This project aims to uncover and clarify phylogenetic relationships between native South American languages. Very little is known about the historical development of the linguistic diversity in this part of the world, and more detailed insights will have a major impact not only on linguistics, but also on genetics, archeology, and cultural anthropology. The approach taken is to digitize available lexical information about the languages in question, and to develop new and innovative computer-assisted methods to quantify the analysis of this information. This quantification will be based on the techniques and experiences of the traditional historical-comparative method, and not use the Swadesh-style approach using wordlists. This novel quantitative approach makes it possible to process more data in a more consistent and faster manner, and as a consequence uncover more evidence for genealogical relations. The availability of more evidence is essential to push back the phylogenetic time-depth beyond the few thousand years to which historical linguistics is traditionally limited. A second key objective of this project is to transform historical-comparative linguistics from a primarily handcrafted scholarly endeavor, performed by individual researchers, into a quantitative and collaborative field of research, involving linguists, mathematicians and computer scientists alike. The project will build a truly interdisciplinary team to improve the interaction between linguistics and mathematics. In this way, not just historical linguistics will profit from methods and insights previously developed in mathematics and computer science, but the special requirements posed by language variation and language change will also reframe and further extend current phylogenetic methods.