Core Viewpoint - The article discusses a significant breakthrough in mathematics, where four mathematicians extended the modularity theorem from one-dimensional elliptic curves to the more complex two-dimensional abelian surfaces, marking a revolutionary step towards a unified theory in mathematics [5][14][46]. Group 1: Historical Context - The proof of Fermat's Last Theorem by Andrew Wiles in 1994 was a monumental event in mathematics, resolving a problem that had persisted for over 350 years [9][10]. - Wiles' proof revealed a deep connection between elliptic curves and modular forms, providing a powerful method for mathematicians to explore properties of elliptic curves through their corresponding modular forms [11][12][13]. Group 2: Recent Breakthrough - In February 2023, a team of four mathematicians proved that a large class of abelian surfaces has corresponding modular forms, extending the modularity theorem significantly [16][45]. - The team members include Frank Calegari, George Boxer, Toby Gee, and Vincent Pilloni, who collaborated to tackle a problem previously considered nearly impossible [14][16][30]. Group 3: Implications and Future Directions - This breakthrough is expected to provide new tools for solving unresolved problems in number theory, similar to how the proof of the modularity of elliptic curves opened new research avenues [20][46]. - The mathematicians aim to prove that all types of abelian surfaces satisfy the modularity condition, which could lead to further discoveries in the field [20][46].