Euclidean Geometry

Euclidean geometry, the study of shapes and spaces based on Euclid's axioms, remains foundational to many scientific fields, but current research increasingly focuses on extending its principles to handle non-Euclidean data prevalent in modern applications. This involves developing new algorithms and models, such as geometric loss functions for map construction and neuro-symbolic frameworks for automated theorem proving, that can effectively manage the complexities of non-Euclidean spaces. These advancements are crucial for improving machine learning performance on diverse data types and for bridging the gap between human geometric intuition and machine understanding of complex systems. The resulting tools and theoretical frameworks are transforming fields ranging from computer vision and robotics to data analysis and optimization.