This week we celebrate the international exchange of students, from high school on up through post-graduate. In graduate level mathematics, the tremendous flow of students from one country to another is unmistakable. At our campus here in New Mexico, and at campuses all over the U.S., foreign students play a major role in mathematics, both in the graduate degree programs in mathematics, and in teaching beginning undergraduates at the level of calculus and pre-calculus. On the other hand, many young American mathematicians go abroad, to Paris, to Budapest, to London or to Moscow, to absorb the different flavor of advanced mathematical study in those countries. In mathematics, national boundaries are almost (but not quite) meaningless. Brazilians and Mexicans study in the U.S., Americans teach in Mexico and Brazil. It is perfectly commonplace for a research paper to be signed by co-authors from three continents. Even during the coldest years of the cold war Russian and American mathematicians sustained their personal-mathematical relationships with each other.
This commitment to a community may be fashioned not only by the shared mathematical legacy and language but may also be the outcome of a sense of isolation young people in this field experience, because it is hard for them to share their thoughts and passion with relatives and non-mathematically motivated friends.
Many talented young immigrants have reported that while they struggle to acquire a new language they can excel in mathematics. Mathematics has its own language, which allows for communication across ethnic and linguistic barriers. This can be a source of attraction for those mathematicians who dislike the parochialism of their own communities, or may even long for a larger, supra-national community. International meetings play a significant role in facilitating exchanges and friendships, even for citizens of countries which have waged war against each other, or may be getting ready for hostilities in the future.
In our book, Loving and Hating Mathematics, we tell at length about the high point of internationalism in mathematics which was attained at Göttingen in the decades before and after World War I. The mathematical school led there by David Hilbert was a magnet for students from the rest of Europe, the U.S., and Japan. And the contributions of those foreign visitors greatly enhanced the accomplishments and prestige of Göttingen mathematics.
The golden years of the mathematical center in pre-WWII Göttingen left a life-long impact on the participants, who tried to create similar broad communities elsewhere when the Nazis took power and they moved to other countries. The outstanding success of Richard Courant in New York is reported at length in Loving and Hating Mathematics, based largely on first-hand knowledge.
This is a guest post by Reuben Hersh and Vera John-Steiner who are co-authors of Loving and Hating Mathematics. Hersh is professor emeritus of mathematics at the University of New Mexico and the coauthor of The Mathematical Experience, which won the National Book Award. He is also the author of What Is Mathematics, Really? John-Steiner is professor emerita of linguistics and education at the University of New Mexico. Her books include Notebooks of the Mind, which won the William James Book Award from the American Psychological Association.