Artificial intelligence (AI) is increasingly of tremendous interest in the medical field. However, failures of medical AI could have serious consequences for both clinical outcomes and the patient experience. These consequences could erode public trust in AI, which could in turn undermine trust in our healthcare institutions. This article makes two contributions. First, it describes the major conceptual, technical, and humanistic challenges in medical AI. Second, it proposes a solution that hinges on the education and accreditation of new expert groups who specialize in the development, verification, and operation of medical AI technologies. These groups will be required to maintain trust in our healthcare institutions.