Between 1947 and 1950, French mathematician Laurent Schwartz went from being virtually unknown outside of France to an international mathematical celebrity. By the mid-1950s, he was a famed world traveler, lecturing in such varied places as Buenos Aires, Tunisia, and the TIFR. Schwartz's emergence as a global mathematician followed a pattern that would have been virtually unthinkable to a prior generation, but became increasingly possible for later generations of mathematicians. I will discuss Schwartz's trajectory in the context of mathematicians' changing discipline in the mid-twentieth century, as well as aspects of Schwartz's theories, personality, and politics that shaped is course. This story shall illustrate several broader claims I am developing about the history of mathematics in the mid-twentieth century, and will explain, in particular, why I have been so keenly looking forward to my research in the TIFR archives.