Explore the intersection of algebraic geometry and data science in this one-hour lecture by Bernd Sturmfels. Delve into methods for determining real algebraic varieties from finite point sets, examining both existing approaches and newly developed techniques. Gain insights into topological and algebraic geometric aspects, including dimension calculation and polynomial definition. Discover practical applications through various datasets, and learn about the implementation of these algorithms in a Julia package. Cover topics such as intrinsic dimension, correlation dimension, dimension diagrams, topological data analysis, tangent spaces, and the connections between algebraic geometry and machine learning. Understand how these concepts apply to real-world examples like cyclooctane datasets and explore their relevance to the broader scientific community.