We are happy to announce that DIAGRAMS’26 will have three keynote speakers.
Fabio Zanasi
Keynote title: Computing with Pictures: the Rise of String Diagrams in Computer Science
For abstract, click here.
Jessica Carter
Keynote title: Diagrams in mathematical practice
For abstract, click here.
Peter Cheng
Keynote title: Representing Knowledge and Thought
For abstract, click here.
Computing with Pictures: the Rise of String Diagrams in Computer Science — Abstract
Computer science was born from mathematical logic, and for almost a century logical formalisms have been the chief notation for studying computational models. These languages are textual and one-dimensional, much like the logical calculi they descend from. Since the 2000s, a different style of reasoning has emerged, based on string diagrams: a two-dimensional, graphical formal language for compositional systems. Once a ‘private’ notation used by category theorists, string diagrams are now widely adopted across fields as diverse as quantum theory, program semantics, electrical circuits, computational chemistry, machine learning, and statistics. Their chief advantage over textual notations is that they make resources explicit: the diagram itself tracks how information is shared, copied, or discarded — as happens with quantum entanglement, concurrent processes, or correlated random variables. In this talk I will survey the theory and applications of string diagrams in contemporary computer science — a development that, a century after mainstream logic chose Frege’s notation over Peirce’s diagrams, gives the diagrammatic side of that old debate its due.
Diagrams in mathematical practice — Abstract
Discussions about diagrams in mathematics most often focus on their role in proofs, reasoning, and establishing the validity of arguments. Yet, beyond mathematical reasoning, diagrams play a range of other roles in everyday mathematical practice. They serve as tools for discovery and computation, and they contribute to understanding – in other words, they have multiple heuristic functions. These latter roles of diagrams will be the focus of my talk. In his influential article On Proof and Progress in Mathematics, the geometer Thurston quickly dismisses the claim that progress in mathematics is accomplished by an accumulation of proofs. Instead, he finds it more interesting to discuss how mathematical understanding is attained. As he puts it, ‘what we are doing is finding ways for people to understand and think about mathematics’. I posit that signs, and diagrams in particular, play a central role in facilitating such understanding. This claim rests on the observation that human cognition is limited, and that what we are able to grasp or perceive depends, in part, on how information is presented. To illustrate this point, I will present cases in which a visual re-presentation of a concept or problem has led to the introduction of new mathematical concepts or proofs. This raises the question of what it is about visual presentations that make this possible. To address this question, I consider in part the notion of a ‘free ride’ and the corresponding theoretical framework developed by Shimojima (1996, 2015). I argue that some mathematical examples conform to this framework. However, mathematical developments can also exceed it, since visual representations may generate entirely new concepts and domains that extend beyond the original target domain. If time permits, I will briefly display other functions of diagrams, including their use as computational tools, and point to the properties that enable them to serve this function.
Representing Knowledge and Thought — Abstract
Five claims will be examined. (1) Existing notational systems are a (or perhaps the) critical barrier to comprehension and learning in many STEM topics. (2) Understanding knowledge-rich topics can be substantially improved by adopting effective diagrammatic representational systems—potentially by a factor of two. (3) Effective representational systems must coherently integrate essential epistemic, representational, and cognitive functions. (4) To naturally deliver these functions, a representational system’s encoding of the fundamental conceptual structure of its target topic must be semantically transparent. (5) Such representational systems can be systematically designed to substantially improve problem-solving and instruction in STEM topics. To substantiate these claims, a dozen studies will be surveyed that contrast novel diagrammatic systems with conventional notations for the same knowledge-rich topics. Some of the diagrammatic systems are historical, but most were specifically invented to investigate the five claims.