There has been extensive attention to near-term and long-term AI technology and its accompanying societal issues, but the medium-term has gone largely overlooked. This paper develops the concept of medium-term AI, evaluates its importance, and analyzes some medium-term societal issues. Medium-term AI can be important in its own right and as a topic that can bridge the sometimes acrimonious divide between those who favor attention to near-term AI and those who prefer the long-term. The paper proposes the medium-term AI hypothesis: the medium-term is important from the perspectives of those who favor attention to near-term AI as well as those who favor attention to long-term AI. The paper analyzes medium-term AI in terms of governance institutions, collective action, corporate AI development, and military/national security communities. Across portions of these four areas, some support for the medium-term AI hypothesis is found, though in some cases the matter is unclear.