I only just realized that Andras Kornai published the book "Mathematical Linguistics" in 2008. I am currently reading it and it is sparking my mind in a number of areas. I highly recommend it, it is a broad view of linguistics from a mathematical perspective.
In this blog I would like to highlight each chapter in turn. We don't get great books to study very often in this field. The first chapter is introductory, but it makes clear the author's rather unique view of things. The most interesting idea put forth there is that mathematical linguistics, viewed as a mathematical theory, is astoundingly complex, and encompasses far more axioms than is typical of well-studied areas of mathematics. This brings Kornai to the analogy with physics, and the idea that mathematical linguistics lies in a "mesoscopic" regime between the microscopic (which can be fully specified and axiomatized) and the macroscopic (which would presumably by typified in mathematics by nonlinear systems that can be chaotic and are impossible to specify axiomatically).