Even now, it is hard for me to comprehensively describe all the things I learned from my parents, Anastacia (1906-2000, a math teacher and businesswoman) and Domingo (1904-1998, a practitioner and professor of mechanical engineering). They were "born educators" because they lived what they preached. It was very easy for me to understand the importance of discipline and hard work for achievement because I saw examples of it daily. The professional careers of my six elder siblings and the enduring closeness of our family ties testify to the supportive environment they created. I was very happy that before I left for Germany, they were chosen UP Parents of the Year in 1964. My father always impressed me with his broad interests and his "lifelong learning" attitude. My mother was tremendously resourceful and had strong business acumen. Despite their caring attitude, they also knew when "to let go" and let their children try out new things on their own.
My first "big step out" was the transfer in Grade 4 to Ateneo de Manila in 1956: I initially attended the local school, St. James Academy (run by Maryknoll Sisters) like my elder siblings. But I perceived a strong favoritism toward female pupils among the teachers and when I complained to my mother about this, she challenged me to try to get admitted to Ateneo. There I learned – as a less "well-to-do" pupil to earn some recognition from my classmates through academic excellence. But beyond that, I really embraced the Jesuit ideal of liberal education, enjoying the substantial library resources and availing myself of the diverse extracurricular activities offered. This learning environment led to my acceleration from Grade 6 straight to high school and four years later my becoming the Ateneo High School Class 1963 valedictorian.
After sophomore year, I decided to go to Germany. There were two main reasons for this move: at the time, the few good Filipino mathematicians were abroad, so I knew I had to continue my studies elsewhere sooner or later. Secondly, I wanted to try out a new educational system, and the German Freiheit der akademischen Forschung und Lehre (which allowed students lots of course choices, self-pacing of studies and even voluntary class attendance), seemed to promise more opportunities for individual development. But back in 1965, maybe it was mainly an 18-year-old looking for independence and adventure.
The move to Germany was a unique and, in many ways, defining learning experience for me. Learning to stand on one’s own in a new social environment – especially coming from the usual caring Filipino family context – was a big challenge. But it enriched my own development in such a way, that when my elder son Felix told us eight years ago that he wanted to do something similar – go to college in the US – my wife and I immediately consented, with only one condition on my part – it had to be a good college. (In the meantime, he has graduated magna cum laude with a double major in Physics and Mathematics from the University of Pennsylvania and is currently pursuing PhD studies in Physics as a Research Fellow of the California NanoSystems Institute at UC Santa Barbara). Independence for me almost meant financial independence: during my first two years in Germany, I had to depend on my parents’ support. But I was determined to get a scholarship – as I had at Ateneo. Due to my outstanding Vordiplom (BS Math equivalent) at Heidelberg University in 1968, I got one from the Deutscher Akademischer Austauschdienst (DAAD). Since then, I have been able to maintain my financial independence.
The transfer to Bonn University after the Vordiplom was the highlight in my learning mathematics. The Sonderforschungsbereich Theoretische Mathematik (a Center of Excellence of the German Science Foundation DFG) had just been established: this institution enabled a steady stream of world-class visitors of different disciplines, and this opportunity of interaction began to attract the best students to Bonn. The Thursday afternoon Oberseminar (Research Seminar) conducted jointly by G. Harder (number theory), F. Hirzebruch (topology), W. Klingenberg (differential geometry) and J. Tits (algebra), all recognized leaders in their fields, uniquely enabled a creative, challenging atmosphere for the different mathematical disciplines to interact. The big problems could be tackled from different viewpoints, leading to new ideas often deepened in discussions at the ensuing tea (and coffee) hour. Another unique component of Bonn’s mathematical research was the annual Mathematische Arbeitstagung (Mathematical Workshop), an informal week-long gathering of the best mathematicians in the world, where only the opening talk was fixed beforehand, and the remaining talks volunteered in several plenary assemblies during the week. A number of important results like Faltings’ proof of the Mordell conjecture were first "announced" at such sessions. The Max Planck Institute of Mathematics in Bonn was established in 1981 as the successor of the Sonderforschungsbereich Theoretische Mathematik. It now ranks together with the Schools of Mathematics at Princeton’s Institute of Advanced Study and at the Institut des Hautes Etudes Scientifiques (in the Paris suburb of Bures-sur-Yvette) as one of the leading centers of mathematical research worldwide.
In this community, I came to understand that, more often than not, really good mathematics emerges from problems whose solution demands contributions from diverse mathematical disciplines ("multidisciplinary mathematics"). I was lucky in my PhD research under G. Harder to experience this first hand: I began with an algebraic problem, motivated by questions in number theory. An important step to the solution was viewing the problem from a three-dimensional topological and geometrical perspective. Finally, I identified an appropriate combinatorial structure (a "cell complex") in that three-dimensional space. Providing a solution involved five different mathematical fields! This structure is now often called the "Mendoza complex" (a term introduced by K. Vogtmann of Cornell University in 1985) in the mathematical literature and, according to a recent review by J. Schwermer of the University of Vienna, "opened the way for quite far-reaching investigations regarding the cohomology of Bianchi groups and related questions in the theory of automorphic forms for these groups." It is surprising (but also gratifying) that even after over 25 years, my thesis is still being cited (in nine new publications in the period 2004-2006).
The ability to do multidisciplinary mathematics is often an indication of the maturity level of a country’s mathematical endeavor. But establishing a community capable of doing this takes time, as the Bonn experience shows. In the Philippines, after over 30 years of focus on combinatorial mathematics, I am convinced it is time to try to move on toward more "multidisciplinary mathematics" research and I look forward to mentoring interested Filipinos, particularly because even this kind of "pure" mathematics is becoming relevant to applications in biology and medicine. However, long before the insight of this research’s relevance to "real-world" problems, a growing interest in applying mathematics in general propelled me in 1980 into the global ICT industry. Part 2 will describe this 22-year sojourn from mathematics to software development, technology management, knowledge management, and back to science.