We focus on the role of diagramming and gesturing in mathematical practice. In most discussions of diagramming in mathematics, including mathematics education research, diagrams are seen as representations of mathematical objects and relations. This view was challenged by the philosopher and historian of mathematics, Gilles Châtelet, who argued that diagramming is a material practice of mathematical invention. His arguments are based on analyses of historical examples of diagrams associated with new mathematical ideas. Guided by his approach, we study the actual diagramming practices of mathematicians, as they work on unsolved problems. By doing so, we aim to identify the various roles that diagrams might play in mathematical invention as well as the material nature of diagramming practice. We hope that a more nuanced understanding of diagramming within mathematical practice will contribute to research on promoting and supporting student diagramming.