Things were different in 1983 when Gyuri Petruska and I first discussed the idea of St. Olaf undergraduates studying mathematics in Budapest; no internet, no e-mail, no fax machines (very few phone lines!), a Warsaw Pact, rent and heat at essentially no charge (in Budapest!) and a world class opera absolutely anyone could afford. But, some things were not so different; powerful and distinctive intellectual communities, deeply rooted traditions of ferreting out and developing mathematical talent, colorful and effective institutions maintaining world class standards in the face of forbidding obstacles, a common opinion that soon all would be lost. I had spent several extended stays in Budapest doing research with the real analysts and by 1983, Petruska and I knew each other pretty well. So he really got my attention when out of the blue he asked:

If there was a mathematics program in Hungary for St. Olaf students, would anyone come?

This question contained the electricity of a real idea! First, it was a very good question. Certainly in 1983, the popular press in the United States was so convinced of U.S. preeminence in mathematics and science that excellence in other programs was all but invisible. Moreover, Hungary was behind the Iron Curtain and parents would be wary of allowing their children to live there. More to the point, the fact that Petruska had asked me this particular question meant to me that he and probably his Hungarian colleagues as well were serious about creating an international opportunity for North American undergraduate mathematics students.

At that point, Petruska and I were thinking in terms of a small scale semester exchange program between St. Olaf and Eötvös University. But things were afoot that we had no idea about.

When Petruska returned to Budapest he spoke with colleagues about the discussions he'd had with me and they responded by outlining what soon was to become BSM. Immediately, Petruska lent his support to the new project. What had happened was this.

A new government regulation had come out according to which universities would be allowed to offer fee based programs to foreign students from the West. A successful program had already been developed for German medical students and the Ministry of Education was encouraging additional programs in several areas including mathematics. Most important, and quite uncharacteristic of a Communist government, the universities would retain a degree of control over how the tuition fees would be spent. Encouraged by this prospect, Vera Sós and Laci became the engines behind a plan to create a school of mathematics for foreigners in Hungary. But the target audience (or even target country!) was not clear at all. In a letter to Laci Babai, a friend from Eötvös University visiting Oregon that fall, wrote that he felt Masters or Ph.D students could be counted on and perhaps a curious undergraduate or two. Sós , on the other hand, was more optimistic about an undergraduate audience, feeling that with appropriate advertising, one could recruit students for a four or five year undergraduate program. Babai was excited at first, but quickly became skeptical. Many years later he relayed his reaction to me as follows:

A graduate program? Students don't pay for that, they receive a stipend from the university. A commitment to go for an entire 4 or 5 year undergraduate program with such a limited scope? The number of applicants would probably be nil, but even if not, the number would be too small to sustain a program. I also quickly discounted all countries other than the U.S. and Canada, for a variety of reasons.

The critical idea came from Gene Luks, Babai's friend and colleague at the University of Oregon with whom he spoke immediately after receiving the letter from . Luks recognized that the right niche was the "semester abroad" for undergraduates. He argued that this niche was taylor made for an Hungarian program, it was a concept Americans were familiar with and all that was needed was to fill it. It was the solution and, as Babai recalled later, "from that moment I was totally committed to creating this program."

Babai coined the name, "Budapest Semesters in Mathematics," and set out to design the curriculum, the brochure, the advertising strategy, etc. As he wrote me of this period:

The curriculum was relatively easy to design; emphasis on combinatorics and number theory came naturally both because they are Hungarian strengths and because they are generally neglected in American curricula. I decided that we should use Paul Erdős's name and fame, he would certainly warmly embrace the endeavour (as he indeed did), so one subject should be called "Conjecture and Proof," adapting Erdős's favorite phrase. I thought the course would be an adaptation of a course taught by Posa at Eötvös University to math education students; eventually it was Laczkovich who filled the title with wonderful contents. History, arts, and Hungarian language seemed the natural choices of non-mathematical subjects.

The brochure was a critical task. My English was quite limited at the time, this made the task several orders of magnitude more difficult. Gene Luks was immensely helpful. I would write a page into the computer, he would correct every phrase, suggest alternatives, I would rewrite it and add another page, etc. After a dozen iterations which consumed my entire holiday season, the brochure was ready, and with it a detailed outline of the program. It was clear that the target starting date of September '84, requested in 's letter, was impossible to meet, so I set the beginning of the program at February, 1985. My communication with Budapest was limited; letters were too slow and the telephone too expensive, e-mail to Hungary did not exist. I knew I was doing the right thing, those at home had to implement it.

Babai's proposed BSM Program found immediate and enthusiastic support back in Budapest and at this point, discussion and planning turned to focused action. It was by no means easy.

Recruiting first-rate faculty to design courses for the future program was not hard, afterall, enthusiastic scholar-teachers were the foundation of the entire enterprise. Finding appropriate institutional support was the difficult part. , Sós , Petruska, and many others worked long and difficult hours trying to identify an appropriate institutional host for the new program. The danger at Eötvös was excessive bureacracy and a rigid power structure; what BSM needed was great flexibility and independence. Several times all seemed lost when a key person or idea came forward which enabled planning to continue. The Director of the Institute of Postgraduate Studies at the Technical University-Budapest, Atilla Horvath, showed courage, wisdom and foresight, by supporting the program from its inception. Horvath, would eventually provide the program with an ideal institutional host, providing classroom and office space, administrative support, and the great flexibility that has been critical to the program. He is but one of many who took leadership; on several occasions, Paul Erdős gave generously of his time to support this program as yet unborn.

Questions of student housing, transportation, orientation and the like did not wait for the academic planning. Rather, all these things were considered simultaneously. Horvath and his Technical University staff had experience with foreign students since the Technical University was the Hungarian site for training engineering students from Vietnam, Cuba, and several Middle Eastern countries. North American students would be different, but at the Technical University, one could build on a solid foundation of experience with international programs. The task of coordinating the logistics were discussed with Dr. Zsuzsa Barta, a chemist who was fluent in English and was an extraordinarily competent administrator. Barta hired a secretary and an Hungarian student of American Studies, Krisztina Szekely to serve as a liaison with the new group of students. This team, working closely with the aforementioned mathematicians planned for housing in private apartments and with families, hired professors to teach the few non-mathematics courses of the program, arranged for classrooms, and the like. Perhaps their most formidable task was to help streamline the red tape faced by North American students wanting to study in Hungary. A professional language school, The Babilon School of Languages, was asked if they could provide an intensive Hungarian language class to BSM students prior to the beginning of each academic term. The Babilon School, which specializes in teaching English and German to Hungarians, was excited about this new venture and designed an entire two-week curriculum just for the Program.

I had little involvement with the program at this stage, but as Petruska and Mik Laczkovich and I were all visiting the University of California-Santa Barbara during the winter and spring of 1984, I was well informed. Babai left Oregon for Simon Fraser University (Vancouver) in January of that year and it was from Simon Fraser that the campaign to deliver the new program continued. Sós did come to the U.S. in the spring of 1984 to give a series of lectures and took the opportunity to visit both Simon Fraser and Santa Barbara for several days. I vividly recall one entire evening spent discussing the events in Hungary and the exciting planning for the first Budapest Semester. The most critical work, though, was now being done at Simon Fraser. Only a handful of people even knew of the planning for a Budapest Semester and certainly no undergraduate students. It's hardly a party if no one shows up!

As Babai told me,

I still had the task of shouting into America's ears, "Here we are, it's great stuff."

The "great stuff" was not clear to the average American, but it was generally known to mathematicians.

1. Hungary had (and has!) a unique mathematical culture which intimately combines excellence in research with excellence in teaching.
2. Budapest, traditionally a bridge between East and West, is a beautiful and fascinating city. Moreover, (and because of Communism) Budapest was safe.

But from the perspective of recruiting mathematics undergraduates to Hungary, the key, but hardly secret, ingredient was Paul Erdős. Erdős was not merely respected by those who knew him, he was loved. And because he was Erdős, nearly everyone knew him! As Babai put it in the very first BSM literature, students would be studying in the Country of Paul Erdős.

Babai needed help and he knew it. Without a penny of funding he had to rely on volunteers and he found them in the collaborators of Erdős, and those who had worked with Erdős collaborators. Indeed, most of those active in the early organization of BSM fell into one of those two categories.

Regional Representatives were recruited and asked to aid the recruiting efforts. Meanwhile Babai asked several leading American mathematicians to lend their names to the Program and compiled an impressive North American Advisory Board for the opening page of the first brochure. One of these early advisors was Joel Spencer who suggested that a North American Director was needed to communicate with students and coordinate BSM activities in North America. He also had someone in mind, `Tom Trotter, "the perfect American," extremely efficient and well organized'. Trotter agreed to serve and immediately went to work establishing the North American headquarters at the University of South Carolina, designing application materials and recruiting students. Ads were placed in the Notices and Focus and mailings were sent to students and individual mathematicians who might have interest in the Budapest Semesters in Mathematics Program.

In September, Babai moved to Chicago and there was nothing to do but wait. In late October there was still no word about student numbers, but by the deadline of November 15, fourteen qualified applicants had been accepted. That was just enough for the Program to break even and the first Budapest Semester began that spring, 1985.

With Trotter leading the North American operation, the program survived the first precarious few years. In time, Trotter moved to Arizona and when his position as Department Head conflicted with the time necessary to direct the North American side of BSM , he asked Babai to find a replacement volunteer. It was at that point that I replaced Tom as North American Director, Bonnie Humke became Program Administrator and that St. Olaf College became the North American headquarters serving as Agent College for the Program. Laci Babai continues as the Program Coordinator, while Gyuri Petruska now served as Hungarian Director. The Program has continued its cooperation with the Technical University-Budapest, but now through the new College International.

Gradually the program increased [from 20-30 students per semester] to its current size of about [55-65] students each semester. At latest count, more than 170 colleges and universities have sent students to the program, many of them several times. These institutions range from great small colleges like Smith, Macalester, Carleton and Pomona to much larger universities such as Berkeley, Harvard, Princeton and the University of Michigan.

The goals of the BSM Program have not changed much over the years, but how we've tried to accomplish them has varied considerably. Indeed, the continuing dynamism of the Hungarian political and social environment has kept us on our toes.

What are the Goals for BSM?

• To provide highly motivated North American undergraduate students of mathematics an opportunity to experience the mathematical as well as the general culture of Hungary. To accomplish this it is important to:
  • Attract the best Hungarian mathematicians to teach in the Program. (Traditionally these mathematicians hold positions at the Mathematical Institute or Eötvös University).
  • Attract North American students who are serious about mathematics, likely to benefit from the experience of mathematics Hungarian style, and who are excited about experiencing the intercultural adventure of living in Budapest.
• To offer housing and living conditions which will be safe and which will embed the students in the larger Hungarian culture.
• To provide an academic environment concomitant with North American student expectations, including library and internet access.

This section is meant to present a broad brush overview of several aspects of the BSM Program:

• Who participates?
• What is the basic calendar?
• What are the classes?
• Who teaches the students?
• How do students receive credit?

Participant Profile

Participation in the BSM Program has tripled since its inception. The mean home school grade point average of a participant is just over 3.7 on a scale of 4, with mathematics grade point slightly higher. Other than the fact that participants are talented and motivated in mathematics they are the most heterogeneous group I have ever been associated with. In general BSM students are an adventurous lot who tend to engage their chosen activities with spirited determination and energy. Several recent participants have used their "spare time" to play in one of the Liszt Academy's orchestras, others have served Hungarian relief organizations aiding refugees from Romania and countries of the former Yugoslavia, several have joined sports teams in swimming, soccer, fencing; all have taken the opportunity to investigate various parts of Hungary and the surrounding European countries. Most of our students attend their first opera in Budapest and many become devotees of the classical musical and intellectual culture which is still vibrant and affordable. Although the BSM Program does not organize outings we do post information concerning cultural events and show students where they can purchase tickets, but little encouragement is needed. These students are competent and engaged!

Academic Calendar

Two semesters are offered each year; each semester comprises fourteen weeks of teaching and one week of comprehensive examinations. Fall Term begins the first week of September and ends in mid December, while the Spring Term begins the first week of February and ends in May. There are midterm breaks in each semester. The aforementioned intensive Hungarian language course offered by the Babilon School of Languages begins about two weeks prior to the beginning of each semester. Although this course is optional, students who attend emerge from the noncredited eighty hours with a solid survival Hugarian.

Students receive orientation materials from the North American Office and both an orientation packet and lecture/discussion at the beginning of each term in Budapest.

Academic Program

Students normally take three to four mathematics courses and one or two intercultural courses each semester. The BSM Program offers Beginning and Advanced Hungarian Language, Central European History and a Hungarian Culture course each semester. About twenty additional nonmathematics courses are available to BSM students through other American programs taught at the College International. A complete listing of these can be found at our website.

The mathematics courses offered by BSM vary slightly from semester to semester depending on what preregistration choices the students have selected and also which instructors are in Hungary at the time.

BSM Core Courses Mathematics

Non-Mathematics

Each course meets 3-4 hours per week. Classes are taught in English by eminent Hungarian professors, most of whom have had teaching experience in North American universities. In keeping with Hungarian tradition, teachers closely monitor each individual student's progress. Considerable time is devoted to problem solving and encouraging student creativity. Emphasis is on depth of understanding rather than on the quantity of material.

The imprint of the Hungarian tradition is particularly prominent in some of the courses. "Combinatorics" and "Topics in Graph Theory" concentrate on combinatorial structures and algorithms, a stronghold of Hungarian mathematics. These courses, along with "Theory of Computing", are a valuable introduction to Theoretical Computer Science. "Number Theory," especially the advanced course "Number Theory B," displays the mark of Paul Erdős's profound influence on the subject. "Conjecture and Proof", even more than other courses, introduces the student to the excitement of mathematical discovery. Concepts, methods, ideas and paradoxes that have startled or puzzled mathematicians for centuries will be reinvented and examined under the guidance of enthusiastic and experienced instructors. The topics covered range from ancient problems of geometry and arithmetic to 20th century measure theory and mathematical logic.

Credits

Upon completion of program, students receive an American style transcript which lists courses taken and a grade (A, A-, B+, etc.). Normally, official transcripts are also sent directly from the North American Office both to the student and to the student's home institution. Course materials are designed so that credits will be easily transferable to North American colleges and universities.

Despite our problems, we in North America are blessed with strong and vibrant intellectual institutions. Particularly in mathematics and the physical sciences, we are flush with good fortune. But success can become a breeding ground for complacency and tunnel vision; there are other countries and communities that have created powerful and successful mathematical and scientific institutions using vastly different formulas than have we. It is in our interests as scientists and educators to find, understand and connect with such communities. This is not so simple as collecting textbooks or hiring faculty. Rather we must understand deeply what makes these scientific communities work, and then adapt that information to improve our own institutions. Robust international programs in science and mathematics, programs that are discipline based and intellectually rigorous, programs that attract our best and our brightest can serve this role.