On 6 December 2022, BMUCO presented a conversation with Maryna Viazovska, the only living woman and second woman in history to receive the Fields Medal, which is often dubbed as the 'Nobel Prize of Mathematics'.
The Faraday Room
Co-hosted with the London Institute for Mathematical Sciences, the event took place in the historic Faraday Room at the Royal Institution—the very space where Michael Faraday once lived and conducted his pioneering experiments.
Prof. Yang-Hui He, BMUCO's scientific advisor, led the discussion alongside board members Rajarshi Maiti and Madhav Tiwari.
The Sphere Packing Problem
"How tightly can you arrange identical spheres in space, like stacking oranges in a grocery store?"
The conversation explored Viazovska's groundbreaking proof of optimal sphere packing in eight dimensions—a problem that had perplexed mathematicians for over four centuries.
At its core, sphere packing asks a deceptively simple question: how tightly can you arrange identical spheres in space? While we intuitively understand the pyramid arrangement in three dimensions, proving the densest configuration in higher dimensions required revolutionary techniques connecting number theory and Fourier analysis.
A Problem Four Centuries Old
For more than 400 years, mathematicians had struggled to prove what seemed obvious in our everyday experience. Viazovska's breakthrough came from recognizing deep connections between:
- Number theory: The study of integers and their properties
- Fourier analysis: Mathematical techniques for decomposing functions
- Modular forms: Highly symmetric mathematical objects
Her proof elegantly demonstrated that the E₈ lattice provides the optimal arrangement in eight dimensions—a result that had eluded researchers since the problem's formulation.
Breaking Barriers
Viazovska also reflected on her journey as a mathematician and the significance of her achievement as a woman in a male-dominated field. Her work stands as a testament to the power of creative thinking and persistence in solving centuries-old problems.
The Fields Medal, awarded to her in 2022, recognized not just the elegance of her proof but its far-reaching implications for mathematics, physics, and our understanding of high-dimensional geometry.
Watch the full conversation:
youtube.com/watch?v=GnSRh5C6IBs