Spanish Heritage in Mathematics and Mathematics Education

Abstract

On the occasion of the 12th ICME, the Spanish Committee of Mathematics Education decided to prepare a national presentation entitled Spanish Cultural Heritage.

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On the occasion of the 12th ICME, the Spanish Committee of Mathematics Education decided to prepare a national presentation entitled Spanish Cultural Heritage.

The presentation takes the form of a series of posters, each of which has a special focus, showing relevant historical events identified according to time and institutions. As a whole, the posters outline a comprehensive historical trajectory devoted to the Hispanic Heritage.

The relevance of mathematics in the relations between Spain and America has remained unbroken since its beginning 520 years ago. Julio Rey Pastor emphasizes the importance and scope of this heritage for its scientific and technological use and its benefits since the discovery of America. Since then, throughout 520 years of continuous cultural cooperation, the mathematical background shared by Spain and the American Republics, people and countries, that have remained solid and permanent.

To present the Spanish Heritage in the ICME 12 of Seoul (Korea), from the Education Commission of the CEMAT (Spanish Mathematics Committee) have been prepared 27 posters, which set out key moments, characters and events in the history of mathematics.

The list of themes chosen is as follows:

• 1. Spanish Heritage in Mathematics and Mathematics Education.

• 2. Mathematics and Science in the Discovery of America.

• 3. The Founding of the First American Universities.

• 4. First Mathematical-Scientific Publication in the New World.

• 5. The House of Trade: Navigation, Cartography, and Astronomy.

• 6. The 16th-Century Mathematics Academy: Philip II, Siliceo, Juan de Herrera.

• 7. Science and Technology in the 16th Century.

• 8. Mathematics in the Baroque Period in Spain.

• 9. Scientific Policy of the First Bourbons. The Jesuits and Mathematics.

• 10. Enlightenment Mathematics. The Reforms of Charles III.

• 11. José Celestino Mutis. An Enlightened Scientist in the New World.

• 12. Jorge Juan and Antonio de Ulloa. Meridian measurement in Quito.

• 13. Educational Reforms in Hispano-America, based on the 1812 Constitution.

• 14. The Compendium of Pure and Mixed Mathematics by D. José Mariano Vallejo.

• 15. 19th-Century Mathematics.

• 16. The Metric System in Textbooks in the Second Half of the 19th Century.

• 17. The Mathematicians of Scientific ‘98.

• 18. Andrés Manjón and the Ave María Schools at the end of the 19th Century.

• 19. The Spanish Republican Exile: the Mathematicians in America.

• 20. Researching Together: Return Journeys.

• 21. The Iberoamerican Mathematical Olympiad.

• 22. Research Centers.

• 23. Journals, research and collaboration in Mathematics Education.

• 24. ICME 8 Seville (Spain), July 1996.

• 25. Miguel de Guzmán (1936–2004) Academic, scientific, and educational legacy.

• 26. Mathematical Research in Ibero-America, Spain and Portugal.

• 27. Spanish Mathematics: the last 20 years.

The posters has been prepared by:

• M. de León and A. Timón, from the Institute of Mathematical Research (ICMAT).

• J. Peralta, from University Autonomous of Madrid.

• A. Maz; N. Adamuz; N. Jiménez-Fanjul; M. Torralbo and A. Carrillo de Albornoz, from the University of Cordoba.

• L. Rico; E. Castro-Rodríguez; J. A. Fernández-Plaza; M. Molina; M.C. Cañadas; J.F. Ruiz-Hidalgo; J.L. Lupiáñez; M. Picado; I. Segovia; I. Real and F. Ruiz, University of Granada.

• I. Gómez-Chacón; M. Castrillón and M. Gaspar, from the University Complutense of Madrid.

• M. Sierra and M.C. López, from University of Salamanca.

• B. Gómez, L. Puig and O. Monzó, University of Valencia.

The main objective of this work was to present the joint activity on mathematics and mathematics education, thought and written in Spanish, conducted by Spanish and American in more than 500 years of history and shared culture. We will stress the links established between Americans and Spaniards, as demonstrated by the information presented. We will underscore the scientific, technological, or cultural value of these events, their subsequent implications, and the social impact they produced in their time.

As there is a common language, a shared history and culture, there are ways of thinking and doing math based on that language, that culture and that history. This work aims show and claim the shared heritage in mathematics and mathematics education in this community. We have done a selection of the information presented in the posters and we will comment it here.

We have organized the posters considering five general comprehensive periods:

• 1. Discovery and colonization.

• 2. The Creole society.

• 3. The Century of Independence.

• 4. 20th Century: mutual assistance and help.

• 5. Current cooperation.

Summary of key moments and ideas of the above mentioned periods.

• 1. Mathematics and Science in the Discovery of America.

On October 12, 1492, a Spanish expedition commanded by Admiral Christopher Columbus arrived at the island of Guanahani and took possession of the land in the name of their Majesties Isabella of Castile and Ferdinand of Aragon. This act of Discovery is essential to the birth of historical modernity and of science. It marks the origin of a sociocultural community, the Ibero-American community, based on the unique relationship between Spaniards and Americans. Columbus’s goal was to reach Asia, that say, the island of Cipangu (Japan), which was thought to be at the same latitude as the Canary Islands. Columbus was not trying to discover a new continent, but rather to “reach the East by sailing West.” The information that Columbus used involved several significant errors and to understand them it was needed a big change of ideas. Toscanelli’s map, reflects the ideas of many navigators and geographers of the period, describes the route that Columbus believed he had travelled. He thus believed that the distance from the Canary Islands to Japan was 800 leagues by west (4,500 km), when it was actually about 3,500 leagues (19,500 km). These data were sufficient grounds for undertaking his first and the subsequent voyages. When Columbus arrives in the Antilles, he was convinced that he has reached the western coast of Asia hence his naming these lands the West Indies (Fig. 1).

Fig. 1

Mathematics and science in the discovery of America

Institutions: the first Universities. Starting with their first years in the colonies, the Crown, the Church, and the religious orders intervene in the area of education to teach and train clergy, government officials, and the middle classes. Their knowledge was classified into study in the trivium (grammar, rhetoric, and logic) and the quadrivium (arithmetic, geometry, music, and astronomy). Founding the Universities and Colleges in America is a historical feat and cultural phenomenon of prime importance, particularly in the first half of the 16th century. The first universities were the universities of Santo Domingo, Lima and Mexico, that were respectively founded in 1538 (Santo Domingo) and in 1551 (Lima and Mexico).

• 2. The Creole Society.

To talk about the Creole society we have fixed our attention in the following ideas:

• Scientific Policy of the First Bourbons. The Jesuits and Mathematics.

• Enlightenment Mathematics. The Reforms of Charles III.

• José Celestino Mutis. An Enlightened Scientist in the New World.

• Jorge Juan and Antonio de Ulloa. Meridian measurement in Quito.

At the beginning of the 18th century, the Jesuits assumed responsibility for educating the nobility, through Seminaries for Nobility, which began in Madrid. This institution’s model of teaching spreads to Barcelona, Valencia, Gerona, and other cities. Based on its model, new centers are founded throughout the 18th century. In Mexico, the Royal Academy of San Carlos of the Noble Arts of New Spain is founded. These centers also trained the American elites. The Seminaries of Nobility become one of the most important centers of teaching and research in America. The Jesuits authored fertile textbooks in mathematics.

José Celestino Mutis y Bosio (Cadiz 1732; Bogotá 1808) Botanist, doctor, astronomer, and mathematician. Mutis developed important scientific work on American soil. He gave the inaugural speech for the Chair of Mathematics at the College of Our Lady of the Rosary in Santa Fe de Bogotá. There, he held the positions of rector and director. He determined the coordinates of Santa Fe de Bogotá, observed an eclipse of a satellite of Jupiter, and was one of the observers of the Transit of Venus on June, 1769.

Jorge Juan y Antonio de Ulloa. They participated in the expedition from 1735 to 1744 to measure an arc of 1º of latitude near the equator and one near the pole, to determine the lemon or orange shape of the earth.

The Royal Academy of Sciences decided to undertake the task of obtaining precise data from two meridian positions at two locations on Earth: Lapland (North Pole) and the Viceroyalty of Peru (the equator). To do this, two expeditions were organized. If the measurements obtained by both expeditions were the same, the Earth was sphere-shaped. If the measurement was greater at the pole, there was flattening at the poles.

If the polar measurement was smaller, the French were right and the lemon shape shall be the model. To carry out the expedition to the cities of Quito and Cuenca, located today in the Republic of Ecuador (Fig. 2).

Fig. 2

Jorge Juan and Antonio de Ulloa. Meridian measurement in Quito

• 3. The Century of independence. We have fixed our attention on the following subjects.

• Educational Reforms in Hispano-America, based on the 1812 Constitution.

• The Compendium of Pure and Mixed Mathematics by D. José Mariano Vallejo.

• 19th-Century Mathematics.

• The Metric System in Textbooks in the Second Half of the 19th Century.

• The Mathematicians of Scientific ‘98.

Conception of education. Spanish resistance to Napoleon’s invasion in 1808 led to the formation of the Courts of Cadiz, which developed the Constitution of 1812, oriented ideologically to exalt and safeguard individual liberty.

The Constitution’s ninth title, dedicated to education, articulated the liberal idea of education, defending the idea of general, uniform education for all citizens and the need to form a Council for Public Education. This Council prepared a report that can be considered the most representative document on liberal ideology in matters of education. The report was published in Cadiz on September 9, 1813, under the following title: Report of the Council created by the Regency to propose the means for proceeding to regulate the various branches of Public Education.

It was established that “education must be universal, uniform, public, and free, and it must enjoy liberty.” This Report formed the basis and origin of the educational reforms put into effect throughout Hispano-America after the revolutions that led to the independence of the Spanish colonies.

The 19th century is a turbulent period in the history of Spain. It begins with the invasions of Napoleon’s armies in 1808 and ends with the Spanish-American War in 1898, known as the disaster of ‘98. The beginning of the 19th century brings the independence of the former colonies in America, giving rise to the new American republics. Spain loses its status as world power. The 19th century ends with the loss of Cuba, Puerto Rico, and the Philippines and the defeat of the Spanish fleet in Santiago, Cuba. Spain concludes its political presence in America. Spain is aware of its cultural and educational decline, a feeling aggravated by the loss of its colonies. It is thought that the military defeat was caused in good part by the country’s scientific and technical backwardness: the crisis of ‘98 (Fig. 3).

Fig. 3

19th-century mathematics

• 4. 20th Century: mutual assistance and help.

Where we are? Who are the leaders? We choose five points to reflect about our common work during the 20th Century.

• Andrés Manjón and the Ave María Schools at the end of the 19th Century.

• The Spanish Republican Exile: the Mathematicians in America.

• Researching Together: Return Journeys.

• The Iberoamerican Mathematical Olympiad.

• ICME 8 Seville (Spain), July 1996. Current research and cooperation (Fig. 4)

  Fig. 4

  

  The Spanish Republican exile: the mathematician in America

  .

• 5. Current cooperation.

To describe this point we selected the following reflections:

• Research Centers.

• Journals, research and collaboration in Mathematics Education.

• Miguel de Guzmán Ozámiz (1936–2004) Academic, scientific, and educational legacy.

• Mathematical Research in Ibero-America, Spain and Portugal.

• Spanish Mathematics: the last 20 years (Fig. 5)

  Fig. 5

  

  Journals, research and collaboration in mathematic education

  .

The goal of the presentation was to show and underline the relevance of the cultural and scientific cooperation in mathematics and mathematics education between Spain and the American Republics over the last 500 years. The presentation seeks to publicize this common mathematical heritage by emphasizing its importance and the far-reaching influence these relationships have had and continue to have for science, technology, and education in our countries.