Number Theory, the African Queen

Walking to the auditorium at the IMSP, in Dangbo, Benin.

Walking to the auditorium at the IMSP, in Dangbo, Benin.

“Mathematics is the queen of the sciences and number theory is the queen of mathematics.” – Carl Friederich Gauss.

This month, I had the incredible honor of teaching at a summer school on “Algebraic Number Theory and Applications” in Dangbo, Benin.  It was a unique opportunity, in part because I had never taught a course like this before, but also because it gave me a chance to visit West Africa, to work with an amazing group of people, and to make new connections with a great group of African mathematicians. In this post, I will share some of my experiences (and photos!) from the trip.

Entrance to the institute. Photo courtesy of Francesco Pappalardi.

Entrance to the institute. Photo courtesy of Francesco Pappalardi.

First, some facts. The summer school was co-funded by CIMPA and ICTP, both Europe-based institutions with a huge commitment to improving mathematics and physics in developing countries. Every year, there are quite a few CIMPA research schools (see here for a list of the 2014 schools), “intended to higher education and research teaching staff. Beginners as well as confirmed scientists who wish to improve or to become initiated to a new field of research can attend the lectures. ” In our case, we had about 40 participants from eight countries (mostly from West and North Africa), ranging from masters and PhD students to established researchers. The seven lecturers were all from different countries (mostly Europe and North America). There were even quite a few women, all of them very talented.

 

Our home for two weeks.

Our home for two weeks.

The school was a two-week affair, with about two classes every day (each one a three-hour block). We would start early in the morning, and take our bus to the Institut de Mathematiques et Sciences Physiques (IMSP) in Dangbo, Benin, then spend the full day at the Institute, and then take our bus ride back. There were seven courses total. The first week the participants learned about elementary arithmetic from Alain Togbe, algebraic number theory from Francesco Pappalardi, binary quadratic forms from Claude Levesque, and p-adic numbers from yours truly. The second week, we learned about finite fields and coding theory from Michel Waldschmidt, Diophantine equations from Florian Luca, and elliptic curves from Jorge Jimenez Urroz. The second week also had a mini-conference with presentations from the participants (which I moderated, gave me a chance to try to be really mean about staying within your time limit), and I also volunteered to give a mini-course on Sage. It was a huge amount of information for the participants, and we also gave them homework (some people even collected the homework!, not me, though). I was amazed at how engaged, interested, and involved all the participants were, even though some of them knew very little about number theory before the school.

Our other home, the bus. This photo was taken during our Saturday field trip, first to an underground city, and then to the castle of Abomey.

Our other home, the bus. This photo was taken during our Saturday field trip, first to an underground city, and then to the castle of Abomey.

At first, I was not even sure why I had been invited (I mean, my colleagues are well-known and established mathematicians, whereas I still think of myself as a newbie). But, as I have learned, you should not question lucky breaks like this, you should just accept them for the amazing opportunities that they are. Of course, it was a little scary to teach a class on material that I had never taught before to a group of mathematicians, some of whom have had Ph.D.s for much longer than I. I prepared by teaching a version of the course at Bates to a group of very brave undergraduates. At least, it gave me the chance to think about how to present the material. All I had to do afterwards was figure out how to teach all of p-adic Analysis in just a six-hour long course.  That part was more challenging, and as you can guess, I never covered all that I intended. In fact, I think I only taught about 2/3 of what I had prepared. Still, I think it was an OK introduction to the subject, and my co-instructors seemed to think I did a decent job. Another huge challenge was the fact that most of the participants (though not all) were francophone, and even though I can ask for basic things and get around with my Tarzan-esque French, I could not give a lecture completely in French. I think it was probably an obstacle for some of the participants, unfortunately (although they would ask questions in French and I did my best to answer them in French). On the other hand, if we really do think the mathematicians we were lecturing to want to be global math citizens, knowing more English could not really hurt.

The participants and lecturers of the summer school. Photo courtesy of Francesco Pappalardi.

The participants and lecturers of the summer school. Photo courtesy of Francesco Pappalardi.

I was very impressed with what my colleagues were able to do in the short amount of time. Like I said, some of them gave a lot of homework, and then collected it. Some of them, like Alain, even had students present solutions on the board and the  gave prizes for most (and best) participation. Florian even got rapt applause at the end of a proof. I learned very much from all these different teaching styles, but that is part of another blog post.

Not everything was perfect though. The institute is basically brand-new, so not all of the bathrooms were working (we had to walk two buildings over every time), and the buildings were slightly empty. I learned that electricity was connected and a whiteboard installed essentially a few days before we started the school, so no wonder not everything was in perfect working order. The biggest gripe, though, would be the lack of reliable internet, which I have clearly become too dependent on. Eventually, we chipped in so one of the participants could share his hotspot with the rest of us (and that worked MUCH better).

Group photo with our hosts in Lome, Togo.

Group photo with our hosts in Lome, Togo.

By this point, if you’re like my family, you might be thinking: “and how much of Benin did you see? did you get a chance to look around much? did you go on a safari?”, and my answer is not a lot, not a lot, and there are no safaris in that part of Africa.  We did have a free afternoon in Cotonou during the first week (in which I learned how bad I am at haggling over prices) and a field trip to Abomey over the first weekend. The rest of the time was very much a loop of “get on the bus, go to the institute (which was gorgeous in itself, just look a the pictures), and come back in the evening”. I did go for runs a few times with Michel and Claude, who by the way are much more fit than I, and that was a great way to get to know the area and the town of Ouando, where we were staying. But this trip, or at least this part of the trip, was a lot more about making the connections, teaching our courses, and just giving the participants a good summer school. I still get emails from students thanking all of us for coming and sharing out knowledge, and I look forward to keeping in touch with many of them for years to come.

Drinking some coconut water at the Togo border. From left to right, Claude Levesque, Michel Waldschmidt, and Jorge Jimenez Urroz.

Drinking some coconut water at the Benin/Togo border. From left to right, Claude Levesque, Michel Waldschmidt, and Jorge Jimenez Urroz.

As I said, I was never sure how I got invited to be a part of this. I was sure as soon as I got invited that I  was the odd woman out (not just because I was the only woman). These guys have all worked with and known each other for years, and I was not sure how my addition was going to work out. I am so lucky that they are such a great group of people, and more importantly that we all quickly grew very close and that I didn’t feel like I was a stranger at all. Much like with a mathematical collaboration, this kind of teaching/touring collaboration works best when it’s a group of people that gets along very well. It was especially important since I managed to invite myself to their post-summer school mathematical tour.

Colleagues and travel buddies. Taken from the roof of the school being built by the Cuori Grandi missionaries in Amakpape, Togo. From left to right, moi, Alain Togbe, Jorge Jimenez Urroz, Michel Waldschmidt, Claude Levesque, and Francesco Pappalardi.

Colleagues and travel buddies. Taken from the roof of the school being built by the Cuori Grandi missionaries in Amakpape, Togo. From left to right, moi, Alain Togbe, Jorge Jimenez Urroz, Michel Waldschmidt, Claude Levesque, and Francesco Pappalardi.

I accompanied the other lecturers to a seminar day in Lome, Togo, and to visit the African Institute for Mathematical Sciences (AIMS) in Ghana (it is worth mentioning that there are several other AIMS campuses in Africa). On the way we stayed at a very inspiring mission in Togo and we got to see some of the sights along the coast of West Africa. My companions continued on to Abidjan in Cote d’Ivoire, but I stayed behind. I actually regret that decision a little, it would have been nice to continue on the tour and to have a few more days with those very nice guys.

aims

AIMS-Ghana. You can’t see from here, but the institute sits on a hill, overlooking a dramatic coastline. Best beach resort ever, with great ocean views AND a library full of math books.

In the end, this was a unique experience, both professionally, as an opportunity for service and teaching, and personally, as a chance to make new friendships/connections and get to know a new part of the world. I am very lucky to have been a part of this, and I am very grateful to the participants and my fellow lecturers/travel companions for making this such a rich experience. I am honored to have been able to take number theory (the “queen of mathematics”) on an African tour.

Ocean view from AIMS-Ghana.

Ocean view from AIMS-Ghana.

For those of you wanting to participate in one of these, like I said, I’m still not sure how one gets invited, but I suspect giving talks, creating connections, and meeting people really helps. If you’re faculty in a developing country, you might want to think about organizing your own CIMPA research school (calls for proposals are out for events to take place in 2016).   You should also look at the ICTP website for news and information on programs sponsored by them.

 

This entry was posted in CIMPA research school, conferences, ICTP, summer school. Bookmark the permalink.

6 Responses to Number Theory, the African Queen

  1. Karl-Dieter Crisman says:

    Great post! It’s worth mentioning that mathematicians outside Africa (including you!) can apply to teach courses at any AIMS campus; see http://www.aims.ac.za/en/apply/structured-masters-course-proposals for details. I know many who have loved the experience. This is usually a three-week commitment during the (US) school year, which can be an intensive in a research area, or a course introducing experimental math with Sage, other numerical things, ODE, etc.

  2. Frances Odumodu says:

    This is a really nice writeup. I am glad I was at the CIMPA school in Benin and that I met everyone. I really learned a lot. Thanks Adriana.

  3. Sezare Abe GNAGNE says:

    I am very grateful for the benefit that you have helped me.
    That boosted me in my research.
    I do not know how to say thank you.
    Please accept my sincere thanks.

  4. Sezare Abe GNAGNE says:

    participant at cimpa-Benin 2014

  5. Andre says:

    It was very nice and I am grateful to all the lecturers.

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