[HM] Transfer of math knowledge to the colonies (#3/3)

Ubiratan D'Ambrosio (ubi@usp.br)
Wed, 17 Feb 1999 06:55:41 -0300

5. The 20th century.

The developments of early 20th century are as yet a practically open
field of research. There is an enormous need for identifying documents
and above all for the preservation of extant sources in the countries,
especially in states and provinces.

When we look into the scenario in the turn of the century, we see an
important effort of Germany to establish areas of influence in the
Southern part of South America. What Lewis Pyenson called the German
Cultural Imperialism is clearly illustrated by looking into the
development of the so-called Exact Sciences in Argentina, the same as
in Chile. A major step to consolidate this influence was the efforts
for the development of the Astronomical Observatory of La Plata.
Richard Gans (1890-1954), a physicist who emigrated to Argentina in
1912, was very influential in the development of Argentinian Science.

In 1917 the Spanish mathematician Julio Rey Pastor (1888-1962) visited
Argentina and there he decided to stay. Indeed, he remained in Argentina
for most of his life, although with frequent returns to and much
influence in Spain. In addition to making important contributions to
mathematics, mainly to projective geometry, Rey Pastor is essentially
noteworthy for his contributions to the history of mathematics,
specially of Iberian mathematics in the 16th century. Rey Pastor also
marked new directions in historiography by drawing attention to the
mathematical achievements that made possible the great age of navigation.
A representative of his contribution is La Ciencia y la Te/cnica en el
Descubrimiento de Ame/rica, Espasa-Calpe Argentina S.A., Buenos Aires,
1942.

A disciple of Rey Pastor in Argentina, Jose/ Babini (1897-1983), became
one of the most distinguished historians of science and mathematics in
Latin America. His career as a driving force of Mathematics in Argentina
is significant. He was a founder of the Unio/n Matema/tica Argentina,
and in 1920 he became Professor at the Universidad Nacional del Litoral.
Besides having written many books and articles in non specialized
periodicals, Babini contributed considerably to scholarship on the Jewish
medieval contributions to Mathematics. His major work was doubtless the
book he wrote with Julio Rey Pastor: Historia de la Matema/tica, Espasa-
Calpe Argentina S.A., Buenos Aires, 1951. This can be regarded as one of
the best internalist books in the history of mathematics written in the
mid of this century. Unfortunately, it has not as yet been translated
into other languages.

In the 1930s, some European mathematicians emigrated to Argentina. Among
them the distinguished Italian mathematician Beppo Levi (1875-1961), who
established an important research center in Rosario, and founded an
influential journal, Mathematica Notae. Well known for his seminal theorem
on the theory of integral, Beppo Levi devoted much of his research to the
history of mathematics. Particularly to be noticed is his book Leyendo a
Euclides, Editorial Rosario S.A., Rosario, 1947, a critical analysis of
the general organization of the Elements.

One of the important and influential mathematics in Latin America was
a disciple of Rey Pastor, Luis Alberto Santalo/. Born in 1911, this
Spanish mathematician had studied with W. Blaschke in Germany and already
had an international visibility when he emigrated to Argentina during
the Spanish Civil war. Santalo/ reached world renown as a founder of
modern Integral Geometry and became a most influential scholar in
Mathematics, Mathematics Education, and the History of Mathematics in
all of Latin America. Besides his important contributions to Integral
Geometry, Santalo/ has important contributions to the History of
Geometric Probabilities, and has published relevant studies on Buffon.

In neighbouring Uruguay, an important tradition of mathematical
research was established early in the 20th century.

A representative of this movement, particularly devoted to the
history of mathematics, was Eduardo Garci/a de Zun~iga (1867-1951).
Garci/a de Zun~iga succeeded in creating a most important library in
the history of mathematics at the Facultad de Ingeneri/a de la
Universidad de la Repu/blica, in Montevideo. His research was mainly
in Greek Mathematics, and his collected works have been published
as Garci/a de Zun~iga, E. Lecciones de Historia de las Matema/ticas
(ed. Mario H. Otero), Facultad de Humanidades y Ciencias de la
Educacio/n, Montevideo, 1992. In mid-century, Rafael Laguardia and
Jose/ Luis Massera were responsible for the creation of a most
distinguished research group in the stability theory of differential
equations in the Instituto de Matema/tica y Estadi/stica de la Facultad
de Ingeneri/a de la Universidad de la Repu/blica, en Montevideo. This
research group, of world reknown, attracted young mathematicians from
all of Latin America and abroad. The military dictatorship established
in Uruguay in 1971 saw in the declared political position of Jose/
Luis Massera and Rafael Laguardia a reason to simply close the
excellent mathematical library at the university and to interrupt all
mathematical research in the country. Of course, Uruguayan
mathematicians went to several countries where they were much
influential. Massera spent all the period of the military regime
in jail and afterwards abandoned mathematical research to pursue a
political career, and Rafael Laguardia died in Montevideo during the
political repression. More than in any other country under military
dictatorship in South America in the sixties, Uruguay reveals how a
flourishing school of mathematical research can be immobilized by
a governmental decision.

In Brazil, the proclamation of the Republic in 1889 reenforced the
influence of positivism. The Escola Militar, transformed in the
Polytechnic School, granted 25 doctorates in Mathematics, most under
comtian influence. In the beginning of the century, a number of young
mathematicians were absorbing the most recent progresses of Europe.
Among them Otto de Alencar, Manuel Amoroso Costa, Teodoro Augusto
Ramos and Lelio I. Gama. In 1916 the Academia Brasileira de Cie^ncias
was founded. With the inauguration of the Universidade de Sa~o Paulo
in 1934, the first university to be operational in Brazil, we see a
new direction in Mathematics. We might say this is the beginning of
systematic research in Mathematics in Brazil. Luigi Fantapie\ and
Gia\como Albanese, distinguished Italian mathematicians contracted by
the University of Sa~o Paulo, respectively in the fields of Functional
Analysis and Algebraic Geometry, were responsible for initiating an
important research school in Sa~o Paulo.

Contemporary developments: after the end of the Second World War.

It is impossible to give in a short paper an account of the important
developments in Mathematics in Central and South America. Some very
important individuals, institutions and events are not mentioned. This
does not indicate a judgement of academic standing. I elected a few
events and names which I esteem to be a good starting point for further
research.

After World War II, a number of European mathematicians emigrated to
Latin America. Particularly important is the presence of Antonio Aniceto
Monteiro, from Portugal, in Rio de Janeiro, and in Bahia Blanca, Argentina.

It is noticeable an unprecedent cultural and economic interest of the
United States in South America after WW II. Particularly, this resulted
in an increasing influence of the United States in the development of
Mathematics in Latin America. Before WW II, Europe was the source of
visitors and the place for Latin Americans to go abroad for studies. We
notice a large number of European mathematicians in Latin America after
Second World War, some looking for employment, and some as part of the
efforts of former colonial powers, specifically France and England, to
preserve they cultural presence in what became known as the Third World.
Instrumental in these efforts were organizations such as the British
Council, ORSTOM and the Coope/ration franc,aise. UNESCO played an
important role in supporting post-colonialist efforts.

The growth of American influence is evident. The Organization of
American States was instrumental in favoring United States influence
and exchanges. The United States became the main destination of a
generation of young students pursuing their doctorates abroad. The
creation of the National Science Foundation set up the model to be
soon followed by practically every Latin American country through
the CONICYTs, CONACYTs and the likes. An effort of the AAAS to
cooperate with homologous organizations in Latin America is also to
noticeable.

In the fifties, a view of the state of Mathematics in Latin American
as a whole was due. An important meeting was convened by the Centro
de Cooperacio/n Cienti/fica de la UNESCO para Ame/rica Latina, in
Montevideo, Uruguay, in 1951, to report on mathematics research going
on in the region. This was the "Symposium sobre algunos problemas
matema/ticos que se esta/n estudiando en Latino Ame/rica".

The very incomplete Proceedings of the Symposium give an idea of
some of the areas deserving interest in Latin America. We learn there
of the work of Leopoldo Nachbin, of the Universidade do Brasil,
who was then doing very advanced research on the Theorem of Stone-
Weierstrass and launching the basis a major school on Holomorphy
and Approximation theory in Brasil; of the advances on Integral
Geometry by Luis Santalo/, one the most distinguished researchers
in this area, in Facultad de Ciencias de la Plata, Argentina; of the
presence of Francis D. Murnangham in Brazil with the mission of
building up a research group on modern applied mathematics and
matrix theory in the Instituto Tecnolo/gico de Aerona/utica, a
model institution of advanced technology sponsored by the Brazilian
Armed Forces and academically modelled upon the M.I.T., in Sa~o
Jose/ dos Campos, Brasil; of Mischa Cotlar, who in the Facultad
de Ciencias de Buenos Aires was doing important work on Ergodic
Theory in cooperation with R. Ricabarra; of Mario O. Gonza/lez, of
the Universidad de La Habana, working on Differential Equations; of
Alberto Gonza/lez Domi/nguez, of the Facultad de Ciencias de Buenos
Aires, working on distributions and analytic functions; of Carlos
Graeff Ferna/ndez, of the Universidad de Me/xico, working on
Birkhoff's gravitational theory; of Godofredo Garcia, of the
Facultad de Matema/ticas de Lima, on General Relativity; of Rafael
Laguardia, of the Instituto de Matema/tica y Estadi/stica de la
Facultad de Ingeneri/a de Montevideo, on Laplace transforms.

We also learn about the presence of Wilhelm Damko"hler, a German
specialist in the Calculus of Variations, who emigrated to the
Universidad Nacional de Tucuma/n, Argentina, and later went to the
Universidad de Potosi/, Bolivia; of Peter Thullen, of the O.I.T.
office in Paraguay, working on Several Complex Variables; of Kurt
Fraenz, of the Facultad de Ciencias de Buenos Aires, on the
mathematical theory of electric circuits. Some visitors who had been
lecturing in South America also participated in the Symposium, among
them Paul Halmos, from the USA.

Invited discussants were Augustin Duran~ona y Vedia, of the Facultad
de Ciencias de La Plata; Roberto Frucht, of the Facultad de Matematicas
y Fisica de Santa Maria, Chile; Pedro Pi Calleja, of the Facultad de
Ciencias de La Plata; Cesario Villegas Man~e, of the Facultad de
Ingeneria de Montevideo.

This "dropping of names" should not be regarded as an account of
what was going on in South America in 1950. Many more individuals were
active in Mathematics. But everyone of the mathematicians attending
the Symposium deserves a study of their life and work and of their
influence in the respective countries. This should be a priority theme
for research in the History of Mathematics in Latin America.

An important, although very incomplete, account of research in
Mathematics going on in Latin America was given by Julio Rey Pastor
in the paper "La matema/tica moderna en Latino Ame/rica", which
appeared in the Segundo Symposium sobre Algunos problemas matema/ticos
que se esta/n estudiando en Latino Ame/rica, Villavicenzio-Mendoza,
21-25 Julio 1954, UNESCO, Montevideo; p. 9-20.

A good perception of the developments of mathematics in Latin
America can be obtained by the study of the "Colo/quios Brasileiros
de Matema/tica", held every two years beginning in 1957 in Brazil
and organized by the distinguished Instituto de Matema/tica Pura e
Aplicada (IMPA), of Rio de Janeiro, of the ELAM: Escuela Latinoamericana
de Matema/ticas, held in different countries, and the strong Latin
American presence in the International Congress of Mathematicians
and other international meetings. It would be extremely useful to
have a repertory of everything that was published in Mathematics by
Latin Americans.

Although the UNESCO Symposium was an attempt to have a picture of what
was going on in mathematical research in Latin America, a number of
mathematicians quite active in several countries of the region were
not invited to the meeting. Looking into the Mathematical Reviews we
might be able to find how representative was this group of invitees
and to identify several other active mathematicians which were not
invited. It would be very interesting to ask why those listed above
were invited while other active mathematicians, of a comparable
qualification, were not. Which were the forces and interests behind
the invitations? In other terms, how political were the invitations?
These and other questions are enough to feed considerable research
in the History of Contemporary Mathematics in Latin America.

To analyse Contemporary History is a difficult task, since we have to
refer to processes still going on and we risk stumbling into personal
and political sensibilities. Several academicians were active in the
period when military regimes took control of the governments of the
countries which were showing strongest vitality in Mathematical research
in South America. The military coups, which occurred sequentially in the
four countries which were more active in Mathematical research: Brazil
1964, Argentina 1966, Uruguay 1971, Chile 1973, originated an important
migratory flux of Mathematicians, indeed scientists in all areas, among
these countries. These movements soon were directed to the few Latin
American countries which were able to keep democratic regimes,
particularly Mexico and Venezuela. After the redemocratization of
Argentina (1983), Brazil (1984), Uruguay (1984) and Chile (1989), some
scientists returned and reclaimed their positions. Others were able to
maintain their positions during the military regimes. And kept these
positions after democratization. The divisory line between opponents
and sympathetic and even collaborators of the military regimes is very
difficult to draw. Obviously, personal conflicts are still latent.

An International Symposium on "La migracio/n de cienti/ficos en los
pai/ses del Cono Sur: determinaciones econo/micas y poli/ticas [The
Migration of Scientists in the Countries of the Southern Cone:
Economical and Political Determinants]", was convened by the FEPAI:
Fundacio/n para el Estudio del Pensamiento Argentino, in July 1986.
The interventions and debates revealed open wounds which remain from
the period of military dictatorship. Although unpleasant and somewhat
painful, it is important to look into this period and its consequences
while some of the protagonists are still alive. I esteem this as an
important and needed research project.

Increasing interest in Mathematics Education and the History of
Mathematics.

An area of research which is growing very fast in Latin America is
Mathematics Education. Until the end of World War II there was
practically no coordination and not even interchange about progresses
and difficulties in the teaching of mathematics in the several levels
of education. A link between all the educational systems was the
result of the influence of colonial times and the use of the colonial
languages. Thus, the entire bloc of Spanish speaking countries would
show similarities and Brazil showing a slight difference. Although
this was a positive factor of approximation, it was also interfering
with the advancements proposed in the English speaking countries.

In the fifties an effort of approximation was made and the influence
of the several waves of the Modern Mathematics movement is undeniable.
A decisive move was the creation of the Interamerican Committee of
Mathematics Education (IACME/CIAEM) by initiative of Marshall H. Stone
(1903-1989). The committees, in addition to studies and researches,
promotes the Interamerican Conferences of Mathematics Education, which
take place every four years.

The international contacts of Latin American mathematics educators and
colleagues from different parts of the world were intensified during
the so-called Modern Mathematics movement.

Although we recognize some interest in the History of Mathematics
since colonial times, in the last decades it became a growing area
of academic interest throughout South America. The founding of the
Sociedad Latinoamericana de Historia de las Ciencias y la Tecnologia,
in 1983, stimulated the organization of national societies devoted
to History of Science, which include sections of History of
Mathematics. Young mathematicians have recently obtained doctorates
in history of mathematics in both Europe and in North America, which
is a hopeful sign of maturity and continuing professionalization of
the subject throughout Latin America. Among the research areas we
see both European Mathematics and Latin American progresses in the
mathematical sciences. A growing interest in contemporary mathematics
in Latin America begins to be noticed.

Additional references for Latin America.

I tried to give an overall, although very incomplete, account of a
vast subject. Mexico has advanced much in the very attractive area
of research in Latin American mathematics. In Central and South America
the field is incipient. Practically all the names mentioned in this
paper, and several others, are open to investigation. A few results
of research are very partial and disperse. The project of an
"Enciclopedia de las Ciencias y las Te/cnicas Iberoamericanas",
proposed by Mariano Hormigo/n, will certainly put together more
information on Central and South America.

A few references and notes:

* Arboleda, Luis Carlos:
Dificultades estructurales de la profesionalizacio/n de las matema/ticas
en Colombia, in La Ciencia Moderna y el Nuevo Mundo, Jose/ Luis Peset
(editor), CSIC/SLAHCT, Madrid, 1985; pp. 27-38.

* Ascher, Marcia:
Ethnomathematics. A Multicultural View of Mathematical Ideas, Pacific
Grove: Brooks/Cole Publishing Company, 1991.

* Azevedo, Fernando de (org.):
As Cie^ncias no Brasil, Rio de Janeiro: Editora UFRJ, 1994 (ed. original
1955).

* Babini, Jose/:
Pa/ginas para una Autobiografia, Pro/logo y notas de Nicola/s Babini,
Asociacio/n Biblioteca Jose/ Babini/, Buenos Aires: Ediciones Letra
Buena, 1992.

* Barradas de Carvalho, Joaquim:
A la recherche de la spe/cifite/ de la renaissance portugaise, 2 vols.
Fondation Calouste Gulbenkian/Centre Culturel Portugais, Paris, 1983;
p. 13.

* Barrantes, Hugo; Ruiz Zun~iga, Angel:
La Histo/ria del Comite/ Interamericano de Educacio/n Matema/tica,
CIAEM/ICMI (to appear)

* Bateson, Gregory:
Steps to an Ecology of Mind, New York: Ballantine Books, 1972.

* Cardoso, Antonio:
As Caravelas dos Descobrimentos e os mais Ilustres Caravelistas
Portugueses, Lisboa: Monografia no 7 do Museu de Marinha, 1984.

* Carr, E. H.:
What is History?, Harmondsworth: Penguin Books, 1968.

* Closs, Michael (ed.):
Native American Mathematics, Austin: University of Texas Press, 1986.

* Comptes-Rendus de l'Acade/mie des Sciences de Paris, tomes XL, p. 1310,
and XLI, p. 100, and Proceedings of the Royal Society, 1856, pp.146-149.
It is quite interesting to read the referee's reports and the reaction
of Gomes de Souza to the fact that Liouville did not give an appraisal
of the paper, according to Gomes de Souza, because of "la petite jalousie".
A thorough study of the scientific works of J. Gomes de Souza is still due.

* Correia, Mendes:
Influe^ncia da Expansa~o Ultramarina no Progresso Cienti/fico, Histo/ria
da Expansa~o Portuguesa no Mundo, Lisboa, 1940, vol. III; p. 468.

* D'Ambrosio, Beatriz Silva:
The Dynamics and Consequences of the Modern Mathematics Reform Movement
for Brazilian Mathematics Education, School of Education, Bloomington:
Indiana University, 1987.

* D'Ambrosio, Ubiratan:
Adapting the Structure of Education to the Needs of Developing Countries
(letter), Impact of Science on Society, vol. 25, no. 1, 1975, p. 94.

* D'Ambrosio, Ubiratan:
Science and Technlogy in Latin America During the Discovery, Impact of
Science on Society, vol. 27, no. 3, 1977, pp. 267-274.

* D'Ambrosio, Ubiratan:
Knowledge Transfer and the Universities: A Policy Dilemma, Impact of
Science on Society, vol. 29, no. 3, 1979, pp. 223-229.

* D'Ambrosio, Ubiratan:
O Semina/rio Matema/tico e Fi/sico da Universidade de Sa~o Paulo. Uma
Tentativa de Institucionalizaca~o na De/cada de Trinta, Temas e Debates,
ano VII, no. 4, 1994; pp. 20-27.

* D'Ambrosio, Ubiratan:
Ethno-mathematics: The Nature of Mathematics and Mathematics Education,
in Mathematics, Education and Philosophy: An International Perspective, ed.
Paul Ernest, London: The Falmer Press, 1994. Many scholars do not agree
with the use of "cultural science". We might say ethnoscience.

* D'Ambrosio, Ubiratan:
Ethnomathematics, History of Mathematics and the Basin Metaphor,
in Histoire et Epistemologie dans l'Education Mathe/matique/ [History and
Espistemology in Mathematics Education] (Actes de la Premie\re Universite/
d'Ete/ Europeenne, Montpellier, 19-23 juillet 1993), eds. F. Lalande,
F. Jaboeuf, Y. Nouaze, IREM, Montpellier, 1995, pp. 571-580;

* D'Ambrosio, Ubiratan:
Ethnomathematics: An Explanation, in Vita Mathematica. Historical
Research and Integration with Teaching, ed. Ronald Calinger, Washington:
The Mathematical Association of America, 1996, pp. 245-250.

* D'Ambrosio, Ubiratan:
Mathematics and Literature, in Essays in Humanistic Mathematics ed.
Alvin M. White, Washington DC: The Mathematical Association of America,
1993; pp. 35-47.

* See the issue devoted to the theme "Science Wars" of the Social Text,
46-47, Spring/Summer 1996. Very revealing of the current status of this
war is the paper of Alan Sokal, and the atacks on Afrocentrism, the
warnings against a "new dark age of irrationalism" and other controversial
disputes going on in the academic world. All come as a consequence of
challenging current epistemological order, what might be seen as an
intellectual fundamentalism.

* D'Ambrosio, Ubiratan:
ETNOMATEMA/TICA. Arte ou Te/cnica de Explicar e Conhecer, Sao Paulo:
Editora A/tica, 1990. A translation is available: ETHNOMATHEMATICS.
The Art or Technique of Explaining and Knowing, tr. Patrick B. Scott,
Las Cruces: NMSU/ISGEm, 1998.

* da Silva, Circe Mary Silva:
Positivismus und Mathematikunterrichte: Portugiesche und franzsische
Einflu"sse in Brasilien im 19. Jsahrundert, IDM, doctoral dissertation,
Bielefeld, 1991.

* da Silva, Clovis Pereira:
A Matema/tica no Brasil. Uma histo/ria de seu desenvolvimento, Curitiba:
Editora da UFPR, 1992.

* Dorn, Harold:
The Geography of Science, Baltimore: The Johns Hopkins University Press,
1991.

* Gerdes, Paulus:
Ethnomathematics and Education in Africa, Stockholm: Institute of
International Education, Stockholms Universitet, 1995.

* Gonza/lez Orellana, Carlos:
Historia de la Educacio/n en Guatemala, Guatemala: Editorial
Universitaria, 1985.

* Hung Hui, Juan:
Tecnologia Naval China y Viaje al Nuevo Mundo del Monje Chino Huei Shen,
III Congreso Latinoamericano y III Congreso Mexicano de Historia de la
Ciencia y la Tecnologia, Ciudad de Mexico, 12-16 de Enero, 1992.

* Kragh, Helge:
An Introduction to the Historiography of Science, Cambridge: Cambridge
University Press, 1987; p. 111.

* Leo/n-Portilla, Miguel:
Visio/n de los Vencidos (Cro/nicas Indi/genas Mexicanas), Historia 16,
1985.

* Mayor, Federico:
Opening Speech at the Conference on "Scientific and Technological
Cooperation in Africa", Nairobi, March 1994.

* Maxwell, Kenneth:
Pombal, paradox of the enlightment, Cambridge: Cambridge University Press,
1995.

* Nicolau, Juan Carlos:
La Sociedad de Ciencias Fisicas y Matematicas de Buenos Aires (1822-1824),
Saber y Tiempo, vol. 2, pp. 149-160, 1996.

* Orellana C., Mauri/cio:
Resumen de las Clases del Curso de Historia de la Matema/tica en Ame/rica
Latina y Venezuela, Caracas: Universidad Pedago/gica Experimental
Libertador, 1991 (mimeographed).

* Pyenson, Lewis:
Cultural Imperialism and Exact Sciences. German Expansion Overseas
1900-1930, New York: Peter Lang, 1985.

* Ramos, Gerardo:
El desarrollo de la Matema/tica en el Peru/ in Yepes, Ernesto (editor),
Algunos aportes para el estudio de la historia de la ciencia en el Peru,
Lima: CONCYTEC, s/d; pp. 15-19.

* Ruiz Zun~iga, Angel (ed.):
Historia de las Matema/ticas en Costa Rica, San Jose/: Editorial de la
Universidad de Costa Rica, 1995.

* Saitta, Armando:
Il programma della Collezione storica, Bari: Laterza, 1955; p. 12.

* Sala Catala/, Jose/:
Ciencia y Te/cnica en la Metropolizacio/n de Ame/rica, Madrid: Theatrum
Machinae, 1994.

* Santalo/, Luis A.:
La Matema/tica en la Facultad de Ciencias Exactas y Naturales de la
Universidad de Buenos Aires en el peri/odo 1865-1930, Cordoba: Boleti/n
de la Acad. Nacional de Ciencias, vol. 48, 1970; pp. 255-273.

* Santalo/, Luis A.:
Evolucio/n de las Ciencias en la Republica Argentina 1923-1972, Tomo I:
Matema/tica, Buenos Aires: Sociedad Cienti/fica Argentina, 1972.

* Sahagu/n, Fray Bernardino de:
Historia General de las cosas de Nueva Espan~a, 2 vols., Mexico: Alianza
Editorial Mexicana, 1989; Tomo 2, p. 478.

* Sertima, Ivan van:
They Came Before Columbus, New York: Random House, 1976.

* Silva, Clo/vis Pereira da:
A Matema/tica no Brasil. Uma Histo/ria do seu Desenvolvimento, Curitiba:
Editora da Universidade do Parana/, 1992.

* Thorndike, Lynn:
The Sphere of Sacrobosco and its Commentators, Chicago: The University of
Chicago Press, 1949; p.1.

* Trabulse, Eli/as:
Ciencia y Tecnologia en el Nuevo Mundo, Mexico: El Colegio de Me/xico,
Fondo de Cultura Economica, 1994.

* Zaslavsky, Claudia:
Africa Counts: Number and Pattern for Teachers, New York: Lawrence Hill,
1979.