Instituto de Matemáticas, UNAM

The Instituto de Matemáticas of the National Autonomous University of Mexico (UNAM) is the oldest mathematics research institution in Mexico. It consists of a primary campus in the Ciudad Universitaria of UNAM in Mexico City as well as three satellite units located at UNAM campuses in Cuernavaca, Juriquilla, and Oaxaca. Areas of investigation at the institute include algebra, analysis, combinatorics, partial differential equations, probability and topology. Faculty are also actively involved in the graduate programs of UNAM.

The Instituto de Matemáticas supports and administers the Casa Matemática Oaxaca, the counterpart of Banff International Research Station which hosts frequent research workshops in all areas of mathematics. The Cuernavaca unit is also host to the Laboratorio Solomon Lefschetz (LaSoL), a collaboration with the French National Centre for Scientific Research dedicated to strengthening mathematical ties between the two countries. A former division of the Instituto de Matemáticas in Morelia, Michoacán has become the Centro de Ciencias Matemáticas, an independent research center within UNAM.

Background

In 1637, the School of Medicine of the Royal and Pontifical University of Mexico (the predecessor institution of UNAM) appointed friar Diego Rodriguez (1596-1668) as chair of astronomy and mathematics, marking the beginning of formal mathematics education in Mexico. This chair was later occupied by Carlos de Sigüenza y Góngora before disappearing in the early 18th century, leading to a period of prolonged stagnation of mathematics education in the colony. By the turn of the 19th century, analytic geometry and differential and integral calculus was incorporated into university curricula. During his travels in Mexico, Alexander von Humboldt remarked upon the impressive mathematical formation of the students of the School of Mines. Under the government of Benito Juárez, Gabino Barreda was appointed to direct the newly founded National Preparatory School (now part of UNAM) and instituted significant educational reforms. Barreda authored calculus textbook aimed at students of the school, which strongly emphasized mathematics and the scientific method.

The National University of Mexico was founded in 1910 with mathematics professor Eduardo Prado (1858-1914) of the Heroic Military Academy as an early faculty member. At this time, the university consisted of the National Preparatory School, the Secondary School for Women, Schools of Fine Arts, Commerce and Political Science, Jurisprudence, Engineering, Medicine, as well as the Normal and Higher Studies Schools. A division of the School of Higher Studies was dedicated to exact sciences and physics, though its mathematics course offerings were scarce. In 1925, the School of Higher Studies became the Faculty of Philosophy and Letters, abandoning scientific pretenses.

In 1932, the Faculty of Philosophy and Letters began offering regular courses in advanced mathematics under the direction of Nápoles Gándara. In 1934, the university hosted a series of lectures by Dutch-American mathematician Dirk Struik who visited at Gándara's invitation. The success of this visit led to university rector Manuel Gómez Morín proposing creation of a separate School of Physical Sciences and Mathematics, which began to operate from March 1, 1936. Research institutes in physics and mathematics were proposed soon afterwards, on December 1, 1937. About one year later, the university council approved the creation of these institutes and the Instituto de Matématicas finally began operations on June 30, 1942 under the direction of Nápoles Gándara.

First years

The Instituto de Matématicas began its activities in a room of the Palace of Mines in the historic center of Mexico City, which also housed the School of Engineering of UNAM, as well as the recently created School of Sciences and Institute of Physics. The institute consisted of three departments: Pure Mathematics which was headed by Alberto Barajas and Roberto Vázquez, Applied Mathematics under Carlos Graef, and Logic and Foundations under Francisco Zubieta. These four researchers and the director comprised the entire faculty of the institute.

After its founding, the first goal that the institute set for itself was the organization of the first National Congress of Mathematicians. In that congress, the Instituto de Matématicas presented its several organizational purposes:

(a) carrying out research;

(b) sending researchers abroad to deepen their knowledge;

(c) inviting foreign researchers to the institute to hold specialized seminars;

(d) the creation of a library specialized in mathematics;

(e) the organization of national conferences in mathematics;

(f) the organization of conferences of international character to be held in Mexico;

(g) publication of research articles.

In this initial meeting, the idea for the formation of the Sociedad Matemática Mexicana (Mexican Mathematical Society) was also presented, becoming a reality on June 30, 1943.

In 1953, the institute moved from the Palace of Mines to the newly constructed Ciudad Universitaria south of the historic center of Mexico City, occupying the 6th and 7th floors of the Tower of Sciences in the center of the new campus.

The frequent visits of distinguished U.S. mathematicians George Birkhoff and Solomon Lefschetz in the years from 1944 to 1966 also indelibly marked mathematics at the institute and in Mexico during this time. With the founding of the institute coming a few months after the attack on Pearl Harbor which thrust the U.S. into World War II, and given the relevance of mathematics to military tactics, the American government considered in beneficial to supervise the development of mathematics in Mexico and the rest of Latin America. George Birkhoff of Harvard University was first charged with this role, and he had a great influence on the early research conducted at the institute. Birkhoff participated in the mathematical physics work of Barajas and Graef, as well as the geometry work of Roberto Vázquez and Javier Barros Sierra. Thanks to their relationship with Birkhoff, Barajas and Graef also visited Harvard. Birkhoff further organized a campaign for book donation to the library of the institute (now known as the Sotero Prieto Library) among his Harvard colleauges.

After Birkhoff suddenly died in 1944, oversight of Mexican mathematics research fell to Solomon Lefschetz. Such was his influence and support that the Mexican government honored him with the Order of the Aztec Eagle. Among his acts benefiting the institute was the administration of a scholarship program for young researchers and bright graduates of the UNAM School of Sciences to go to Princeton University to obtain their doctorates.

Further, Lefschetz gave many seminars and focused energy on fomenting research at the institute in the areas he considered important, such as algebraic geometry, algebraic topology, and differential equations. In 1956, with Lefschetz' essential support, the Instituto de Matématicas organized the International Symposium of Algebraic Topology held at Ciudad Universitaria, attracting the most noted specialists in that area. The talks given at this event were later collected in memoirs published in 1958 with the support of UNESCO. In 1959, the institute organized the International Symposium of Differential Equations with similar characteristics.

References

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