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This conference provided a focused venue to investigate the history of mathematics during a particularly active time in the discipline, that is, roughly between the turn of the 20th century and 1950. Using the lens of transition to explore this vibrant period, the organizers brought together mathematicians, historians of mathematics and historians of science to explore ideas and offer insights from different perspectives. With this wide range of scholars in attendance, speakers had to give careful thought to the presentation of their work. This extra effort not only yielded a sterling set of talks but also inspired scholars to rethink their own work. The restricted time period revealed an almost unexpected richness in the history of mathematics as the conference participants observed and discussed points of connection between the people, places and ideas from fields as seemingly diverse as class field theory, mathematical physics and algebraic geometry, among others. The extended abstracts below reflect the critical roles of community, politics, and institutions in the history of mathematics at this time. They also call attention to interesting questions related to the collective actions involved in transitions and the ``stable" places in between. The organizers placed an especial emphasis on the presence of and contributions by young scholars. In particular, the conference schedule included almost a full day of presentations by graduate students and recent recipients of the Ph.D. Their fresh perspective fostered a vibrant spirit during the meeting. One of the first-time participants to Oberwolfach remarked that ``this Institute has everything you need." This ``everything you need" includes the intangible components of Oberwolfach that give the most meaning to the experience. The conference participants especially appreciated the interesting mix of people and talks we enjoyed during our week at the MFO. While the idea of transition may have brought us together initially, it is the continued ``mathematical talking" that will create further conversations and investigations.