Large language models (LLMs) are making waves in various fields, including mathematics. While they can solve complex equations and even generate proofs, they often lack the deeper understanding and intuitive leaps that characterize human mathematical thought. Current datasets used to train these AI systems focus on the *result* of mathematical work – the final proof – rather than the often messy, iterative *process* that gets us there. This limitation hinders LLMs from truly grasping the nuances of mathematical reasoning and becoming genuine collaborators for mathematicians. Researchers are now exploring how to bridge this gap by creating datasets that capture the entire mathematical workflow. Imagine a mathematician grappling with a problem. They might start by exploring related literature, formulating conjectures, testing examples, hitting dead ends, and trying different approaches before finally arriving at a solution. These intermediate steps, often absent from traditional mathematical texts and datasets, are crucial for training LLMs to reason like mathematicians. This new research proposes several innovative ways to capture these hidden processes. One approach involves transcribing lectures, discussions, and even informal mathematical vlogs to expose LLMs to the dynamic nature of mathematical thinking. Another involves structuring datasets around “motivated proofs.” Unlike traditional proofs that simply present a sequence of logical steps, motivated proofs explain the *why* behind each step, offering insights into the thought process and strategies employed. Think of it as showing your work, but for a proof. This approach not only makes proofs more understandable for humans but also provides a richer learning signal for LLMs, encouraging them to develop a deeper, more intuitive grasp of mathematics. The challenge lies in the complexity of this task. Mathematical workflows can be highly intricate and vary significantly across different fields. Creating datasets that capture this diversity requires careful consideration of various factors, including the level of abstraction, the types of tools used, and the specific reasoning strategies employed. Additionally, collecting data from real-world mathematical practice raises important ethical considerations about privacy and the potential impact on researchers’ natural workflow. However, the potential rewards are immense. By teaching AI the art of mathematical proof, including the human element of intuition and exploration, we can create powerful tools that not only solve problems but also help mathematicians push the boundaries of knowledge and accelerate scientific discovery across numerous disciplines.