Abstract: What does it mean to understand shape? How can we measure it and make statistical conclusions about it? Do data sets have shapes and if so how to use their shape to extract information about the data? There are many possible answers to these questions. Topological data analysis (TDA) aims at providing some of them using homology. In my presentation aimed at broader audience I will describe a novel approach to TDA. I will illustrate how TDA can be used to give a machine intelligence to learn geometric shapes and how this ability can be used in data analysis.