AI and the End of Math As We Know It

AI is looming large over all aspects of our lives, and this is especially true when it comes to large language models. Their promise is to make our work easier, and to multiply the impact our efforts have a thousandfold. Yet, there is also an implied threat that they can replace humans altogether and make most of us redundant. When it comes to mathematics, both the promise and the threat seem to be more pronounced than in any other field. After all, math education and research have a long history of leveraging technology to great effect. At the same time, a field based on structure and logic is a prime candidate for AI to subsume.

In this presentation, we will investigate the potential and likely implications of the emergence of AI on mathematics. We will explore what AIs are good at, what they might become better at, and what their relationship with humans in the world of mathematics might ultimately turn out to be. We’ll discuss the implications on teaching, learning, doing, and leveraging mathematics, and what math tools could look like in a world where AI is ubiquitous.

Experimental Mathematics: Using Maple to Analyse Some Conjectures Involving Matrices and Polynomials

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An Integral View on Dimensional Analysis: Scaling Invariants for Parameter Reductions in Dynamical Systems

Dimensional analysis, also known as parameter reduction, is a recommended practice before analyzing a dynamical system, such as a physical system or biological model. The Buckingham Pi Theorem shows how linear algebra can be used to bring out dimensionless variables, as power products of the original variables, which simplifies the analysis. One issue that arises, however, is that the powers provided by the Pi Theorem can be fractional, resulting in roots, and thus they require some care when determining the regions of positivity of the variables.

In this talk, I will present an algorithm involving scaling invariants that performs a similar transformation into dimensionless variables, but the results only involve integer powers and so are much easier to work with. I will also provide a simple rewriting algorithm, in the form of substitutions, that can be used to find the induced equations in the dimensionless variables.

This talk is based on: E. Hubert & G. Labahn. Scaling Invariants and Symmetry Reduction of Dynamical Systems. Foundations Computational Mathematics. 13:4 pages 479-516 (2013)

Two-Eyed Seeing: Mathematics and Indigenous Traditions and Cultures

Elder Albert Marshal of the Mi’kmaw Nation describes “two-eyed seeing” as the ability to see with the strength of Indigenous knowledge from one eye while seeing with the strength of Western knowledge from the other. This dual perspective can be applied to many aspects of life, including mathematics.

In this presentation, I will explore the concept of “two-eyed seeing” and the field of ethnomathematics, the study of the relationship between mathematics and culture first introduced by Brazilian educator and mathematician Ubiratan D'Ambrosio. I will address some of the dynamics between these two concepts and illustrate them with several examples. These examples will include a brief analysis of the geometry evident in a traditional Haida Nation hat, as well as the work of contemporary Salish artist Dylan Thomas.

In addition, I will discuss a project that used mathematical modeling of a traditional Tla’amin Nation stone fish trap to communicate cultural, engineering, environmental, and mathematical ideas. This project was a collaboration with the Tla’amin Nation and the Callysto Program, an online education tool that helps students in elementary and high school learn about and apply data science skills.