We plan to track how research areas rise and fall over time, and to look for early signals of emerging fields, using the words mathematicians choose for their thesis titles and the subjects they work in. We want to separate the fields that are simply large from those actually gaining momentum, and forecast where the fastest-moving subjects and keywords are heading. Along the way we hope to explore where in the United States particular fields flourish, and whether research is spreading more evenly across the country or staying concentrated in a few places.