Mathematics

Topology

Topology studies the properties of spaces that remain invariant under continuous deformation — stretching, bending, but never tearing. In biology, protein folding is fundamentally a topological problem: a linear chain of amino acids must navigate an astronomically large conformational space to find its functional three-dimensional shape. Topological data analysis (TDA) now reveals hidden structures in high-dimensional clinical datasets that traditional statistics cannot detect. The persistent homology of neural connectivity maps shows how the brain organizes information across scales.