathematical Modeling Attempts".