Eli Bagno

Eli Bagno, Thierry Dana-Picard, Shulamit Reches

The emergence of ChatGPT has been rapid, and although it has demonstrated positive impacts in certain domains, its influence is not universally advantageous. Our analysis focuses on ChatGPT's capabilities in Mathematics Education, particularly in teaching basic Linear Algebra. While there are instances where ChatGPT delivers accurate and well-motivated answers, it is crucial to recognize numerous cases where it makes significant mathematical errors and fails in logical inference. These occurrences raise concerns regarding the system's genuine understanding of mathematics, as it appears to rely more on visual patterns rather than true comprehension. Additionally, the suitability of ChatGPT as a teacher for students also warrants consideration.

Eli Bagno, David Garber

A symmetric function is called Schur-positive if it admits an expansion in the Schur basis with nonnegative coefficients. In this paper, we study the Schur-positivity of symmetric functions naturally associated with set partitions, with respect to a descent set function that considers i as descent, if i and i+1 share a block in the partition. The Schur expansion involves hook-shaped Young diagrams, and the corresponding coefficients are given by Touchard-Riordan polynomials, which enumerate matchings by their number of crossings.

Eli Bagno, Thierry Dana-Picard, Shulamit Reches

As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this paper, we analyze sessions with ChatGPT around topics in basic Linear Algebra. We reflect the process undertaken by the ChatGPT along the recent year in our area of interest, emphasising the vast improvement that has been done in grappling with Linear Algebra problems. In particular, the question whether this software can be a teaching assistant or even somehow replace the human teacher, is addressed. As of the time this paper is written, the answer is generally negative. For the small part where the answer can be positive, some reflections about an original instrumental genesis are given. Communication with the software gives the impression to talk to a human, and sometimes the question is whether the software understands the question or not. Therefore, the reader's attention is drawn to the fact that ChatGPT works on a statistical basis and not according to reflection and understanding.