Understanding the mathematical shape of data that neural networks learn from can provide valuable insights into their inner workings. In my senior thesis, I delve into this concept using a mathematical approach called Topological Data Analysis. I demonstrate how neural networks are skilled at grasping complex data by reshaping it mathematically. Essentially, they simplify the data by grouping similar elements together into distinct 'blobs.' This process allows them to make sense of the information they receive and perform tasks more effectively.