PAULUS GERDES – In Memoriam
(Translation: Sofia Gonçalves, Laurentian University, Canada)
Paulus Gerdes and Ubiratan D’Ambrosio
The world was saddened by the death of Paulus Pierre Joseph Gerdes, on November 11th, the day he would have reached 62 years of life. In a broad sense the world is deprived of a great educator, of an interesting and rigorous thinker and researcher, and a great friend for those who had the opportunity to meet him and be with him. Our condolences to the family and to his disciples, colleagues and friends.
My relationship with Paulus was very special. I met Paulus, in the mid-70s, a young man of just over 20 years. He was one of the first adherents to the ethnomathematics movement, which was being initiated; he became a leader in the area.
His life trajectory was very special. He was born in the Netherlands, in a traditional family. His father was the equivalent to a minister of state for religious cults. Paulus studied at the University of Nijmegen, where he received a Bachelor’s Degree (with honors) in Mathematics and Physics in 1972. He had a humanitarian mission experience in Vietnam, returned to Nijmegen, did a Baccalaureate in Cultural Anthropology in 1974 and in 1975 finished a Master in Mathematics. Still in the Netherlands, he became a professor in the “Centro do Terceiro Mundo”, with links with the liberation movements and the anti-apartheid in Southern Africa. By the end of 1976 he went to Mozambique, becoming a Mozambican citizen and creating a family. Since his arrival, he was a professor at the University Eduardo Mondlane until 1989, when he transferred to the Pedagogical University, remaining there until the end of his life.
In 1986, he completed a Doctorate at the University of Dresden, Germany, with a thesis on O Despertar do Pensamento Geométrico and in 1996 he returned for a second Doctorate with a thesis on Geometria Sona: Reflexões sobre tradições de desenhar na areia entre os povos da África ao Sul do Equador, at the University of Wuppertal, Germany.
As an academic, Paulus was responsible for numerous contributions to the theorization of craft and the formulation and solution of mathematical questions of the imaginary and folk craft. All his contributions have important implications for pedagogy with strong socio-cultural roots.
Paulus was one of the most important researchers on Ethnomathematics, always trying to analyze the historical and epistemological foundations of mathematics and proposing important pedagogical innovations. He managed to organize a very active group of young researchers, bringing together mathematicians and educators. The publications of the group, mainly in Portuguese and English, are an important resource for those interested in conducting research on Ethnomathematics worldwide. Many of these publications are generously available to all interested parties, for free or at low cost, in the publisher’s website “Lulu.com” where Paulus published almost all of his books.
In addition to academic activities of research, Paulus has always been involved with Education, especially Mathematics Education. The way he associated research and education is exemplary. In Maputo in 1989, he founded the “Centro de Pesquisas em Etnomatemática – Cultura, Matemática e Educação” and, thanks to his innovative proposals, he was very successful in attracting to Mozambique academics from around the world, interested in his research projects.
As a historian, Paulus Gerdes contributed significantly to the understanding of the history of mathematical ideas, theories and practices, in the African continent. His concern was to organize the historical context of existing practices and theories found in various African cultures. His main focus was a wide bibliographic research on the History of Mathematics in Africa. The results of his research have been crucial to mathematics historians worldwide.
His concerns went beyond identifying other Mathematical thinking models. He felt that creativity could be improved if cultural dignity was restored. The post-apartheid period in South Africa had many repercussions throughout the African continent. It represented a new and important space for the development of the creative potential of the native populations. Ethnomathematics proved to be an important strategy for the rebirth of African creativity and Paulus Gerdes was always extremely skilled at channeling that potential to form a numerous generation of researchers in Mathematics Education.
He was responsible for a change of attitude in regards to crafts and folklore. Crafts have been considered of minor importance in reflections on science and mathematics in the world, and its use in education have been neglected. Paulus recovered, from his search with artisans, the fundamental importance of craft as a basis for the historical development of mathematics. The most important primary sources for his research were artisanal practices. The research on these practices reveal the theoretical foundation of Paulus’ work.
Paulus Gerdes acknowledged that the culture of people, of artists, of artisans constitutes an endless source for mathematical research and Mathematics Education. Mathematics professors of all levels can learn, from their students, what is characteristic of their cultures. The students can show the way to achieve a practice. The makings of artisans, fishermen, peasants, in short, of all the groups that master a practice, are based on knowledge that has been developed by arduous paths, over generations. I emphasize in a very special way the exemplary attention that Paulus dedicated to women in the evolution of African cultures.
As Paulus Gerdes highlighted well in his writings and in his lectures, when studying a demonstration, it is rarely understood how the result was discovered. The path that leads to a discovery is, in general, very different from the paved road of deduction. In poetic language, Paulus tells us that “A via da descoberta abre-se serpenteando por um terreno de vegetação densa e cheio de obstáculos, às vezes aparentemente sem saída, até que, de repente, se encontra uma clareira de surpresas relampejantes. E, quase de imediato, a alegria do inesperado “heureka” (gr. “achei”, “encontrei”) rasga triunfantemente o caminho.”
In fact, Paulus was a poet in his thinking as a philosopher, mathematician, anthropologist, and educator.
To mourn a poet of life so dear to all of us and irreplaceable, I ask for help to a very beloved poet who also left us prematurely, Facundo Cabral. His farewell to a friend expresses very well my feelings.
Cuando Un Amigo Se Va
Cuando un amigo se va, queda un espacio vacio
Que no lo puede llenar la llegada de otro amigo
Cuando un amigo se va, queda un tizón encendido
Que no se puede apagar ni con las aguas de un rio
Cuando un amigo se va, una estrella se a perdido
La que ilumina el lugar donde hay un niño dormido
Cuando un amigo se va, se detienen los caminos
Y se empieza a revelar el duende manso del vino
Cuando un amigo se va, salopando su destino
Empieza el alma a vibrar por que se llena de frio
Cuando un amigo se va, queda un terreno baldío
Que quiere el tiempo llenar con las piedras del astillo
Cuando un amigo se va, se queda un árbol caído
Que ya no vuelve a brotar por que el viento a vencido
Cuando un amigo se va, queda un espacio vacio
Que no lo puede llenar la llegada de otro amigo.