Chasing after the Leibniz’s project that had for object to transcribe human languages in the form of a logical calculus, George Boole and Ernst Schröder proposed to analyze natural languages in using an algebraic notation. These first outlines gave rise to the emergence of formal linguistics. One century after, mathematical linguistics took shape in two ways. On one hand, Chomsky suggested different accounts of a formal syntax and, on the other hand, categorial grammars pursued the dream of an algebraic linguistics. Chomsky having himself contributed to destroy his approach, the 21th century can be characterized by the survival of the categorial perspective. The aim of this formal trend is to implement the syntax and the semantic of natural languages thanks to a universal algebraic notation. In this communication, I would like studying the current evolution of formal linguistics. More precisely, I’ll evaluate if formal contemporary linguistics is more « realistic » than the one of the last century. In order to do that, I ‘ll point out the different challenges and perspectives that formal linguistics has to take up (syntactical and semantical appropriateness of the algrebraic description, computational suitability, psychological relevance, …) and I’ll underline the original features of this approach that, because it is mainly elaborated by mathematiciens and computer scientists, prioritizes some empirical fatcs that linguistic descriptive theories describe easily.