Since neural networks, and especially transformers, became dominant, production AI has largely settled on a small set of mathematical assumptions and rarely revisits them. The research literature has questioned these assumptions for years, but the alternatives have not crossed over into the systems most of us actually build, so in practice we keep pushing the same architectures further rather than asking a more fundamental question: are we even using the right mathematical approach in the first place?

This talk focuses on one place where that question bites hardest: how we represent meaning and retrieve it. Many modern AI systems built in Python lean heavily on embeddings and similarity metrics such as cosine similarity, particularly in components like hybrid search. The usual setup treats representations as points in a flat, Euclidean space and measures relatedness by angle. That choice is convenient, but it is not neutral, and it quietly limits what these systems can capture.

We will look at how embeddings and similarity metrics are used in practice, what inductive biases they introduce, and where they start to break down.

From there we will introduce alternative perspectives such as hyperbolic spaces and manifold-based representations that capture hierarchy and structure with far less distortion than flat space. A third lens comes from the theory of moving frames.

We will keep all of this intuitive, with a simple illustrative example in Python.

Take-home message: the mathematical choices behind AI systems are not neutral. If we question the geometry and structure we assume, we can better understand the limitations of current approaches and open the door to more suitable ways of representing meaning and relationships.

Target audience: Python developers, data scientists, and engineers working with machine learning or AI systems who want to understand the foundations behind embeddings, similarity, and retrieval.