There is wide recognition of the educational benefits of a period of study abroad. MIT organizes these visits through the Global Education Office.
Here are some programs of various types in Mathematics that recent MIT Mathematics majors have attended. Several of them have kindly sent reports of their experience and invite you to contact them if you want more information.
An established program consisting of a full year at Cambridge University, England.
As the name indicates, this is a one-semester program in Budapest, Hungary. The language is English.
A one-semester program at the Independent University in Moscow. The language is English. Here is a letter from an MIT math major who attended this program in the Spring of 2004. The American Mathematical Society administers National Science Foundation grants to cover some of the costs. Deadline September 30 for Spring, March 30 for Fall.
This program is for one or two semesters at France's premier science and engineering school, in French. Deadline February 15th (for 2010 applications, we have been granted a grace period until March 1). Late applications for admission in January 2011 will be accepted until October 31, 2010. Here is a report from an MIT math major who took a postgraduate year there, in general terms and with specific reference to the mathematics program.
This program assists in organizing student visits to a variety of other French institutions.
Study or conduct research in Germany.