## Mathematics in Chile, a half-century of steady development

During the International Congress of Mathematicians "ICM 2014", held in South Korea, the Mathematical Society of Chile was invited to present an overview of the rapid mathematical development in Chile in the last 50 years. We give below a version of their presentation:

**Mathematics in Chile, a half-century of steady development**

Chile is located on the very tip of South America, occupying a long strip of land between the Andes Mountains and the Pacific Ocean. With almost 800,000 square kilometres of territory, reaching from the northern limits with Peru all the way down to Antarctica, Chile has an incredible variety of climates, ecological diversity and natural wonders.

Situated within the Pacific Ring of Fire, and located atop the Nazca and South American tectonic plates, Chile has a population of around 17 million people, and today is one of South America's most stable and prosperous nations. Its unique geography also allows for rich mineral deposits, primarily copper and nitrates, as well as significant agricultural resources. Economic development is based in commodities, including copper exports, which reach about a third of the world's copper supplies. Additionally, agriculture, particularly fruits and wine production, and tourism represent two other major sources of income for the Chilean economy.

Biology, in particular ecology and natural sciences, was the first of the sciences to be developed in Chile. Chemistry and Physics soon followed. The starting point of Chilean Mathematics can perhaps be traced back to 1964, fifty years ago, with the return of the first Chilean Mathematician doctorate Jaime Michelow, after finishing his Ph.D. in the United States.

Although mathematical research in Chile only began to take off in the late seventies, it is growing vigorously and the country is becoming a regional centre of mathematical research. Chile's rate of mathematical publications per capita has been increasing sharply. It now doubles that of its nearest Latin American competitor.

Nonetheless, this rate is still about a third of that of other developed countries, so that there is ample room for growth and cooperation.

Mathematics in Chile before 1960 was limited to that required for the education of professionals. Between the years 1890 and 1930, essential contributions to academic curricula were made by German mathematicians hired by the Chilean government for this specific purpose, but there was no centralized effort to pursue mathematical research and development.

During the sixties, the only options for those who wished to study mathematics in Chile were the Instituto Pedagógico, which specialized in training school teachers, or the Schools of Engineering of some universities.

During this time, a state decision was made to prepare academics in basic sciences for both teaching and research. Several Chilean universities, including the Universidad de Concepcion (1960), de Chile (1965) and Técnica del Estado (1967), created the first programs of Bachelors in Science and Mathematical Engineering. Most of the graduates of these pioneering programs pursued graduate studies abroad.

Specifically, the government decided to create the Department of Sciences at the University of Chile, aiming to train scientists in Basic Sciences including Biology, Chemistry, Physics, and of course, Mathematics. These high quality and high performance programs had mostly international faculty members, who settled in Chile to watch the ongoing political process.

In 1970, reflecting the interest of investigators to pursue further studies in Mathematics locally, the first Master in Mathematics program in Chile was created. The Bachelors in Academic Mathematics (LAM for its initials in Spanish) trained the first generation of graduate mathematicians in Chile.

The original goal of this master program was to train faculty members of Chilean universities who had no formal mathematical training, giving them a solid foundation for further research and teaching; in the beginning its Faculty consisted mostly of young and enthusiastic foreign mathematicians.

Later on, this program grew to also encompass young students, who under fellowships granted by the Ford Foundation continued their graduate studies abroad.

In the mid 60's, the department of mathematics was created in the School of Engineering at the Universidad de Chile and the specialization in mathematical engineering was developed. At the end of the 90's, this department gave origin to the Center for Mathematical Modelling, which has played an important role in the growth of mathematical research in Chile and in the formation of PhD's in this area.

At the beginning of the seventies, about ten Chilean Mathematics Ph.D.s had returned to the country after finishing their degrees abroad. In parallel, between 1970 and 1980, about a hundred mathematical bachelor degrees were granted in Chile from the newly founded University math departments. Highlighting the interest and commitment of this new generation of Chilean scientists, many of them went on to pursue graduate programs in the US and France. Mathematical research per se in Chile was still only beginning, and the training of upcoming researchers remained in the hands of internationally renowned faculty.

In 1973, the military coup d'etat took place in Chile, and universities lost many of their students and academics. In addition, international faculty working in Chile emigrated, and mathematical progress in Chile was stalled until the beginning of the 1980s, when a massive return of mathematical doctorates abroad began.

By 1981, there were around 45 Chilean Doctors in Mathematics working in the country, and a similar number of them remained abroad.

A landmark event in the development of Chilean science occurred around that time. In 1981, a national state program for individual competitive grants was created (FONDECYT), following the template of the National Science Foundation in the US. In 1982, two major grants were awarded for Mathematics, and this number increased to six grants in 1983. The awards were US $16,000 annually. Currently, in 2014, FONDECYT funds 230 grants for the area of Mathematics, each for US $ 35,000 annually.

The first doctorates in Mathematics programs in Chile were created at the Universidad Católica (1972) and Universidad de Chile (1986). At the same time, Chilean students going abroad for their degrees enlarged the spectrum to other countries, such as USA, France, Germany, and Brazil.

The Chilean Mathematical Society (SDMACHI) began to meet informally in the late 1970's; it became legally incorporated in 1983, when several young Ph.D.'s returned to the country after obtaining their degrees abroad.

During those years of political oppression, SDMACHI ensured the continuance of science development in Chile, replacing the frozen state and government initiatives towards science. With this is mind, the Chilean Mathematical Society began to connect and repatriate Chilean mathematicians abroad. In 1981, it organized the first Mathematical Symposium in Chile, a quadrennial event that remains to this day.

SDMACHI also established a schedule of one national meeting annually. Additionally, two regional meetings, in the North and South of the country, and a mathematical week in Valparaíso, are regular events each year. All these general meetings now attract participants from neighbouring countries, such as Argentina, Brazil, Peru and Bolivia.

In 2010, SOMACHI organized the First Joint Meeting with the American Mathematical Society; the event was an acknowledgement to Chile's level in mathematics, attended by mathematicians from all the Americas and the rest of the world.

The Chilean mathematical community has always considered contributing to middle and high school math education one of its responsibilities. Throughout the years, it has organized teacher-training workshops, and collaborated with the Chilean government to plan and execute high school curriculum and set higher standards for Math teachers. Additionally, it has published textbooks for teacher training and development, and a magazine for high school mathematics teachers.

SOMACHI also organizes the National Mathematics Olympiad, a yearly event meant to discover young talented mathematicians. Aimed at middle and high school students, it offers an amazing opportunity to broaden their scientific and cultural horizons. Since its inception in 1989, the Math Olympiads have attracted about 78.000 students, and among those who have participated we find renowned professionals of many areas, as well as active mathematicians. Chilean mathematical delegations have thus represented our country at the International Mathematic Olympiad since 1994.

Another important landmark in the development of Chilean mathematics was the granting of a triennial award in 1984 by the United Nations Development Program (PNUD). Assembled by the Chilean mathematical community, the administration of this award was handled by SDMACHI.

The PNUD award funded research fellowships and international mathematician scholar visits to our country. This award allowed the Chilean mathematical community to purchase 40 different high-impact Mathematic journal collections for the first time. Most importantly, it set the standards for most future scientific funding research initiatives, by assigning the funds based on strict scientific quality.

The PNUD award thus had a quantitative and qualitative impact in Chilean mathematics, so much that Chile then entered the International Mathematical Union (IMU) at level 11.

The Andes Foundation, a private Chilean institution, strongly supported the development of mathematics in Chile from 1984 to 2004. Its guiding principles set standards for future governmental science funding policies. Its particular consideration towards the Chilean mathematical community meant supporting doctoral fellowships, internships abroad, and math Olympiads, among others.

After the public referendum that ended the military dictatorship in 1990, the development of mathematics in the country had a significant acceleration. Several Chilean mathematicians returned, and a number of new initiatives for research funding were initiated by the succeeding governments. There was also renewed interest from abroad to increase collaboration and to study and work in Chile.

After the return of democracy in 1990, the Chilean government has funded several scientific research initiatives, including the following.

Ring Grants: funding of research projects with a strong collaborative and multidisciplinary core, where several groups from different institutions can apply individually or as a consortium.

Millennium Science Initiative: funding for the formation of new Institutes and Research Centers in Natural and Exact Sciences.

Basal Financing and FONDAP: funding for the formation or maintenance of Centers of Science and Technology of Excellence. The main goal of this funding opportunity is to power Chile's economic development through substantial long-term funding.

Presidential Chairs in Science: awards that directly supported the work of investigators with a distinguished career.

By 1994, Chile has 93 mathematicians, with 109 publications that year. The first lines of research are formalized, and two doctorate programs are operating out of universities.

In the year 2000, researchers from the department of mathematical engineering of the Universidad de Chile created the Center for Mathematical Modelling with financing from the program FONDAP of CONICYT. Its objective is the development of mathematical modelling of complex problems from engineering and other sciences. The CMM is also an associated research centre with the National Center for Scientific Research of France (CNRS-UMI 2807).

At this time as well, research nodes away from the capital of Santiago are developed, including the Universidad de Talca, Universidad Católica del Norte, Universidad Técnica Santa Maria, and Universidad Católica de Valparaiso.

At the end of the 90's decade, mathematical research in Chile reached a peak in production, both in quality and quantity of publications generated. Presently, there are several research areas coordinated into strong research groups, holding permanent seminars and organizing periodic international events of a specialized character. This vibrant and dynamic mathematical community attracts students and investigators from around the world.

In 2005 the Chilean Academy of Science together with the Chilean Scientific Societies conducted a study of scientific research in Chile and devoted a chapter to mathematics. From the list of active researchers compiled then by the Chilean Academy of Science one can see that (in mathematics) about 28% were trained in the United States, 30% in Europe, 13% in Brazil, and 17% in Chile.

At present there are approximately 350 research mathematicians working in Chile: two for each 100,000 inhabitants.

In its 2005 study, the Chilean Academy of Science tried to give a rough measure of mathematical activity in Chile. It counted the yearly number of papers reviewed by the American Mathematical Society having at least one author based in Chile and divided by the Chilean population.

It concluded that in 2003 Chile was producing a yearly total of about 14 mathematical papers per million inhabitants. The corresponding figure for Uruguay, its nearest Latin American competitor under this measure, was nine. For Argentina it was seven , and for other countries like Mexico or Brazil the figures were still lower. For 2013 Chile's figure has risen to nearly 25, setting its activity level at nearly twice the nearest Latin American country. Although this is a sign of healthy growth in Chilean mathematics, it still has a long way to go.

Typical figures for developed countries are around 60 mathematical publications per million inhabitants. The Chilean government is conscious of this and has greatly increased the number of scholarships available to Chilean students for doctoral studies inside and outside Chile. Increased cooperation with Chile should result in a substantial increase in Chilean graduate students studying at universities abroad.

**Message from the President of the Chilean Mathematical Society**

I would like to extend my most grateful thanks to the International Mathematical Union for the opportunity to showcase the development of mathematics in Chile.

As with most stories, some details of this experience are uniquely Chilean and will not apply to the global picture. Some fundamental elements are simply not quantifiable , but perhaps learning from the Chilean experience can guide those who are now developing science policies in their own countries.

I would first like to highlight the spirit and disposition of the pioneers of mathematical development in Chile at the end of the sixties. They are examples of selflessness to our current generations, dedicating their research lives to the development of science with the utmost academic spirit and objectivity.

This was, of course , the foundation of a long-standing tradition of inter-institution and inter-group cooperation for Chilean mathematics, and of an objective and impartial funding allocation system , always choosing quality over quantity.

This spirit of cooperation and high-quality research became the core message of the SOMA CHI, who just like our pioneers, has always supported young researchers. For example, all of SOMACHI-organized scientific meetings in Chile have outstanding student scholarships, ensuring that young mathematicians can attend and interact with fellow researchers and leaders in the field . Twenty six years ago, SOMACHI also created the Math Olympiads, an event that has translated into a tangible increase in mathematicians in our country and has helped educate the public to the wonders of Mathematics.

In the beginning, we depended on international cooperation to help sustain and develop the budding mathematical network in Chile. Today, we still maintain those strong connections with the rest of the world, but we have come into our own in areas like education, publications and research. We believe that now has come the time to share our story with you, and hope that our experience in the development of mathematics in Chile will be useful for those who wish to follow.

**Main Mathematical Research Areas in Chile**

Biomathematics

Complex Geometry

Dynamical Systems

Functional Analysis

Group Theory

Inverse Problems and PDE Control

Mathematical Physics

Matrix Theory and Applications

Model Theory

Non-Associative Algebras

Number Theory

Numerical Analysis

Optimization Theory

Partial Differential Equations

Quadratic Forms and Integral Lattices

Representation Theory

Spectral Theory

Stochastic Analysis

Complex Geometry

Dynamical Systems

Functional Analysis

Group Theory

Inverse Problems and PDE Control

Mathematical Physics

Matrix Theory and Applications

Model Theory

Non-Associative Algebras

Number Theory

Numerical Analysis

Optimization Theory

Partial Differential Equations

Quadratic Forms and Integral Lattices

Representation Theory

Spectral Theory

Stochastic Analysis