Magnetic levitation is poised to revolutionize industrial automation by integrating flexible in-machine product transport and seamless manipulation. It is expected to become the standard drive technology for automated manufacturing. However, controlling such systems is inherently challenging due to their complex, unstable dynamics. Traditional control approaches, which rely on hand-crafted control engineering, typically yield robust but conservative solutions, with their performance closely tied to the expertise of the engineering team. In contrast, learning-based neural control presents a promising alternative. This paper presents the first neural controller for 6D magnetic levitation. Trained end-to-end on interaction data from a proprietary controller, it directly maps raw sensor data and 6D reference poses to coil current commands. The neural controller can effectively generalize to previously unseen situations while maintaining accurate and robust control. These results underscore the practical feasibility of learning-based neural control in complex physical systems and suggest a future where such a paradigm could enhance or even substitute traditional engineering approaches in demanding real-world applications. The trained neural controller, source code, and demonstration videos are publicly available at https://sites.google.com/view/neural-maglev.