https://sguzman.github.io/marginalia/tags/tda/Recent content in Tda on MarginaliaHugoen-usThu, 12 Feb 2026 00:00:00 +0000https://sguzman.github.io/marginalia/posts/topology/Thu, 12 Feb 2026 00:00:00 +0000https://sguzman.github.io/marginalia/posts/topology/A comprehensive, historically grounded survey of topology: its 18th-century precursors (Euler and early structural problems), its formal birth in the late 19th century (Poincare and analysis situs), its 20th-century axiomatization and algebraic revolution (point-set topology, homology, homotopy), and its modern frontiers and applications (manifold theory, low-dimensional topology, and topological methods in data science, physics, and engineering). The piece emphasizes topology’s qualitative viewpoint - invariance under continuous deformation - and maps major subfields and conceptual bridges to geometry and analysis.