On December 9, 2025, Andrey Rodin delivered a talk entitled “The End of Theory and The Topological Data Analysis in Biomedical Research” at the conference “Fibonacci’s Garden 2: The Epistemology and Ethics of Formal Methods in the Sciences”, held in Lübeck, Germany.

Topological Data Analysis (TDA) is a relatively new technique used for analysing large datasets, which comprise high-dimensional, usually incomplete and often noisy data. Among some other fields of data-driven research TDA proved particularly effective in the Life Sciences including the neuroscience, biomedicine, genomics and evolution studies. For a philosopher of science TDA is interesting for several reasons. First, it provides an example of effective application in science of a mathematical theory, to wit the Algebraic Topology, which has been earlier thought of as highly abstract and fully detached from the world of human experience. Second, TDA supports a powerful visualisation technique that allows one to literally see on a computer screen various topological shapes of given datasets and thus to grasp their essential features. As a universal mathematical tool for science TDA can be compared with more traditional mathematical tools such as Partial Differential Equations (PDEs). But the way in which TDA helps scientists to represent and understand relevant empirical data is clearly not the same. Analysing recent examples from the Life Sciences we give some preliminary answers to the question What sort of scientific understanding of empirical phenomena TDA may possibly provide?