Deconstructivist Mathematics
Rem (Simuli, Inc.)
Abstract: I work as a mathematical developer and are currently interested in fully relational models of computations.
In this talk, we will explore the relationship between mathematical intuition and formal rigor, delving into the philosophical and structural foundations of mathematics. The main aim is to examine the process of formalizing mathematical intuitions, highlighting how this process can itself be formalized within a mathematical framework. The layers of abstraction offered by Category Theory mirror the progression from computational to conceptual reasoning. We start from apparent dichotomies appearing in diverse fields of knowledge, such as axiomatic versus structural foundations of mathematics. We then go over the impact and implications of the crisis of foundations, the role of circularity in mathematical reasoning, and the importance of fostering alternative approaches to learning and teaching mathematics. Through allegories, metaphors, and analogies, we illustrate how mathematical concepts can be represented and understood in different contexts, emphasizing the interconnectedness of mathematical ideas. We conclude by advocating for a holistic view of mathematics, one that transcends traditional dichotomies and embraces the dynamic, evolving nature of mathematical thought.
This talk is aimed at both mathematicians and philosophers, offering a deep dive into the structural and philosophical underpinnings of mathematics, while also providing practical insights into the development and teaching of mathematical concepts.
Moderator: The talk will be moderated by Nathan Haydon. Nathan is a philosopher working on methods of reasoning in logic and science. Much of his work is inspired by Charles S. Peirce, including Peirce’s pragmatism and Peirce’s formal developments in diagrammatic logic. Along these lines, Nathan has most recently been working on the logic of string diagrams. Finally, Nathan is also interested in the broader ethical and meta-ethical positions that follow from scientific reasoning.
artificial intelligencecategory theory
Audience: researchers in the topic
Series comments: The name "Relatorium" combines "relator" with the Latin root "-ium," meaning "a place for activities" (as in "auditorium" or "gymnasium"). This seminar series is a platform to relate ideas, interact with math, and connect with each other.
In this series, we explore math beyond what we usually hear in standard talks. These sessions fall somewhere between a technical talk and a podcast: moderately formal, yet conversational. The philosophy behind the series is that math is best learned by active participation rather than passive listening. Our aim is to “engage and involve,” inviting everyone to think actively with the speaker. The concepts are accessible, exploratory, and intended to spark questions and discussions.
The idea of relatability has strong ties to compassion — creating space for shared understanding and exploration - which is the spirit of this seminar! This is a pilot project, so we’re here to improvise, learn, and evolve as we go!
| Organizers: | Priyaa Varshinee*, Tim Hosgood*, Niels Voorneveld |
| *contact for this listing |