The objective of our research project is to gain a better and deeper understanding of the different types of gestures and diagrams and the functions they have in visual-spatial communication in both mathematics and logic. In particular, we aim (i) to investigate practices of visual-spatial communication in the field of mathematics and logic based on historical case studies on gestures and diagrams and (ii) to develop educational tools to enhance teaching practices in those disciplines. This research project seeks to fill research gaps at the intersection of philosophical reflection and doing mathematics and logic.