From Math Olympiad to Diplomacy

Let’s start by talking about your role in the field of mathematics. Can you tell me what inspired you to pursue a career in mathematics and your specific concentration areas?

“It was the beauty, the universality, and the challenge of mathematics that attracted me to it. Also, the passion of my teachers when I was 11-12, [and] the mystery that sometimes surrounds mathematics. People often are in awe when you say that you are a mathematician or that you study mathematics. Plus there was a local math olympiad that was being organized. That made me want to advance in doing [and] reading more mathematics [as well as] solving more mathematical problems.
 

"My specialty, or specific concentration area, is related to combinatorial study of Representation Theory, the study of symmetries, and of algebraic and arithmetic algebraic geometry. That is the study of geometry using algebra and algebraic tools, and when you add arithmetic to it it means problems arising from number theory. That is my research focus, and the idea is to try and recognize patterns [as well as] collect objects because you have Combinatorics behind. One can say that I am a pure mathematician.”
 

Is pure mathematics more difficult than other types of mathematics?

“Not necessarily. For me, applied mathematics is more difficult. Pure mathematics, in this case, means that you are looking at problems purely from a mathematical point of view and you are studying them without necessarily looking for models to apply them to, outside of mathematics. But in reality, there is a unity of mathematics and even those that do pure mathematics end up contributing to applications of mathematics. Then there are some who do applied mathematics who advance the theory of pure mathematics. The two are two parts of the same [whole].”


"Can I make a comment on people who say they are 'not very good at math?'

“Often, when I meet people, and they find out that I am a mathematician there are two strong reactions. One is of the people who say “I’m not good at math!” and they are thankful that they have made it so far without mathematics. There is also the class of those that says ‘Oh I was always excellent at math,’ ‘I could have actually become a mathematician if I wanted to.’ Part of this is related to the fact that mathematics is generating strong emotions among people because mathematics is often used as a tool to rank students: at a university, at a high school, at other levels. I think that we need to change that because mathematics is not about ranking students. It should be a way of thinking that enriches everyone’s lives.

"Let’s say I am a writer. I would assume that the probability is very high that the person speaking with me is not the future Nobel Prize winner in Literature. [But] that doesn’t somehow generate these strong emotions among people [the same] as when you say that you’re a mathematician. This, I think, is something that we as a mathematical community need to address, and society as a whole. Because we lose many people, who just shut down their brains, because they say ‘math is not for me.’ While it’s true that you can thrive and have a very good life without mathematics, you can say the same thing about having a good life without knowing who Shakespeare was. But it would be a life which would not be as rich and as colorful.

"It is unfortunate that we present mathematics as something that is unique to all those ‘bright kids.’ There are many bright kids who are not mathematicians, and statistically many more [who are not mathematicians]. There is work somewhere that we need to do. The reality is that this is a problem, a challenge, everywhere around the world.”

I noticed you took this passion for math and formed the Kosovar Mathematical Society in 2008. Can you tell me more about this?

“In 2008, I obtained my Ph.D. from the University of Chicago and I was planning to go back to Kosovo. I wanted to do something to give back to the community that had helped me. Also, because I lived in Kosovo during a particularly challenging period during the 90s, I thought that it would be important to give back to the community. The direct contribution that I thought I could make was by creating a local math society, which I did together with a number of colleagues. We managed to then organize seminars, conferences, and a local version of the Math Olympiad. Then our participants could take part in the International Math Olympiad. That was important because, this way, many of my former students went through this path and some went to universities around Europe. Some even came to the U.S.

“For me, it was about using something that I had. Namely this experience, but also I had [become] somewhat famous in Kosovo and thought I should use my fame for something positive, and [to] extend this passion to a new generation. I am delighted that among these participants, these students, I have many who are extremely bright and talented. The challenge is how to keep that community together, because as with many countries around the world, there is this 'brain drain.' A community that stays together and that contributes to science [is not so easy to maintain] in a smaller country that doesn’t necessarily have the means. That is the next step, but I am very proud that I have some brilliant students who are doing very well.”

Can you explain what the International Math Olympiad is and why it’s important for mathematicians from Kosovo to attend?

“This is the most famous math competition for high school students [and] has been going on for decades now. [However], there is a tendency to reduce pre-university education math to these competitions, which is also wrong. This [competition] is one of the tools available to promote mathematics, to promote discussion among young mathematicians [and] young high school students, who are interested in mathematics. [As well as] to make sure local communities, in this case the math community in Kosovo, [are] connected and communicate with their peers around the world.

"This is what the International Math Olympiad is, but this is only one vector of operation of the Math Society that I created. Incidentally, we were supported by many mathematicians from around the world - it was not just a local initiative! It was…but I was helped by many international actors.

"Math is both a universal language and it can cause universal confusion. We [mathematicians] are here to make sure that the latter doesn’t happen too much.”

As a math professor, do you have any specific goals in educating the next generation of mathematicians? What do you hope to see for the future of mathematics?

“I attempt to approach it a little bit like a theater play: where it’s true there’s a light that shines over the stage - but the point is that you are trying to enlighten the audience. I just hope it’s not a Greek Tragedy when I teach! But my aim is to make sure students appreciate the mathematical thinking and structures, that they are able to then become critical thinkers, use the tools of mathematics to apply them in various walks of life, and of course the passion. I hope [this passion] is contagious, where they take whatever they want to do and move it one step further - advance it.

“So if they want to become mathematicians, that’s great! But they don’t have to become mathematicians. They can use mathematics in many professions. For me, when I am in front of my students, I try to also understand them and this is part of the challenge: making sure that what you are saying is relevant, not just to the syllabus but also making sure that [it] becomes relevant to their education. In the end, there’s this ‘noble’ idea of educating the future generation of those that will change the world. I am happy if I’m part of that effort. [However] in mathematics, you have to convey the material, some messages, and also this passion [for math].”

What level courses are you teaching here at the University of Maryland?

“I am teaching two [undergraduate] courses. One is 'Introduction to Calculus,' a 100-level course. The other is a 400-level course, mostly for math majors. It’s a course on groups, rings, and fields. This is abstract algebra. They are two different experiences. One course is a larger course with students who are not always thrilled to have another math midterm, but who have been very good about working hard. I am very happy that they’re taking my course. Then another smaller group of students who have already decided that they want to do math or will use math in their fields and so now they are learning more advanced notions.

“I’ve taught many courses and I like the challenge of both going in front of a somewhat skeptical audience and also in front of a hungry audience. That’s why I made the comparison [earlier] with theater play and a performance. You have to really give a lot of energy to make sure the messages go through. But I have been very positively impressed about what I have seen so far among the students here.

“The [benefit of] 'Universality of Mathematics' is its application in many fields. That’s why it’s a required course!”

You also held several respectable diplomatic positions between Kosovo and France in your lifetime. Does this have any overlap with your knowledge of mathematics, for those of us who may not understand diplomacy roles well?

“I think people are more inclined to understand what diplomats do than what mathematicians do! But in my case, I had this opportunity to serve as an ambassador of Kosovo to France and also, during a period, to Portugal, Monaco, and Andorra, covering from Paris as a non-resident Ambassador. That was something that I was asked to do by the state authorities in Kosovo. I was already promoting the Francophonie, the French Language, in Kosovo. I was also fairly active in the political life in Kosovo, [so] it seemed very natural to accept this. It was an exceptional experience. Of course, mathematics doesn’t overlap in the classic sense because you’re not trying to do research about a diplomatic mission, but it is about advancing knowledge and understanding: trying to understand the other parties, trying to forge relations, trying to understand the quality of those relations, giving context and understanding context, and building networks.

“All of this is something that is useful in academia. I think that in the current age, we live practically under a period where mathematics and mathematical ideas have revolutionized our way of life. It is essential to have people who understand various parts of [the] human endeavor, including sciences and mathematics, contribute equally to other parts of human endeavor. It should not be a complete surprise if you have someone who has a background in sciences doing diplomacy because that adds to the spectrum of people with certain skills who can transfer them in their discussions. These days, in our digital era, diplomacy is essential to understand a bit better how people function. There is space for more scientists to be included in [diplomacy]. It is true that mathematicians have a reputation of being socially awkward, but I think a little bit of champagne helps!”

How has being a diplomat between Kosovo and France [and the other nations has] positively impacted you as an international scholar?

“One of the reasons why I like modern academic environments is because you get to meet people from different corners of the world who have different backgrounds and different viewpoints. You learn from them, even if you disagree with them. [I think] that is fundamental to an environment that is open and promotes academic freedom. I was lucky to have been exposed to this throughout my education and professional career. [I also had] this phase where I was a diplomat at a very big and important capital, [which I hope] has contributed to opening up my horizons and further forging these networks of cooperation. I think it has also made me appreciate the conversations with others [and] the necessity to share and learn more from one another. Because of the way academic life is structured, teaching, research… you often don’t have enough time to converse with other people. Being in an environment where conversation was essential, for me, was an interesting and positive experience.

 “I might add one thing: I was very lucky to be posted in France where I have many friends and where I was accepted. I appreciate, and always tried to learn more about the French language and culture. I am now proud to have, in my family, kids who are French speaking as well.”

Are there any experiences you credit specifically to your area of study, pure mathematics?

“Apart from this universality of mathematics, which is extremely important, when discussing with people we’re transcending cultures and all sorts of differences. One thing that has had an impact was the idea that ‘I am contributing to constructing knowledge and advancing human-kind by adding very little, minuscule contributions…but in an irreversible way.’ This is something that you don’t necessarily get [as] a diplomat. You can contribute to having some agreement or deal between two countries, but that agreement could end up not being applied or [ending] in a few years time. Whereas with mathematics, if you are proving something that is true, you are advancing human knowledge. I find that very beautiful and satisfying. That’s something that I like [about mathematics]; the idea that what I have been studying lies at the intersection of a number of mathematical fields. You’re always trying to understand things in a number of domains and trying to compare them, see the relations between them, find patterns that are common…that is the type of problem I like to address when I’m thinking about research. This is something that has become a part of my intellectual existence: both curiosity and a desire to understand things. That’s what I hope to transmit to my students and future generations.”

Is there anything really specific that is credited to you in mathematics that you feel has started this push to transmit future knowledge?

“I’m only a miniscule contributor in a number of fields, but I like challenges. There’s this classic thinking that there are two types of mathematicians: those that solve problems and those that create theories. I would probably belong more to the first category. I am happy that I have solved some problems, but I would like to solve more! At some point, it becomes not just about solving problems but about understanding them. If you solve them, then you’re happy! But I have worked on a number of problems related to Combinatorial Aspects of Representation Theory, where I hope I have left a little bit of a mark [despite] the giant mathematicians working in this field.”

Do you have any advice for younger people who may be pursuing either of these career paths?

“I hope that younger mathematicians will carry their torch and enlighten [the] future generations. In particular, [I hope they will] contribute to the understanding and advancement of mathematics, to its use in society… but at the same time, think about how they can contribute to a more peaceful, more prosperous world where there’s more understanding between individuals, nations, and communities. That’s my wish and hope [for the future].

“I would like to add that I am delighted that currently I am able to both contribute to UMD and its students and also learn from them. In particular, I am grateful for the very warm welcome that I received at the very active and distinguished Math Department here at UMD.”