aerial spraying

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A mathematician finds his way through adversity

A diplomatic conflict between Ecuador and Colombia stemming from the controversial aerial spraying of herbicides onto coca fields as an antidrug measure does not sound like a likely subject for mathematical research. But as Ecuadorian mathematician Hermann Mena was finishing his Ph.D. in 2007, he thought his research might be able to provide some answers that could help settle the dispute. Mena’s attempt to determine whether Colombia had respected the no-spraying zone along the border that was meant to keep the herbicide glyphosate from drifting into Ecuador went on to become a highlight of his young career.

But while Mena found opportunities to grow as a mathematician in his native Ecuador, he was also confronted with bureaucracy and a lack of autonomy. Eventually, after failing to be promoted to full professor, Mena decided to leave the country to pursue his research elsewhere. Today an assistant professor at the University of Innsbruck in Austria, Mena, 36, nonetheless continues to contribute to Ecuadorian science, and he encourages students to pursue their passion for mathematical research wherever they are.

My main motivation was, and still is, improving science in my country.

–Hermann Mena

A blossoming interest

Mena didn’t have an easy path into mathematics. Born to a family of modest means in the largely indigenous city of Otavalo, he had to balance school with assisting his grandfather in his blacksmith workshop to help support his family. From an early age, Mena also nurtured a passion for sports, often skipping homework to play soccer. One day, upon discovering that he hadn’t completed his math assignment, “a teacher punished me by making me stand in front of the class and say I was no good at math,” Mena recalls.

But when he was about 15, Mena, whose family had moved to the capital city Quito, surprised his math teacher one day by formulating a theorem that partially solved a challenging mathematical problem. This and other similar episodes encouraged him to pursue his knack for mathematics. He went on to earn a Bachelor of Science degree in the natural sciences and engineering from the National Polytechnic School (EPN) in Quito, followed by a Master of Science degree in pure mathematics. For his master’s thesis, Mena worked on a mathematical model of the astrophysical phenomenon of solar flares.

In 2002, just as he was finishing his master’s degree, the first Ph.D. program in mathematics to be offered at an Ecuadorian university became available at EPN. The program—which was run in collaboration with the Technical University of Berlin (TU Berlin) and the German Academic Exchange Service, a funding organization that supports the international exchange of students and researchers—involved joint supervision by advisers in the two countries and research stays in Germany. Volker Mehrmann, a TU Berlin professor who taught classes at EPN as part of the program, says it aimed to fill a void. Before then, “you could not get a Ph.D. [in math] in the country. All the teachers had been educated abroad,” Mehrmann says.

Hermann Mena

Hermann Mena

Courtesy of Hermann Mena

Mena had found some opportunities to do his Ph.D. abroad, but with the new program in place, he decided to stay at home. “My main motivation was … showing … people that one can do good quality research in a developing country like Ecuador,” he says. Mena did his Ph.D. at EPN under the supervision of Chemnitz University of Technology mathematician Peter Benner (now at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg), in the area of optimal control—a branch of applied mathematics that tackles problems like how much water must be diverted from a river to avoid flooding a city.

With mathematics still a young research field in Ecuador, Mena suffered from a lack of local access to certain areas of expertise, he admits. Overcoming such obstacles required much hard work, determination, and encouragement by his father, who “always told me to do what I love,” Mena says. Yet, for aspiring mathematicians in the less developed countries, “[t]here is no good reason to give up,” Mena says. “In math, you don’t need a laboratory. A computer and a few books are enough.”

By the time Mena earned his doctorate in 2007, he already had two peer-reviewed papers in international journals under his belt. “He was the best student in the class, and those were selected students,” says Mehrmann, who taught Mena during his visits to EPN. Upon graduating, Mena decided to leave Ecuador for a year to do a postdoc in Benner’s group in Chemnitz. Upon returning, he took an associate professorship at EPN, intending to help improve science in Ecuador and to be closer to his family.

A hard-to-crack problem

As he was beginning his professorship, in response to one of the Ecuadorian government’s first calls for science projects to fund, Mena proposed to look into Columbia’s aerial spraying of glyphosate, an issue heavily covered by the Ecuadorian press at the time. Starting in 2000, with support from the U.S. government, Columbia had intensively sprayed the herbicide to try to destroy the country’s illegal coca fields. With Ecuador’s growing concerns over the potential drift and toxic effects of glyphosate, in 2005 the two countries signed an agreement that Colombia would not spray within 10 kilometers of the border. In 2008, however, Ecuador filed a lawsuit at the International Court of Justice at The Hague, alleging the Colombian spraying had caused damage to people, crops, and the environment on Ecuadorian ground and demanding indemnification and prevention of further contamination. Mena’s proposal to take an optimal control approach to model the aerial glyphosate spray drift along the Ecuador-Colombia border won him government funding.

Mena provided a mathematical model and numerical simulations of the phenomenon, but the next step—using evidence of the presence of glyphosate in Ecuador to determine whether Colombia had respected the no-spraying zone—proved more challenging. Although the work provided some evidence supporting the claim that Colombian planes had failed to respect the limit, Mena did not feel that the results were sufficiently certain for him to testify at The Hague, because parameters such as the height and velocity of the Colombian planes were unknown. Estimates of data like temperature and wind velocity also had to be used in some border areas, which were under control of FARC (the Revolutionary Armed Forces of Colombia) and were not easily accessible for measurements, he adds.

Given the limited information available, Mena “did the best one can do scientifically,” Mehrmann says, commending Mena’s effort to address a problem relevant to society. Moreover, although the two countries reached a friendly settlement in 2013 and Colombia announced the halt of the aerial spraying last May, Mena’s model is not specific to the herbicide and may be applied to similar situations.

Although it is difficult to quantify how much, Mena also contributed more broadly to the development of mathematical research in Ecuador. Part of the $200,000 grant he received for the glyphosate project went into building a computational cluster at EPN, where the Center of Mathematical Modelling in Key Development Areas was created a few years later. Furthermore, Mena helped shape the future development of mathematics and basic sciences at the Yachay City of Knowledge, an ambitious national government project to create a leading academic and industry hub in northern Ecuador.

Finding a home

Despite his achievements, Mena soon felt confronted with insurmountable obstacles. In Ecuador, funding is always a great concern, Mena says. Also, “I was burdened with a lot of [teaching] hours and bureaucracy,” he adds. And Ecuadorian universities tend to be “very politicized and hierarchical, [which] is a general problem in underdeveloped countries.” Talented scientists who return after a stay abroad often don’t manage to persist in their objective of doing research in Ecuador, observes Mena’s former collaborator Enrique Quintana Ortí, a professor at the Jaume I University in Castellón de la Plana in Spain, “because … infrastructure is scarce and administrative tasks are abundant.”

Hermann Mena running a triathlon in Berlin in 2012

Hermann Mena running a triathlon in Berlin in 2012

Credit: FinisherPix.com

The last straw came in 2012, when, following a selection process that Mena qualifies as controversial, he failed to be appointed as a full professor at EPN, a turn of events that “hurt [me] a lot,” he says. Mena eventually decided to leave for Austria, taking his current assistant professorship at the University of Innsbruck in 2013. “In Europe, professors are much more autonomous,” he says.

Today, Mena continues to explore complex optimal control problems, most of them closely related to his personal interests. For example, over the years he has pursued his passion for sports as an amateur triathlon athlete, and he is now developing a mathematical model for shoulder and arm movements to try to help climbers optimize their performance. In another project, Mena has set out to identify the optimal cooling process for making stiff and malleable pieces of rail out of steel. “It reminds me of how blacksmiths cool a sword,” he says, hearkening back to his days in the workshop with his grandfather.

But “my main motivation was, and still is, improving science in my country,” Mena says. With funding from the Austrian Science Fund, Mena is working on producing a simulation of El Niño, which “causes millions [of U.S. dollars] in damage in Ecuador,” to better understand the climate phenomenon. “The idea is that the results of the project are available to authorities,” Mena says, adding that he is working on building ties with Yachay Tech to ensure adequate transfer of knowledge. Mena also continues to support Ecuadorian students by regularly forwarding them announcements of summer schools or study abroad opportunities and writing them recommendation letters.

In many ways, “doing mathematics in an underdeveloped country is very difficult,” Mena says. But this isn’t to say that mathematicians who live there cannot gain a good education or do good research, he adds. In spite of the difficulties, so far “I got 90% of my [published] scientific results in Ecuador. … If I had the opportunity to go back to my country to do math, I would do it.” Regardless of his bittersweet experience, “I always encourage Ecuadorian students to do research, and above all fight for what they want.”

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