Experimental Mathematics Lab
The Experimental Mathematics Lab promotes and coordinates experimental activities in mathematics at the University of Luxembourg.
We are all accustomed to the idea of experiments in physics, chemistry or biology. But mathematics can be done at an equally experimental level, often using computational methods. This applies to statistics, algebra, analysis, geometry, and other flavours of mathematics, and includes
- visualising complex mathematical objects
- using computers to work with examples that go beyond what is possible using pen and paper
- finding patterns in complicated data
Even in highly abstract areas of mathematics the value of experimentation has increased dramatically in recent years, with computers, programming languages and computer algebra systems getting stronger and easier to use.
There is a gallery with some highlights of the results of previous projects, and you can find an overview of past projects to get a good feeling for how mathematics can be experimental. Some projects have also led to publications by undergraduate students!
We made a promotional video in 2023:
Since its inception, there have been
- 131 students
- working on 128 projects
- supervised by 56 supervisors
Some of the work of our students (names in bold) has also been published:
- Jie Chen, Filipa Gonçalves Marques, Didac MartÃnez Granado, Antonella Perucca, Sanny Schwartz: Congruence theorems for triangles involving angle bisectors; preprint on Orbilu
- Antonella Perucca, Nathaniel Sagman, Guillaume Verfaillie: Congruence theorems involving heights for triangles and convex quadrilaterals; International Journal of Geometry, vol. 14, no. 2, 2025, 76-85.
- Jilly Kevo, Are all weakly convex and decomposable polyhedral surfaces infinitesimally rigid?; Rose-Hulman Undergraduate Mathematics Journal: (2024) 25(1), article 6
- Francesco Grotto, Antonella Perucca, Tatjana Van Steenbergen Bergeron: Rubik's snakes on a plane; The College Mathematics Journal, (2024) 55(4), 317–327
- Antonella Perucca, Joe Reguengo De Sousa, Sebastiano Tronto: Arithmetic billiards; Recreational Mathematics Magazine, (2022) 9(16), 43–54
- Antonella Perucca, Flavio Perissinotto, Steve Mendeleev: Three-dimensional arithmetic billiards; preprint on Orbilu
How to participate?
Mathematics students at the University of Luxembourg can participate in the Experimental Mathematics Lab at several stages of their studies. Within the context of these courses you can take a look at what is currently offered.
Updates
- February 17 2025
- project proposals for next semester are available
- September 13 2024
- project proposals for next semester are available
- May 18–19 2024
- exhibition of some experimental mathematics projects at the Luxembourg Museum Days, with a dedicated website explaining the different exhibits