The Nesin MathematicsVillage in TurkeyKrishnaswami Alladi and Gabriela Asli Rino Nesin

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Ali Nesin with surprisingly tame hair.

PREFACE:

Krishnaswami Alladi

In August 2014, my wife, Mathura, and I wereon a three-week visit to Turkey. I participatedin a conference on algebra and number theoryin Samsun on the Black Sea coast in northernTurkey, and after that we went on a one-weeksightseeing tour of Turkey. Professor Ali BülentEkin of the University of Ankara, who was oneof the organizers of the conference and my hostin Turkey, graciously offered to take us on a1,500-mile journey to see several ancient historicalsites of the Greek, Roman, and Ottoman periods.One of the places we visited was Selçuk, a townwhich is close to the city of Izmir and known forthe well-preserved ruins of Ephesus, as well asthe not-so-well-preserved ruins of the Temple ofArtemis, one of the Seven Wonders of the AncientWorld. After a long, enjoyable, but tiring day of

Krishnaswami Alladi is professor of mathematics at the Uni-versity of Florida. His email address is alladik@ufl.edu.

Gabriela Asli Rino Nesin is a graduate student in computerscience at the University of Leicester. Her email address isgarn1@le.ac.uk.

DOI: http://dx.doi.org/10.1090/noti1258

sightseeing, Ali Bülent suggested at dinner that weshould see the Mathematics Village on the outskirtsof Selçuk that very night. It was late, and so I feltthat the Mathematics Village might be closed. ButAli Bülent said that it was only 9 p.m., and the nightwas young. So we departed for the MathematicsVillage right away without any appointment to seeanyone.

The Mathematics Village is nestled in a moun-tainous region in the village of Sirince, and it wasquite scary as Ali Bülent navigated the narrowunpaved roads to reach the Village. It was pitchdark as we parked, but in the glare of our headlightswe suddenly saw a female student emerge from apath, proceed to her tent, pick up a notebook, andhead back along the path from which she came. Sowe knew we were at the right place and followedthat path. A lovely set of buildings loomed verysoon, and we were greeted by a cheerful bandof students. We were taken immediately to theterrace where Prof. Ali Nesin, the founder of thiswonderful institution, and his daughter, Gabriela,were in discussion with students at dinner. Theyspontaneously invited us to join them at dinner,but we had to decline the kind invitation since wehad already dined in Selçuk. Gabriela then showedus around this remarkable place. We were simplyoverwhelmed by what we saw.

The Mathematics Village is a unique institution.It offers short but intense courses to mathemat-ics students from high school and college. Thestudents are immersed in mathematics for thefew weeks they are there, learning from the pro-fessors who teach, as well as from discussionsamong themselves. The students could relax inthe evenings by playing Ping-Pong or cards orby simply reading in the excellent library or inthe wooded environs. Most students are housedin stone and clay houses, but as demand almostalways surpasses capacity, some have to be put upin tents. At the time we visited, there were aboutfour hundred students in attendance. Teaching isvoluntary; while the Mathematics Village does not

652 Notices of the AMS Volume 62, Number 6

provide honoria for the teachers, it provides freeaccommodations and meals. It is a sylvan settingin which to either learn or teach mathematics. Aswe toured the Village, I was impressed to see somestudents in discussion in front of a blackboard ina courtyard and some others in the library, even inthe late hours. So in the midst of the sightseeingtour, we had a wonderful opportunity to visit thisremarkable institution.

Gabriela, who occasionally volunteers at theVillage as well, has described the conceptionand evolution of this rather unique educationalenterprise.

THE MATHEMATICS VILLAGE:PAST, PRESENT, AND FUTURE

Gabriela Asli Rino Nesin

The most popular T-shirt for sale at the NesinMathematics Village these days depicts a distractedmathematician who, after having completely filledhis blackboard with a gigantic equation, simplykeeps going on the wall next to it. The captionunder it reads “Mathematicians without borders….”It is quite fitting (pardon the pun), both to thesteady expansion of the Mathematics Village overthe past seven years and to the voluntary natureof the Village; hence the parallel to the famousMédecins Sans Frontières.

The Nesin Mathematics Village is a small non-governmental organization that has “colonized” ahillside near Izmir, Turkey, and has dedicated itselfexclusively to the nonprofit teaching and practiceof mathematics. Based on the academia of ancientGreece, it is a place where mathematics is doneat every hour, in any place, and in any position,horizontal or vertical. In the next few pages I willattempt to give a taste of what the MathematicsVillage does. But first, I will start by describinghow the idea originated and how it graduated fromidea to reality. I will then describe the variousprograms taking place there each summer and thevarious facilities available both to aspiring andcard-holding mathematicians. Finally, I will showhow one can take part in this enterprising project.

OriginsAziz Nesin and the Nesin Foundation

The wild-haired, bearded, and bespectacled mathe-matician on the T-shirt bears a strong resemblanceto the man who founded the Village, Ali Nesin.Although he has become a somewhat well-knownfigure in Turkey, he owes part of that fame to his fa-ther, Aziz Nesin. Aziz was one of the most famousand prolific writers in Turkey and at the same timean important leftist figure, penning many worksof political satire. This and the fact that he wasmost likely the first publicly self-declared atheist

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The Village from afar. The two blue domes (oneof which is almost hidden) are the female andmale Turkish baths. The large white building onthe right is the library.

in Turkey, made him beloved to some and a swornenemy to others.

In the seventies the income from his booksallowed him to open the Nesin Foundation,anonprofit organization taking in children fromdisadvantaged families and giving them a homeas well as sending them to school until theycompleted their education (including universitystudies). What, one might ask, does this have to dowith mathematics? Essentially, the MathematicsVillage’s land and assets are owned by the NesinFoundation, and their destinies are as such veryclosely tied. Furthermore, the basic principlesgoverning both are essentially the same: access toknowledge, education, and freedom.But now let us describe how the need for aMathematics Village became apparent, startingtwelve years before it opened.

Bilgi University and Its Mathematics SummerSchools

At Aziz Nesin’s death in 1995, Ali left his post asassociate professor at the University of Californiaat Irvine in order to take over direction of theNesin Foundation in Istanbul. As luck would haveit, in 1996 a private university named Istanbul BilgiUniversity was preparing to open its doors andhired Ali as head of the Department of Mathematics.He quickly gathered a small but tightly knit groupof Turkish and foreign academics which graduallygained the reputation of providing one of the bestmathematics educational programs in Turkey. Thedepartment was extremely ambitious: the studentswere taught axiomatic set theory the first year,including ordinals, cardinals, the Axiom of Choice,Zorn’s Lemma, and even nonstandard numbers.

The advantage of a small department wasthat staff were able to follow students almostindividually. In a class of four, one absentee meant

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Özlem Beyarslan teaching a high school lectureon vector spaces in the Aziz Nesin Amphitheatre.

25 percent of the class was missing; it wasn’tuncommon to get a phone call when one hadoverslept. However, it soon became apparent thatmore time was needed to rectify the holes left byTurkey’s test-oriented high school education thanwas accounted for in the curriculum.

From 1998 onward summer schools of a monthand a half were therefore organized in variousvacation spots in Turkey, where students wouldstudy during the day and swim and bond in theremaining time. However, these summer schools(although partially funded by Bilgi University)became more and more expensive. There were otherlogistical problems: they once had to improvisewhiteboards by sticking paper behind windowpanes, and it is virtually impossible to provetheorems with Enrique Iglesias blaring in thebackground. Ali began to think that the only wayto get something done right was to do it himself.

Meanwhile, an old friend of Ali’s, Sevan Nisanyan,was building a picturesque hotel in a small villagenear Selçuk, Izmir, called Sirince.

How the Village Was Built

In 2007 Ali Nesin bought a 2.5-acre plot of land onekilometer from Sirince and started construction onit according to the plans drawn up by Sevan andhim (quite modest to begin with, although theyhave mushroomed over time). Sevan Nisanyan wasinstrumental in making the Village the place it istoday; his architectural knowledge, good taste, andboundless energy have been invaluable.

That first summer of 2007 around one hundredstudents, mostly from Bilgi University, attendedthe summer school at various times. Most sleptin tents. Besides attending the usual six to eighthours of lectures, students and lecturers cookedand cleaned for the whole group, planted trees, andhelped the construction workers carry materialsand build walls.

The structures were, and still are, built outof stone slabs, straw and clay. The first lecturehall, the Robert Langlands Lecture Hall, was builtaround an old tree which still juts out of its rooflike a sentinel. Huge wooden beams from old traintracks were used to build the steps of the AzizNesin Amphitheatre, and the climbing vines whichtoday provide its much-needed fresh green shadewere planted.

Legal Issues

The area in and around Sirince is designated aprotected area, making authorization for construc-tion very difficult to obtain, since it is firmlyunder the control of local authorities. Although theMathematics Village is outside the protected area,authorization for construction was never grantedowing to antipathy toward the Nesin name. One ofthe objections raised was that it was illegal to es-tablish an educational facility without permissionfrom the government, even though the Mathemat-ics Village is a nonprofit organization, does notconduct exams, or offer degrees or diplomas.

The struggles are far from over. Despite all this,the Village believes that as community support andinternational recognition grow, these persecutionswill disappear. Furthermore, a strong communalfeeling is born in trying to overcome such obstaclestogether.

The Mathematics Village TodaySummer School Social Structure

By 2009 facilities had expanded so much thatmany more students from other universities couldbe accepted, and Bilgi students ceased being amajority. As the summer schools gained momen-tum, postgraduate students also started attendingthem. They volunteered to teach, attended classesthey were interested in, and had opportunitiesto chat to and collaborate with colleagues andprofessors from around the world—an ideal andrelaxed academic environment.

A standard fee to attend the Mathematics Villagewas decided upon, but it quickly became apparentthat many university students could not affordthis, as they were often no longer supported bytheir parents. The Village accepted the studentsanyway, paying for their accommodations andfood costs out of its own pocket and naturallyfinishing each summer with a significant deficit.Even the support of the Turkish MathematicalSociety and the generous donations from theTurkish population (many of them from familiesthat could barely afford such donations) could notcompensate for the losses. Due to high demandand as a way to partially counteract the deficit,the Mathematics Village decided to expand its

654 Notices of the AMS Volume 62, Number 6

audience to high school students, starting fromthe age of fourteen.

The high school summer schools have sincebecome a huge hit, with the number of applicationsmore than triple actual capacity. Although somegrants are provided for disadvantaged students,the families of most high school students are morethan able and happy to pay the modest fee ofUS$500 for two weeks. It has become a badge ofhonor for a family to have sent a child to theMathematics Village. As a result, the Village nowcarefully makes sure that the student really wantsto attend and is not caving in to the pressureof his or her family. On the other hand, therehave been a couple of cases of kids running awayfrom home to the Mathematics Village when theirparents refused to let them come to “the atheistcamp”! Whatever surplus the Village obtains fromhigh school fees is channelled toward grants forundergraduate and postgraduate students lackingthe means to attend.

During their two-week stay, all high schoolstudents will be under the responsibility of a “bigbrother or sister,” akin to scout leaders and almostalways university students who have volunteeredfor the role. They make sure their group attendsclasses, goes to bed on time, and generally avoidshurting itself (no mean task considering it iscomposed of hormonal beings in close proximityto Sirince, renowned for its fruit wine!).

Since the number of official staff at the Villageis very low, it mostly operates on the communemodel. Upon their arrival, students are split up intosmall groups containing a mixture of high schooland university students, with a roughly equal ratioof each. For the next two weeks, these groupswill complete the necessary chores to be done inthe Village. One day a group will help the cookpeel potatoes, the next day it will be on rubbishduty, on the third day responsible for replenishingthe various water coolers scattered around theVillage, and so forth. Surprisingly enough, far fromcomplaining about this work, many students feelthat they have significantly contributed to life atthe Village, thus getting a feeling of ownership andcommunity which does not leave them even yearslater.

Course Structure

The courses are organized in two-week blocks inorder to fit the length of students’ stays.

Ordinary high school education in Turkey isgeared toward the university entrance examina-tions. As a result, the emphasis is on memorization,mindless competition, and end result rather thanthought processes. The Mathematics Village aimsto counteract this by giving high school studentsa glimpse of what university-level mathematics is.

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View of the library conference hall from thesecond floor.

They learn to think for themselves, argue coher-ently, and spot logical fallacies. Most importantly,they see the process of solving a problem whosesolution is not known beforehand. As an example,an exercise that Ali Nesin often does with a groupof new students is to determine whether the math-ematical group generated by the Turkish alphabetand with all of the students’ names as relatorsgives the trivial group. Students are encouragedto participate, and it often gets difficult to quietdown the shouting out of ideas from every cornerof the classroom.

High school students learn about such diversetopics as graph theory, probability, combinatorics,game theory, and basic analysis and algebra. Theseare supplemented by eclectic exercise sessionswhere students are introduced to such problemsas Hilbert’s Hotel and encouraged to constructtheir own proofs.

An excerpt from a conversation between astudent (who attended for the first time at the ageof fourteen) and Ali Nesin when they met at a booksigning shows the results:

“You came to the Village, didn’t you?” Ali asked.“Yes, four times actually,” he said.“Did it make a difference?”“A big one.”“How’s that?”“Sir, when I first came I didn’t understand

anything. Only the last two days I vaguely hadthe feeling I was getting it. More than the thingsI understood, I was so happy to have finallyunderstood something that I came back the nextyear. The first week I understood nothing again, butI understood everything that was being done thesecond week! On my third visit I missed nothing.On the fourth I was guessing the teacher’s nextsentence… High school feels boring now.”

The university-level teaching is organizedaround themes if the lecturers’ time permits,allowing not only for concentration of research

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Students and teachers listening to a lecture inan open-air theater.

interests but also preparing the ground for coop-eration between colleagues in the same or relatedfields. This year, for example, the second andthird weeks saw courses called Reflection Groups,Introduction to Classical Groups, FundamentalGroups, and Three Groups Every MathematicianHas to Know. The range of subjects is too wideto cover here, but university students can learnabout anything from Lie algebras to Fourieranalysis, from measure theory to representationtheory of groups. Some classes can be said tobe interdisciplinary between mathematics andphilosophy, physics, or computer science, suchas Recursion Theory, Gödel’s IncompletenessTheorem, or linear programming.

All teaching at the Village is voluntary. In return,lecturers’ accommodations and meals are free.Given this, the number of academics who havedecided to teach at the Maths Village over the yearsis truly impressive. Lecturers have come from allover the world, including Alexandre Borovik fromManchester, Edriss Titi from UCI, Max Dickmannfrom Paris 7, and Ryan O’Donnell from CarnegieMellon. This list is by no means exhaustive, aslisting all contributors here would be impossible.

Apart from the regular teaching, people whodo not have enough material for an entire courseor simply wish to talk about their own researchgive seminars in the cool evening breeze at theAziz Nesin Amphitheatre, organized from 9 to11 p.m. and attended by whoever wishes to or hasenough energy left. These evening talks are veryinformal—many bring their wine left over fromdinner—and are the perfect opportunity to getcolleagues’ ideas and input to one’s research.

Facilities

The physical structure of the Village today hasexpanded to contain sixteen dorms (capacity169), two amphitheatres, two closed and four

open-air lecture rooms, one male and one femalehammam (Turkish baths), twenty-nine single ordouble rooms/houses, a fully functional kitchenand cafeteria, a small shop and a magnificenttwo-story library with a cool breezy terrace in frontof it. Even though housing capacity is constantlyexpanding, many students still stay in tents andtherefore pay discounted fees.

The library has an open-plan central areadecorated with geometric mosaics. Two giganticwheel-like chandeliers light a conference hall onthe ground floor, seating one hundred fifty. Onthe second floor balconies overlook the hall; thisis where the bookshelves are. Their half-emptinessshows optimism for the future: the library is eagerto accept donations of old books and journals. Thesecond floor also holds tables for silent working.It is one of the most peaceful places in the Village,not least because it offers an absolutely unfetteredview of the opposing valley. However, the library isfar from the only place for working; several isolatedareas are available throughout the Village for thosewho want to escape the excessive friendliness oftheir colleagues.

Around fifteen paid staff and nearly one hundredvolunteers work there every year. The two-weekcycles start and end on Sundays, and on that daynear-perfect organization is needed to take care ofthe departure and arrival of hundreds of studentswithout devolving into utter chaos. Ali Nesin sitsdown with each individual undergraduate studentto advise them on which classes they can attendgiven their background.

No one knows how he manages it, but the cook,Chef Asım, puts out three delicious meals a dayand cake at tea time on top of it all.

There are no TVs or broadcast music, althoughthere are occasionally film screenings on the projec-tor in the library. Some evenings students take outtheir musical instruments—a guitar, occasionally asaz or a kemençe—and give an impromptu concert.Traditional and modern Turkish songs are played,and the listeners join in. To avoid disturbing peoplewho have work to do or need to get up early toattend class, these mini music sessions are oftenheld on Wednesday evenings, as Thursdays are theofficial day off in the Village.

Each Thursday, a vacation activity is organized.It can be a trip to the nearby Kusadası, to the furtherbut much more beautiful Kusadası National Parkbeach, or a boat tour. Those who wish can organizetheir own trips, for example, to the historical ruinsin Selçuk or the neighboring famous ancient Greekcity of Ephesus. Alternatively, one can stay in theVillage to catch up on sleep or work in the varioussecret corners of the Village on the hammocks orswings and couches.

656 Notices of the AMS Volume 62, Number 6

More MathematicsPast Conferences, Workshops, and ResearchGroups

The main focus of this article has been summerschools, as they are the most active periods of theyear for the Nesin Mathematics Village. However,for many years now the Village has also hostedvarious workshops and conferences throughoutthe year.

There are various winter schools held duringJanuary and February. Some of the workshopswhich have taken place at the Village are the Alge-bra and Analysis Workshops in January–February2014 and October 2013 respectively, the Mathe-matical Evolution Workshop in September 2013,the Computer Science Workshop in October 2012,and the Workshop on Function Field Arithmetic inJune 2014. In May 2014 a summer school AroundValuation Theory was held. The XV Antalya AlgebraDays conference, traditionally held in Antalya, asthe name indicates, was held in the MathematicsVillage in May 2013. Some of the invited speakerswere Gregory Cherlin, Martin Ziegler, Ian Leary,and Serge Bouc. The seventeenth edition of thisconference will be held in the Village as well, inMay 2015.

Recently, the Mathematics Village has started anew initiative whereby research groups of any sizecan gather in the Mathematics Village for intensiveperiods of work and collaboration. I personallysaw the benefit of this initiative; the day after wearrived, my supervisor and I sat down to work ona problem that had been eluding us for a longtime at 9 a.m. after a nice breakfast. Three hourslater, we had the basis of a paper—the air of theMathematics Village is inspiring!

How You Can Use or Contribute to theMathematics Village

As described above, the Nesin Mathematics Villageis a perfect place to organize a conference or aworkshop. The communal feeling of the Village isvery likely to leak into any activity taking placethere, and the relaxed and intimate surroundingsfoster communication and collaboration amongparticipants. The same holds for research groups;there are uncountably many corners of the Math-ematics Village where a small group can holeup and discuss to their hearts’ content withoutdistractions.

Volunteers for teaching are always welcome.Unfortunately, all high school courses must betaught in Turkish, as the students do not necessarilyknow foreign languages, but any undergraduateor postgraduate course may be taught in English.One of the most common pieces of feedback I havegotten from lecturers at the Mathematics Village is

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The boy in the purple shirt follows the solutionand explains it to a classmate.

how astounded they are at the level of enthusiasmof the students; the sheer hunger for knowledgethey have is truly admirable, especially consideringthat attending these courses is entirely due topersonal interest and does not provide any coursecredits or diploma of any kind.

Teaching and research need not be exclusive.Here is Alexandre Borovik’s account of one of hismany experiences at the Village:

“For me, the Village is a place of research; I comethere to work with my friends and co-authors,Adrien Deloro from Paris and Sükrü Yalçınkayafrom Istanbul. We are working on several looselyrelated projects focused, roughly speaking, onachieving a better understanding of the group SL2

at a very detailed, “subatomic” level. To get sometaste, see our preprints. The Village is a paradisefor work in a small group.

The strange name of the course that I taughtlast August in the Village is mentioned above:Three groups every mathematician has to know.The groups were the three most famous formsof SL2: SO3(R), PGL2(R), and PSL2(C). For ourprojects, I needed to refresh and sharpen myunderstanding of these groups, and bring it intoa usable state; what better way to do so than togive, from first principles, relaxed and free flowinglectures on these groups, and to make them asaccessible to listeners as possible? Can you quicklyexplain—and in the simplest possible way—whythe cross-product of vectors inR3 is the Lie algebraof SO3(R)? Or Dirac’s cup trick? Of course, I gavedue attention to geometries of the groups, andpaid tributes to glorious names associated withthem: Euclid, Lobachevsky, Minkowski.

When you teach to absolute novice learners,you learn, too. Perhaps occasionally I slippedinto the entertainment mode and used juicyhistorical morsels, such, say, as polishing ofspherical stone vases in Egypt during the OldDynasty (or, in mathematical terms, classificationof 3-dimensional subalgebras in the Lie algebra of

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A M E R I C A N M AT H E M AT I C A L S O C I E T Y

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A high school student solves a problem on theblackboard while lecturer Mübe Kanuni looks on.

“sliding vectors”, that is, infinitesimal isometriesof the 3-dimensional Euclidean space)—but forme it was a way to relax after intensive researchsessions.

I do not know any other mathematical establish-ment in the world where you may find this level offusion of research and enlightenment.”

Future Plans for the Mathematics Village

Some events are already planned for the upcomingyear, apart from the usual summer school: forexample, the CIMPA Research School on LeavittPath Algebras and Graph C∗-algebras or the 2ndColloquium on Existentialism.

Due to extensive interest from departmentsof philosophy, one of the new projects at theMathematics Village is to build an attached Philos-ophy Village on the new land purchased. Housingis already being built there, although for now itmostly houses the overflow from the MathematicsVillage. Eventually, it may be possible to constructan Arts Village as well, planned as a communalarea providing (mostly plastic) artists with studios,to be used as a kind of artist’s retreat.

Apart from this, construction at the MathematicsVillage itself is still very much in progress. Morehousing is being built in the hopes that eventuallyall students will be able to stay in dorms ratherthan tents.

Ambitious plans are not lacking at the Mathemat-ics Village! Neither are enthusiastic and generousvolunteers who do their best to bring them to lifeand without which the Village could not survive.But more plans, more volunteers, and more inputare always welcome, and its residents are alwayseager to share their pride in the Village with anyvisitors.1

1For more information, visit the Village’s webpagematematikkoyu.org/eng/.

658 Notices of the AMS Volume 62, Number 6