LLMs have been studied in recent linguistics as potential models of humans' linguistic abilities. Here we discuss an entirely different use of AI, namely as a co-scientist, to help construct and assess linguistic theories (we refer to the result as "Co-Linguistics"). Since the 1960s, linguistics has developed theories that are in principle mathematically formalizable, often in the language of formal language theory or model theory. The AI revolution in mathematics will thus have consequences in linguistics-but with an essential twist: proving new theorems is rarely the linguist's goal. Rather, one seeks to find the best set of axioms to derive empirical statements. AI could accelerate research by making existing theories fully explicit, by comparing competing theories, and more ambitiously, by proposing new theories (in machine learning, this relates to "program induction"). It will also help assess theories by accelerating the identification and test of crucial predictions, thanks to unparalleled access to data (in machine learning, this relates to "active learning"). While the cycle from theory evaluation to theory construction may give rise to recursive and possibly autonomous improvement of linguistic theories, humans remain central: linguists provide scientific directions and evaluate theories conceptually, and experimental participants are needed to assess empirical predictions that are outside the reach of LLMs.