Diagrams and Mathematical Practice

Organizers: Jean-Yves Beziau, Rio de Janeiro, Brazil (jyb.unilog@gmail.com) and Andrei Rodin, Nancy, France (andrei.rodin@univ-lorraine.fr)

Jean-Yves Beziau is a Swiss Logician, Philosopher and Mathematician, PhD in mathematics and PhD in Philosophy. He has been living and working in different places: France, Brazil, Poland, Corsica, California (UCLA, Stanford, UCSD), Switzerland. He is currently Professor at the University of Brazil in Rio de Janeiro, former Director of Graduate Studies in Philosophy and former President of the Brazilian Academy of Philosophy. He is the creator of the World Logic Day, yearly celebrated on January 14 (UNESCO international days), the World Logic Prizes Contest, the founder and Editor-in-Chief of the journal Logica Universalis  and South American Journal of Logic, the book series Logic PhDs,  Studies in Universal Logic and area logic editor of the Internet Encyclopedia of Philosophy.   He has published about 200 research papers and 30 edited books and Special Issues of Journals.

Andrei Rodin is a lecturer in Poincaré Archives, University of Lorraine (France) working in the history and philosophy of mathematics and philosophical logic. He is the author of Axiomatic Method and Category Theory (Springer 2014) and a number of articles. Andrei Rodin’s Ph.D. thesis (1995) is on the axiomatic and conceptual structure of the first four Books of Euclid’s Elements; in 2020 he defended the Habilitation thesis on The Axiomatic Structure of Scientific Theories.

Workshop description
Mathematical practice is classically articulated around three notions: definitions, axioms, and proofs. Blaise Pascal gave a short and clear masterful description of this articulation in his short booklet De l’esprit géométrique et de l’art de persuader (1657), giving some rules for these three notions. Later on, Alfred Tarski was strongly influenced by this booklet, as shown by his 1937 Paris talk “Sur la méthode deductive”. But, if nowadays if it is common to think of proofs with diagrams, in particular after the three volume book Proofs without Words (1993, 2000, 2015) by Roger B.Nelsen, the question of the uses of diagrams for stating and representing axioms and definitions has not yet been systematically studied. This workshop aims at promoting these uses (considering the interaction between the three notions).

Moreover, diagrams are convenient as illustration and source of inspiration, for conceptualization and understanding, also important features of mathematical practice.

This workshop is open to reflections on the functioning of diagrams as well as inquiries about the philosophy of mathematics,  the nature of reasoning and proving, through a diagrammatic methodology.

Keywords: Definition, Axiom, Proof, Postulate, Truth, Reasoning, Symbol, Category Theory, Model Theory, Proof Theory, Set Theory

Call for Participation
We call for abstracts about how diagrams can be used in mathematical practice as well as abstracts explaining how the use of diagrams in mathematics can enlighten the nature of mathematical practice. Sampling of questions and topics appropriate for this workshop includes but is not limited to:

  • Is a proof by diagrams of the same value as a formal proof without images?
  • Can we use diagrams for stating axioms and postulates?
  • How can we use diagrams for definitions?
  • What is the meaning and function of diagrams in category theory, model theory and proof theory?
  • What are the proper diagrams for set theory?
  • Diagrams for visual understanding, including the use of color, of mathematical notions
  • Diagrams, symbolization, and conceptualization
  • Diagrams and the ontology of mathematical objects
  • Diagrams in metamathematics

Abstracts should be between 300 and 500 words and should be submitted to diamapra2024@protonmail.com by May 15, 2024. Authors will receive notification of acceptance to the workshop before June 7, 2024, when registration for the main conference opens. Participants in the workshop must register for the full conference. 

A selection of submissions will be considered for publication in the Springer Nature book series Studies in Universal Logic.