7th HLF – Lecture: A personal journey into the world of mathematics
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Birkar, Caucher
In this talk I will talk about my personal story with an emphasis on mathematical education and research. In particular I will talk about the challenges I faced and the factors that shaped my academic life. The opinions expressed in this video do not necessarily reflect the views of the Heidelberg Laureate Forum Foundation or any other person or associated institution involved in the making and distribution of the video.
 Now I'm glad to introduce the next speaker, Hocher Birkar from Cambridge. Hocher Birkar moved from Wotan, Iran to Britain in his childhood and he was educated in Britain. Apparently he did very well there because as a student he got a fellowship of London mass society as the most promising student. He fulfilled the promise and got Fields Medal last year in Rio de Janeiro. Wikipedia says that Hocher Birkar means migrant mathematician. In that sense I am also Hocher Birkar as are many people in this room. Hello everyone and thank you very much for the kind introduction. So I will, the title of my talk suggests, I will talk more about my personal life and also the education journey. One reason for this is that last year I gave a talk here also and it was all about mathematics and nothing else. This time I wanted to do something a little bit different to make it a bit more maybe entertaining but also in the way I'm hoping to tell you a few things especially for the young people how I did mathematics and how I approached mathematics, how I thought about mathematics and some of the challenges I faced and maybe you can find some advice there, some tips for your own journey. So I was born in a city called Medi-1 or officially it's called Medi-1, it's actually not really correct, it should be Medi-1. In Kurdistan on the border of Iran and Iraq you can actually even walk to the border just would take you maybe one hour or something like that. So we were very close and the region I lived in is it has a lot of mountains so it has a climate in a sense that is similar to Europe, it's not very dry, it's actually quite green but we have four seasons so each season is quite different from the others. Here you have you see some pictures of the city and then nearby surrounding of the city. I was born in a village just opposite the city not inside the city itself. So as many of you know Kurdish people live in the Middle East and our region is divided into four countries Iran, Iraq, Turkey and Syria and we have had lots of problems especially the last 100 years we have been in really terrible shape until quite recently just even the cup even last year there were Kurdish cities being destroyed just really for for not good reasons just almost artificial reasons. So it's life has been very difficult for us especially because there are four countries not just one we have to deal with four different countries and they are all actually they all don't like each other but except on the issue of the Kurds when it comes to this issue they all unite and make life even more difficult for us. Anyway so when I was a few months old the there was a revolution in Iran and even before that it was a bit chaotic and then a few months after I was born there was a revolution so the whole government changed and everything changed and when I was about two years old then the Iran-Iraq war started which lasted for eight years and since we were living on the border we were we were just trapped in the middle of the war which there was no way to really escape. Most of the threat was aerial fortunately in my region my city there was never land invasion it was always aerial and it was quite often you see airplanes coming and dropping bombs and especially when I was in primary school so these eight years covered all my primary school years and very often we were in classrooms and then instead of after the lecture going to to have some fun in the middle of the lecture the airplanes would come and we would just run out and the only thing we knew to do was run through the mountains but we did that very very often and when there is a war a war disrupts everything including education although there were schools but as you can imagine in such an environment schools can't be really very good and the school that I started to study it was just a normal house and turned into a school there were like three rooms and with a lot of children so you can imagine the conditions were not very great but still I am very grateful to those teachers who in that kind of environment that kind of circumstances they didn't give up on teaching us so I am really grateful to them and the war of course poses a lot of dangers also indirectly not just the bombing but also in directories so for example one other thing that we did very often as children were playing with explosives because you could find them everywhere especially small ones like bullets if you just worked around two three minutes you would find some bullets and we did it we made it even more dangerous by making a fire and then putting these bullets into the fire and what we did was we dig some holes around the fire when we put the bullet in them and we would just jump into the holes and see what happens the bullets were flying everywhere but it's really amazing that no one got hurt playing all these games I mean there were other people injured or even killed later on but at least at that time all these plays actually didn't lead to anyone's death or even injury my ancestors were there were aristocrats we used to have a lot of land in the area and I think they enjoyed life they had a good life but unfortunately sometimes before I was born we basically lost all of these privileges because the government at some point decided to redistribute the land and they did it in a quite funny way they invited all the aristocrats in the region the king of the time the like yeah there was a kingdom at the time and then he said we will have like a festival and said you all come to have fun and then they put all of them in prison some of them they never returned we never know what happened to them like my great grandfather never returned we never know what happened to him suppose he died at some point so we we lost the power but we still had some pieces of land and we continued to do farmers so by my time we were just simple peasants we didn't really have privileges but since my ancestors they enjoyed themselves the local people actually didn't like us very much because they saw that we come from the same line of people who didn't treat them very well so they tried to revenge on us sometime and also make life a bit difficult anyway so we my parents were doing farming and I also did farming as all my brothers and sisters in the family we spent a lot of time farming until I finished undergraduate that was basically normal life whenever there was farming in spring and summer we did even the day before examinations we would still do farm but fortunately my father he took education very seriously and he thought that that's the only way to go ahead farming is not the future for us we have to study and we have to get degrees and do some other kind of jobs but also education in a sense also had value not just for getting a job but just to know knowledge also was appreciated so that was lucky for me that they just gave us the idea that that's the only way to go you should not think about anything else education and so we all attended school and we tried to do our best in fact my father even before I became six which was the official age to go to school he took me just informally to school to the local school and he even himself came to sit with me just to make me feel good with the school because some children even now when they go to school for the first time they are really afraid but he just wanted to eliminate that and make me feel good so that later on I will study better but for the first time that I felt any special connection with mathematics was when I was in grade five I remember that once we had an exam and I did very well but I didn't actually study very well and I was a bit surprised how I got a very good mark almost 100 without spending too much time doing mathematics so I think that's the first time that it attracted my attention in a special way because I tried generally to do good in all the courses but this one somehow made an impression on me but also luckily in that year we had a really good school a really good teacher unlike maybe the especially the grade four where we had a teacher who used to beat us really very very often so maybe this is not very familiar to you but at that time beating was very beating was very common in schools so the teachers could beat us and when I was in grade four the only thing I remember from that year is that the teacher was beating us so bad but fortunately this guy in grade five he did not even have a diploma so basically he had himself partial education but just naturally he was a really very peaceful and kind person and also he was creative in the way he approached teaching for example he would take us outside with the nature especially in spring which is very beautiful and he would just teach there like for one and two hour so that made a lot of difference that's much better than just sitting in a classroom all the time and he also organized competitions with nearby schools even in other villages we would go somewhere in the nature and we would start to compete and I usually in that year I was responsible for the mathematics section of the competitions so that was all good but what made the biggest difference was my older brother he was himself interested in engineering and science in general but I have no idea where he got his ideas because there wasn't really I mean there were schools textbooks and so on but the way he approached learning and education was completely different from everyone else in the region not only in in our family he was extremely creative he would always try to invent things design things build things the kind of thing that no one else would even think about so as one example he for example at some point he was printing himself there was no printing machine except in official places but he just invented printing by his own he carved out some plastic sheets all the letters and then he could actually print out things and people would think that this is an official letter from some government agency and some of the other things he did like he built a projector he even made animation for it and he would show us all the children in the neighborhood he's his animation he's moving so he was really extremely creative and that was great for me to have someone like that next to me just to follow as an example even if he didn't try to teach me still to have someone like you like that in your family in your neighborhood it's really can make an extremely big difference but at some point he also tried to teach me a bit more advanced mathematics and also physics for example calculus so that was when I was about maybe 11 years old but other children would learn that four years maybe four years later so I learned that much earlier four five years earlier and then but also what was important about his approach was that he didn't teach me so that I get a good grade he just saw that learning these things is just really exciting just you learn it for the sake of learning or for inventing something not just to be good in school that was really also it made a really big difference on my approach to education and to learn so if you if you ask me who is the most influential person in your education I think this is the guy so he maybe started all these things and now surprisingly all the people in my family my sibling they all ended up to be engineers except me who took it wrong the path me anyway so by the time I got to high school my brother was already in university so we were separate but I just followed this line of mathematics and also up to some extent of physics but at some point I realized that the reason I like those physical physical things is actually because of the mathematics so at some point I just in a way forget about the physics and just concentrated on the mathematics in really like high concentration and there were a few things about mathematics that I really liked one of those things is that mathematics is really precise there is no arguments and fighting and things once you prove something and your colleagues verify it then it's proved and there is no argument it's not like philosophy or literature or politics and that that kind of subject so even in physics you have like different theories it's not always the same theory but mathematics just once everything is precise and I really like that and also in mathematics when you establish something it stays there forever whatever people proved 2 000 years ago 3 000 years ago is still correct is still there and it's not going to disappear again if you compare to physics 200 years ago and now it's completely different computer science is even much much faster even if you don't if there is a program that you used 50 years ago even if it's still correct but you just don't use it anymore you just replace it by something else but the mathematics is kind of immortal it just stays there for forever and then mathematics is also beautiful all the things that I try to learn I found them just to be really there's some kind of beauty in it which I think brings mathematics very close to ours but it's just the beauty is a little bit different you you need a special language to understand this beauty it's like poetry if someone reads a chinese poetry to you and if you don't know chinese language then there is no way you can appreciate that that poetry you can translate but much of the beauty is lost in the translation it's the same with with mathematics you need the language you need a background to appreciate this beauty to see the beauty and but fortunately I went into mathematics enough to see this beauty already in in high school but it's not all just about beauty I saw that is also exciting to do mathematics there is a joy in doing mathematics when you solve a problem there is some kind of joy in that and I think in that sense mathematics is a bit similar to sports when play when you play football maybe you don't care so much about the beauty of the game but you just feel that there is some kind of joy some kind of enjoyment in playing football some kind of excitement and I think for me when I do research a lot of it has to do with it so when I learn things from other people yeah I appreciate the beauty but when I do mathematics myself is more this fun and excitement which is similar to sports and finally mathematics is also useful so that was maybe one other reason that attracted me to mathematics is yeah we have pure and applied math but quite often pure math also ends up to be applicable to some world problems anyway but the problem for me was in high school that I was totally isolated there was not one single person to ask what should I do what should I read how should I approach mathematics there was no internet at the time there were no computers where I lived and until I entered university I lived in my hometown and I left only twice to go to a nearby city and there also I couldn't find many people but I could at least buy some books so it was total isolation then I had to decide all by myself what to do what I should read and how I should think about mathematics that can be maybe it that makes life very difficult and maybe doesn't work for everyone but I think maybe that was good for me just this isolation taught me how to be independent how to learn things by myself and not rely on school and teachers and lectures and this experience proved to be extremely useful in later years when I entered university when I did PhD and so on so fortunately the local library for some mysterious reason had really excellent mathematics books and if you at least at the time when I read those books there was a log of people who took this book from the library and almost all of them were taken just by me or by me and maybe some else by mistake so I don't know why they put these books in the library but that happened to be a very good coincidence for me so I read a lot of these books and I still remember some of those books which are also famous in the West for example there is a book about the life of mathematicians it's called Men of Mathematics it's just the biography of especially all the generation and mathematics all the way from Euclid and from the Greeks until 19 and early 20th century and just reading the life of these people that they spend most of their time discovering things it just felt to me it was really so exciting I couldn't see any other way of living basically I couldn't imagine going to work in a shop or something like that I thought that this is really the way I should also be and there were also lots of books for example this book by Corant and Robbins is called What Mathematics is a quite big book and in this book you find introduction to many parts of mathematics like algebra and number theory geometry topology and all kind of things so this is much more advanced than high school and by reading all these books especially books like this then I got acquainted with many ideas from modern mathematics and that proved to be very useful in later years when I entered university so at that time I liked more the geometric side of the mathematics especially classical geometry like projective geometry but also topology already for example in this book about analysis you see matrix metric spaces and a lot of topology but also in this book about this what's mathematics there is also section about topology and for example you learn about Euler number Euler characteristic and these topological spaces and I just found those things to be really very nice and very beautiful but so in a way this is one of the points maybe I can put it as an advice you have to go outside school system you have to go outside university system to really learn something deep if you only stick to your lecture your lecture notes then well you can still succeed I suppose but if you really want to be successful you have to go out if you like a subject already for example if you are undergraduate if you like in mathematics suppose that you like algebra then there is no reason why you should not go and pick up some books about algebra and read them just the algebra books in undergraduate are not enough you can just if you like a topic just follow that topic yeah try to do your best in your exams and lectures but also you have to really go out of the box so I learned that in high school and that was really amazing but also already at in in high school I saw that just reading mathematics is not enough yes there is beauty and so on there but if I don't do it myself then I just don't get the satisfaction that I want again this is similar to let's say football if you just go and watch football then yes you can enjoy but when you play yourself it's actually much more enjoyable you get a lot more by doing it yourself so I try to also do research and I guess I proved certain things maybe not important at all but that's not the point the point is just try to do research just try to prove something new this can be done already in high school but in undergraduate definitely it can be done it doesn't have to be very important you don't have to publish it but just that experience of trying to do something new will be amazingly useful later when you do a phd in this age I mean in many universities I think they also for example in Cambridge they encourage this at least to pick up a topic learn about it and if you can prove something new great if not that's not the end of the world so maybe that's another important piece of advice anyway when I was about 15 or 16 I decided to be a mathematician that's it at that point I decided my my life basically and I think that was really great just to have a direction precise direction of what you want to do with your life I think the earlier maybe the better unless if you pick the wrong that's the wrong thing I mean if you want to yeah I mean at that age of course you never know what people do if they decide to play video game for the rest of their lives obviously that's not a good idea but I think if anyone in high school decide to be a mathematician a physicist a computer scientist an artist or whatever I think they would not regret it that's my feeling I mean if they are genuinely passionate about whatever subject so anyway the lectures the school were not really so much useful to me so at the last year the final year of high school I just dropped out of the school there was a parallel system where you could just go at the end of the year take the exam so you didn't have to attend lectures and and think that that also worked for me probably I should have done it much earlier anyway I entered university university of Tehran to do undergraduate in pure mathematics and for the first time I met actual mathematicians people who actually wrote articles and published it before that I had never seen even one but there I saw people actually doing mathematics but also there was a much much better library than what I had in my home city so the environment obviously was much better I was not totally isolated again although in a way I was you could say isolated because the way I approached mathematics was quite different from all my classmates because I just continued my line from high school the way I did mathematics in high school I just continued the same way in university so we come again to the same point that you have to pick a topic you have to pick something that you are passionate about and just follow it and you don't have to follow it forever so when I was first year undergraduate I just picked a book about algebraic topology and I learned a lot of things about algebraic topology like fundamental groups homology theory and so on I didn't become a topologist but I never regret that I read it books in first year undergraduate they had nothing to do with exams with lectures because the first topology course we had was four years later so this was just on my own that I was interested in topology and that's it especially here I saw this interaction between algebra on one side and topology on the other side and that was really exciting and later I come back to a similar point in the second year I picked up some books about commutative algebra and I just felt that I like this topic commutative algebra and just read a lot about it so this book for example here you see is one of the standard textbooks of graduate courses in commutative algebra and in fact that year I met a guy who was doing a master in mathematics in pure mathematics and we talked a little he is a speciality was commutative algebra we talked a little bit and he was amazed that he was amazed that almost everything he learned in his lectures I already knew and then I told him that it was just for fun I liked the topic and then I read about it but in the third year I had the same person happen to be my roommate and he was reading a book all the time he was by his side sometimes very excited sometimes annoyed and angry and then I got curious what is in this book that is so so much into this book all the time reading the book and it happened to be this book of Shafari which about algebraic geometry is one of the like the basic graduate level courses in algebraic geometry I got also interested and just picked up the book and starts to read I realized that a lot of those things that I learned in commutative algebra actually all came from algebraic geometry much of it here you have not only the algebra but also the geometry and there is basically a dictionary between algebra commutative algebra and geometry whatever you say in one side can be translated into the other side and vice vice versa so I that was really amazing I mean this connection between algebra and geometry was in a sense more profound than in the algebraic topology a case here the connection was much much more stronger and I just got hooked and I never left this field so I have been doing algebraic geometry for the last 20 something years and it all started here with this book but in the fourth year I also try to read with more advanced algebraic geometry especially this standard and scary book of heart showing about algebraic geometry this is written in a more modern language language of schemes not in a classical language it follows the style the school of alexander groten dick I couldn't understand much here I mean that's the impression most students have when they read this book because it's very abstract there is some geometry there but actually it's very hard to see the intuition but I was lucky again because I had read the classical version of algebraic geometry first when I arrived here I had a lot of actually intuition from from the classical side of the theory but groten dick also happened to be a really great source of inspiration for me both his school of mathematics was somehow very appealing to me but also his life and his personality so many of you I guess already know that he was a basically a stateless person living in France for a very long time and I don't know if finally he got citizenship in France or not but at least when he was active he actually was a stateless person at least to me I think he is should be if you pick two three mathematicians in all history I would put this guy maybe on the top anyway in the year 2000 I moved to the UK and the first year I couldn't study I was there basically as a refugee but fortunately all was sorted out in one year for many other people it takes much much longer it can take 10 years but I was lucky I think that I just spent one year dealing with immigration and so on and in 2001 I started to do a PhD course in Nottingham University advised by Ivan Fesenko a number theorist but I had already decided to be an algebraic geometry and there was no algebraic geometry in this department in this university so Ivan was a very helpful very supportive he comes from the Russian school of mathematics where they learn a great deal of mathematics in basically every subject so they are not narrow he knew a lot of algebraic geometry but still to do research in algebraic geometry you need someone professional algebraic geometry so in the first year just after a few months I went to the Newton Institute in Cambridge there was a program about algebraic geometry especially biorectional geometry for five months and I just go went to stay there in fact the organizer told me you cannot come to attend this thing but Ivan insisted a lot send them a lot of emails they finally agreed I go there without any support so I went there rented a room on my own and just attended the seminar so maybe that's another piece of advice don't stay all the time where you study travel you can go to other places you can not just for workshops and conferences you can visit other places for a month for two months for three months you are not going to lose anything you will just meet other people and that can be first of all you learn a lot of stuff from other people but also when you apply for jobs you need someone to write letters for you if you spend all your time in your own institution you can only ask your advisor and no one else but if you visit other people they will be happy to write letters for you so anyway I went to Cambridge at the end of this program I met Slava Shokurov another Russian mathematician but this guy is now a proper algebraic geometry and he agreed to be my second PhD advisor in fact in the first two years I picked up some very difficult problems they are still open not solved and not surprisingly I couldn't prove much about those things and I did all the thing about my PhD basically in the third year with help of Shokurov in 2004 I finished PhD moved to Cambridge after a short stay in Warwick and again during actually the the PhD I spent also five months in Hopkins John Hopkins University I spent two months in Moscow State University so you see in total I have been away for more than a year during my PhD study so I really can't emphasize this point enough that you better get out and travel as much as you can and let me also say a few things generally about mathematicians life as a mathematician I think maybe more generally as an academic usually consists of doing three things research so at least in top university that's number one teaching and also there is service so you have to make time for all these activities and I'm afraid to tell you the order you get the more senior you get the less time you will have the more responsibilities you will have because you get more things to do you will have family responsibilities you will have a lot more things to worry about so the PhD time is actually the freest time of your life probably and also to be a successful mathematician you need a lot of qualities you you need a strong internal motivation that's the only way that can sustain you for a long time to do hard work but that applies to any other subject you have to concentrate really very highly and then you have to be very patient because it doesn't go well all the time sometimes it goes wrong sometimes you were for months for a year for two years in the end you can't show anything for it because you couldn't prove what you were trying to prove at least in chemistry if you have some idea you test something at least you can say I tried this and it didn't work but you can't do that in mathematics you can't say I tried it and it didn't work and you have to manage your time very well because in mathematics usually we don't have a lab so other people can't tell you what to do you have to decide on your own how to use your time how to manage everything so in reality we do two jobs we do we are mathematicians but we also manage us we have to manage our own life and our research in the last couple of minutes let me also tell you a bit more outside mathematics so in my case I think being a curd the Kurdish culture helped me a lot in my life in so many ways for example during the war in all those really extremely difficult times the culture helped us to survive you could see people all the time joking and just mentally to be happy that's extremely important I think it's really relevant for this day also even if there is no war for example I can claim that people in my village in the war time were more happy than people now in Cambridge it's just there is material and there is mental activity there is these I think different of course they are related but they are different to be happy just psychologists can't make you happy you need culture to be happy you need social life but these all are in the context of culture so sometimes when I in general I'm interested in psychology as some of my people in my family and I get quite annoyed when I see these solutions of when people I have depression or whatever just I don't know deep breath and I do this and that that's not going to work you need people around you to support you you need a culture you need a social structure so that's why I am a great supporter of cultures honestly I don't care about country what I like our culture those should survive because it's important for the survival of humanity in the long term diversity of cultures is like diversity in in biology so for ecosystem to survive you need biodiversity I think for human to survive you need diversity of cultures I really hate to live in a world where everyone speak the same language everyone eat the same food everyone wear the same dress it's just extremely boring one reason I like mathematics is because of this diversity there are so many ideas of different kinds I like music because I think of it of this diversity there are so many types of music so many ways that you can enjoy and I think it's the same with with culture and the human life so that's why I try to teach my kid as Danco Kurdish he learned Kurdish who now he speaks fluently from only one person because there is no other Kurdish speaking person in the neighborhood so he learned it from just one person so that also proves another point that you can teach a language by just your own okay I will stop here you
 Now I'm glad to introduce the next speaker, Hocher Birkar from Cambridge.  Hocher Birkar moved from Wotan, Iran to Britain in his childhood and he was educated in Britain.  Apparently he did very well there because as a student he got a fellowship of London  mass society as the most promising student. He fulfilled the promise and got Fields Medal  last year in Rio de Janeiro. Wikipedia says that Hocher Birkar means migrant mathematician.  In that sense I am also Hocher Birkar as are many people in this room.  Hello everyone and thank you very much for the kind introduction.  So I will, the title of my talk suggests, I will talk more about my personal life and also the  education journey. One reason for this is that last year I gave a talk here also and it was all  about mathematics and nothing else. This time I wanted to do something a little bit different to  make it a bit more maybe entertaining but also in the way I'm hoping to tell you a few things  especially for the young people how I did mathematics and how I approached mathematics,  how I thought about mathematics and some of the challenges I faced and maybe you can find some  advice there, some tips for your own journey. So I was born in a city called Medi-1 or  officially it's called Medi-1, it's actually not really correct, it should be Medi-1.  In Kurdistan on the border of Iran and Iraq you can actually even walk to the border just  would take you maybe one hour or something like that. So we were very close and the region I lived  in is it has a lot of mountains so it has a climate in a sense that is similar to Europe,  it's not very dry, it's actually quite green but we have four seasons so each season is quite  different from the others. Here you have you see some pictures of the city and then nearby  surrounding of the city. I was born in a village just opposite the city not inside the city itself.  So as many of you know Kurdish people live in the Middle East and our region is divided into four  countries Iran, Iraq, Turkey and Syria and we have had lots of problems especially the last 100 years  we have been in really terrible shape until quite recently just even the cup even last year there  were Kurdish cities being destroyed just really for for not good reasons just almost artificial  reasons. So it's life has been very difficult for us especially because there are four countries not  just one we have to deal with four different countries and they are all actually they all  don't like each other but except on the issue of the Kurds when it comes to this issue they all  unite and make life even more difficult for us. Anyway so when I was a few months old the  there was a revolution in Iran and even before that it was a bit chaotic and then a few months  after I was born there was a revolution so the whole government changed and everything changed  and when I was about two years old then the Iran-Iraq war started which lasted for eight years  and since we were living on the border we were we were just trapped in the middle of the war  which there was no way to really escape. Most of the threat was aerial fortunately in my region  my city there was never land invasion it was always aerial and it was quite often you see  airplanes coming and dropping bombs and especially when I was in primary school so these eight years  covered all my primary school years and very often we were in classrooms and then instead of  after the lecture going to to have some fun in the middle of the lecture the airplanes would come  and we would just run out and the only thing we knew to do was run through the mountains  but we did that very very often and when there is a war a war disrupts everything including  education although there were schools but as you can imagine in such an environment schools can't be  really very good and the school that I started to study it was just a normal house and turned  into a school there were like three rooms and with a lot of children so you can imagine the  conditions were not very great but still I am very grateful to those teachers who in that kind of  environment that kind of circumstances they didn't give up on teaching us so I am really  grateful to them and the war of course poses a lot of dangers also indirectly not just the  bombing but also in directories so for example one other thing that we did very often as children  were playing with explosives because you could find them everywhere especially small ones like  bullets if you just worked around two three minutes you would find some bullets and we did it we made  it even more dangerous by making a fire and then putting these bullets into the fire  and what we did was we dig some holes around the fire when we put the bullet in them and we  would just jump into the holes and see what happens the bullets were flying everywhere  but it's really amazing that no one got hurt playing all these games I mean there were other  people injured or even killed later on but at least at that time all these plays actually didn't  lead to anyone's death or even injury my ancestors were there were aristocrats we used to have a  lot of land in the area and I think they enjoyed life they had a good life but unfortunately  sometimes before I was born we basically lost all of these privileges because the government at some  point decided to redistribute the land and they did it in a quite funny way they invited all the  aristocrats in the region the king of the time the like yeah there was a kingdom at the time and  then he said we will have like a festival and said you all come to have fun and then they put all of  them in prison some of them they never returned we never know what happened to them like my great  grandfather never returned we never know what happened to him suppose he died at some point  so we we lost the power but we still had some pieces of land and we continued to do  farmers so by my time we were just simple peasants we didn't really have privileges  but since my ancestors they enjoyed themselves the local people actually didn't like us very  much because they saw that we come from the same line of people who didn't treat them very well  so they tried to revenge on us sometime and also make life a bit difficult anyway so we my parents  were doing farming and I also did farming as all my brothers and sisters in the family we spent a  lot of time farming until I finished undergraduate that was basically normal life whenever there was  farming in spring and summer we did even the day before examinations we would still do farm  but fortunately my father he took education very seriously and he thought that that's the only way  to go ahead farming is not the future for us we have to study and we have to get degrees and  do some other kind of jobs but also education in a sense also had value not just for getting a job  but just to know knowledge also was appreciated so that was lucky for me that they just gave us  the idea that that's the only way to go you should not think about anything else education  and so we all attended school and we tried to do our best in fact my father even before I became  six which was the official age to go to school he took me just informally to school to the local  school and he even himself came to sit with me just to make me feel good with the school because  some children even now when they go to school for the first time they are really afraid but he just  wanted to eliminate that and make me feel good so that later on I will study better but for the  first time that I felt any special connection with mathematics was when I was in grade five  I remember that once we had an exam and I did very well but I didn't actually study very well  and I was a bit surprised how I got a very good mark almost 100 without spending too much time  doing mathematics so I think that's the first time that it attracted my attention in a special way  because I tried generally to do good in all the courses but this one somehow  made an impression on me but also luckily in that year we had a really good school a really good  teacher unlike maybe the especially the grade four where we had a teacher who used to beat us  really very very often so maybe this is not very familiar to you but at that time beating was very  beating was very common in schools so the teachers could beat us and when I was in grade four the  only thing I remember from that year is that the teacher was beating us so bad but fortunately  this guy in grade five he did not even have a diploma so basically he had himself partial  education but just naturally he was a really very peaceful and kind person and also he was creative  in the way he approached teaching for example he would take us outside with the nature especially  in spring which is very beautiful and he would just teach there like for one and two hour so that  made a lot of difference that's much better than just sitting in a classroom all the time and he  also organized competitions with nearby schools even in other villages we would go somewhere in the  nature and we would start to compete and I usually in that year I was responsible for the mathematics  section of the competitions so that was all good but what made the biggest difference was my older  brother he was himself interested in engineering and science in general but I have no idea where he  got his ideas because there wasn't really I mean there were schools textbooks and so on but the way  he approached learning and education was completely different from everyone else in the region not only  in in our family he was extremely creative he would always try to invent things design things  build things the kind of thing that no one else would even think about so as one example he  for example at some point he was printing himself there was no printing machine except in  official places but he just invented printing by his own he carved out some plastic sheets all the  letters and then he could actually print out things and people would think that this is an official  letter from some government agency and some of the other things he did like he built a projector  he even made animation for it and he would show us all the children in the neighborhood he's  his animation he's moving so he was really extremely creative and that was great for me to have someone  like that next to me just to follow as an example even if he didn't try to teach me still to have  someone like you like that in your family in your neighborhood it's really can make an extremely  big difference but at some point he also tried to teach me a bit more advanced mathematics and also  physics for example calculus so that was when I was about maybe 11 years old but other children  would learn that four years maybe four years later so I learned that much earlier four five years  earlier and then but also what was important about his approach was that he didn't teach me  so that I get a good grade he just saw that learning these things is just really exciting  just you learn it for the sake of learning or for inventing something not just to be good in school  that was really also it made a really big difference on my approach to education and to learn  so if you if you ask me who is the most influential person in your education I think this is the guy  so he maybe started all these things and now surprisingly all the people in my family my  sibling they all ended up to be engineers except me who took it wrong the path  me anyway so by the time I got to high school my brother was already in university so we were  separate but I just followed this line of mathematics and also up to some extent of physics  but at some point I realized that the reason I like those physical physical things is actually  because of the mathematics so at some point I just in a way forget about the physics and just  concentrated on the mathematics in really like high concentration and there were a few things  about mathematics that I really liked one of those things is that mathematics is really precise  there is no arguments and fighting and things once you prove something and your colleagues  verify it then it's proved and there is no argument it's not like philosophy or literature or politics  and that that kind of subject so even in physics you have like different theories it's not always the  same theory but mathematics just once everything is precise and I really like that and also in  mathematics when you establish something it stays there forever whatever people proved  2 000 years ago 3 000 years ago is still correct is still there and it's not going to disappear  again if you compare to physics 200 years ago and now it's completely different computer science  is even much much faster even if you don't if there is a program that you used 50 years ago  even if it's still correct but you just don't use it anymore you just replace it by something else  but the mathematics is kind of immortal it just stays there for forever and then mathematics is also  beautiful all the things that I try to learn I found them just to be really there's some kind of beauty  in it which I think brings mathematics very close to ours but it's just the beauty is a little bit  different you you need a special language to understand this beauty it's like poetry if someone  reads a chinese poetry to you and if you don't know chinese language then there is no way you can  appreciate that that poetry you can translate but much of the beauty is lost in the translation  it's the same with with mathematics you need the language you need a background  to appreciate this beauty to see the beauty and but fortunately I went into mathematics enough  to see this beauty already in in high school but it's not all just about beauty I saw that is also  exciting to do mathematics there is a joy in doing mathematics when you solve a problem there is some  kind of joy in that and I think in that sense mathematics is a bit similar to sports when play  when you play football maybe you don't care so much about the beauty of the game but you just  feel that there is some kind of joy some kind of enjoyment in playing football some kind of  excitement and I think for me when I do research a lot of it has to do with  it so when I learn things from other people yeah I appreciate the beauty but when I do mathematics  myself is more this fun and excitement which is similar to sports and finally mathematics is also  useful so that was maybe one other reason that attracted me to mathematics is yeah we have pure  and applied math but quite often pure math also ends up to be applicable to some world problems  anyway but the problem for me was in high school that I was totally isolated there was not one  single person to ask what should I do what should I read how should I approach mathematics  there was no internet at the time there were no computers where I lived and until I entered  university I lived in my hometown and I left only twice to go to a nearby city and there also I  couldn't find many people but I could at least buy some books so it was total isolation then I had  to decide all by myself what to do what I should read and how I should think about mathematics  that can be maybe it that makes life very difficult and maybe doesn't work for everyone but  I think maybe that was good for me just this isolation taught me how to be independent how to  learn things by myself and not rely on school and teachers and lectures and this experience  proved to be extremely useful in later years when I entered university when I did PhD and so on  so fortunately the local library for some mysterious reason had really excellent mathematics  books and if you at least at the time when I read those books there was a log of people who took  this book from the library and almost all of them were taken just by me or by me and maybe some  else by mistake so I don't know why they put these books in the library but that happened to be a very  good coincidence for me so I read a lot of these books and I still remember some of those books  which are also famous in the West for example there is a book about the life of mathematicians  it's called Men of Mathematics it's just the biography of especially all the generation  and mathematics all the way from Euclid and from the Greeks until 19 and early 20th century  and just reading the life of these people that they spend most of their time discovering things  it just felt to me it was really so exciting I couldn't see any other way of living basically I  couldn't imagine going to work in a shop or something like that I thought that this is really  the way I should also be and there were also lots of books for example this book by Corant  and Robbins is called What Mathematics is a quite big book and in this book you find introduction to  many parts of mathematics like algebra and number theory geometry topology and all kind of things  so this is much more advanced than high school and by reading all these books especially books  like this then I got acquainted with many ideas from modern mathematics and that proved to be  very useful in later years when I entered university so at that time I liked more the  geometric side of the mathematics especially classical geometry like projective geometry  but also topology already for example in this book about analysis you see matrix metric spaces  and a lot of topology but also in this book about this what's mathematics there is also  section about topology and for example you learn about Euler number Euler characteristic and  these topological spaces and I just found those things to be really very nice and very beautiful  but so in a way this is one of the points maybe I can put it as an advice you have to go outside  school system you have to go outside university system to really learn something deep  if you only stick to your lecture your lecture notes then well you can still succeed I suppose but  if you really want to be successful you have to go out if you like a subject already for example  if you are undergraduate if you like in mathematics suppose that you like algebra then there is no  reason why you should not go and pick up some books about algebra and read them just the  algebra books in undergraduate are not enough you can just if you like a topic just follow that  topic yeah try to do your best in your exams and lectures but also you have to really go  out of the box so I learned that in high school and that was really amazing but also already at in  in high school I saw that just reading mathematics is not enough yes there is beauty and so on there  but if I don't do it myself then I just don't get the satisfaction that I want again this is  similar to let's say football if you just go and watch football then yes you can enjoy but when  you play yourself it's actually much more enjoyable you get a lot more by doing it yourself so I try to  also do research and I guess I proved certain things maybe not important at all but that's not  the point the point is just try to do research just try to prove something new this can be done  already in high school but in undergraduate definitely it can be done it doesn't have to be  very important you don't have to publish it but just that experience of trying to do something new  will be amazingly useful later when you do a phd in this age I mean in many universities I think  they also for example in Cambridge they encourage this at least to pick up a topic learn about it  and if you can prove something new great if not that's not the end of the world so maybe that's  another important piece of advice anyway when I was about 15 or 16 I decided to be a mathematician  that's it at that point I decided my my life basically and I think that was really great just  to have a direction precise direction of what you want to do with your life I think the earlier  maybe the better unless if you pick the wrong that's the wrong thing I mean if you want to  yeah I mean at that age of course you never know what people do if they decide to play  video game for the rest of their lives obviously that's not a good idea but I think if anyone in  high school decide to be a mathematician a physicist a computer scientist an artist or whatever I think  they would not regret it that's my feeling I mean if they are genuinely passionate about whatever  subject so anyway the lectures the school were not really so much useful to me so at the last  year the final year of high school I just dropped out of the school there was a parallel system where  you could just go at the end of the year take the exam so you didn't have to attend lectures and  and think that that also worked for me probably I should have done it much earlier  anyway I entered university university of Tehran to do undergraduate in pure mathematics and for  the first time I met actual mathematicians people who actually wrote articles and published it before  that I had never seen even one but there I saw people actually doing mathematics but also there  was a much much better library than what I had in my home city so the environment obviously was  much better I was not totally isolated again although in a way I was you could say isolated  because the way I approached mathematics was quite different from all my classmates because I just  continued my line from high school the way I did mathematics in high school I just continued the same  way in university so we come again to the same point that you have to pick a topic you have to  pick something that you are passionate about and just follow it and you don't have to follow it forever  so when I was first year undergraduate I just picked a book about algebraic topology and I learned a  lot of things about algebraic topology like fundamental groups homology theory and so on  I didn't become a topologist but I never regret that I read it books in first year undergraduate  they had nothing to do with exams with lectures because the first topology course we had was  four years later so this was just on my own that I was interested in topology and that's it  especially here I saw this interaction between algebra on one side and topology on the other side  and that was really exciting and later I come back to a similar point  in the second year I picked up some books about commutative algebra and I just felt that I like  this topic commutative algebra and just read a lot about it so this book for example here you see  is one of the standard textbooks of graduate courses in commutative algebra and in fact that  year I met a guy who was doing a master in mathematics in pure mathematics and we talked a  little he is a speciality was commutative algebra we talked a little bit and he was amazed that  he was amazed that almost everything he learned in his lectures I already knew and then I told him that  it was just for fun I liked the topic and then I read about it  but in the third year I had the same person happen to be my roommate and he was reading a book all  the time he was by his side sometimes very excited sometimes annoyed and angry and then I got curious  what is in this book that is so so much into this book all the time reading the book and it happened  to be this book of Shafari which about algebraic geometry is one of the like the basic graduate level  courses in algebraic geometry I got also interested and just picked up the book and starts to read  I realized that a lot of those things that I learned in commutative algebra actually all  came from algebraic geometry much of it here you have not only the algebra but also the geometry  and there is basically a dictionary between algebra commutative algebra and geometry whatever  you say in one side can be translated into the other side and vice vice versa so I that was  really amazing I mean this connection between algebra and geometry was in a sense more profound  than in the algebraic topology a case here the connection was much much more stronger  and I just got hooked and I never left this field so I have been doing algebraic geometry for the last  20 something years and it all started here with this book  but in the fourth year I also try to read with more advanced algebraic geometry especially this  standard and scary book of heart showing about algebraic geometry this is written in a more  modern language language of schemes not in a classical language it follows the style the school  of alexander groten dick I couldn't understand much here I mean that's the impression most  students have when they read this book because it's very abstract there is some geometry there but  actually it's very hard to see the intuition but I was lucky again because I had read the  classical version of algebraic geometry first when I arrived here I had a lot of  actually intuition from from the classical side of the theory but groten dick also happened to be  a really great source of inspiration for me both his school of mathematics was somehow very appealing  to me but also his life and his personality so many of you I guess already know that he was  a basically a stateless person living in France for a very long time and I don't know if finally he  got citizenship in France or not but at least when he was active he actually was a stateless person  at least to me I think he is should be if you pick two three mathematicians in all history  I would put this guy maybe on the top anyway in the year 2000 I moved to the UK  and the first year I couldn't study I was there basically as a refugee but fortunately all was  sorted out in one year for many other people it takes much much longer it can take 10 years  but I was lucky I think that I just spent one year dealing with immigration and so on and in 2001  I started to do a PhD course in Nottingham University advised by Ivan Fesenko a number  theorist but I had already decided to be an algebraic geometry and there was no algebraic  geometry in this department in this university so Ivan was a very helpful very supportive he  comes from the Russian school of mathematics where they learn a great deal of mathematics in  basically every subject so they are not narrow he knew a lot of algebraic geometry but still  to do research in algebraic geometry you need someone professional algebraic geometry  so in the first year just after a few months I went to the Newton Institute in Cambridge  there was a program about algebraic geometry especially  biorectional geometry for five months and I just go went to stay there in fact the organizer told  me you cannot come to attend this thing but Ivan insisted a lot send them a lot of emails they  finally agreed I go there without any support so I went there rented a room on my own and just  attended the seminar so maybe that's another piece of advice don't stay all the time where you study  travel you can go to other places you can not just for workshops and conferences you can visit  other places for a month for two months for three months you are not going to lose anything you  will just meet other people and that can be first of all you learn a lot of stuff from other people  but also when you apply for jobs you need someone to write letters for you if you spend all your  time in your own institution you can only ask your advisor and no one else but if you visit  other people they will be happy to write letters for you so anyway I went to Cambridge at the end  of this program I met Slava Shokurov another Russian mathematician but this guy is now a  proper algebraic geometry and he agreed to be my second PhD advisor in fact in the first two years  I picked up some very difficult problems they are still open not solved and not surprisingly I couldn't  prove much about those things and I did all the thing about my PhD basically in the third year  with help of Shokurov in 2004 I finished PhD moved to Cambridge after a short stay in Warwick  and again during actually the the PhD I spent also five months in Hopkins John Hopkins University  I spent two months in Moscow State University so you see in total I have been away for more than  a year during my PhD study so I really can't emphasize this point enough that you better get  out and travel as much as you can and let me also say a few things generally about mathematicians  life as a mathematician I think maybe more generally as an academic usually consists of  doing three things research so at least in top university that's number one teaching and also  there is service so you have to make time for all these activities and I'm afraid to tell you the  order you get the more senior you get the less time you will have the more responsibilities you  will have because you get more things to do you will have family responsibilities you will have  a lot more things to worry about so the PhD time is actually the freest time of your life probably  and also to be a successful mathematician you need a lot of qualities you you need a strong  internal motivation that's the only way that can sustain you for a long time to do hard work  but that applies to any other subject you have to concentrate really very highly  and then you have to be very patient because it doesn't go well all the time sometimes it goes  wrong sometimes you were for months for a year for two years in the end you can't show anything for  it because you couldn't prove what you were trying to prove at least in chemistry if you have some  idea you test something at least you can say I tried this and it didn't work but you can't do that  in mathematics you can't say I tried it and it didn't work and you have to manage your time  very well because in mathematics usually we don't have a lab so other people can't tell you what to  do you have to decide on your own how to use your time how to manage everything so in reality we do  two jobs we do we are mathematicians but we also manage us we have to manage our own life and our  research in the last couple of minutes let me also tell you a bit more outside mathematics so in my  case I think being a curd the Kurdish culture helped me a lot in my life in so many ways for  example during the war in all those really extremely difficult times the culture helped us to survive  you could see people all the time joking and just mentally to be happy that's extremely important I  think it's really relevant for this day also even if there is no war for example I can claim that  people in my village in the war time were more happy than people now in Cambridge it's just  there is material and there is mental activity there is these I think different of course they are  related but they are different to be happy just psychologists can't make you happy you need culture  to be happy you need social life but these all are in the context of culture so sometimes when I in  general I'm interested in psychology as some of my people in my family and I get quite annoyed when  I see these solutions of when people I have depression or whatever just I don't know deep  breath and I do this and that that's not going to work you need people around you to support you  you need a culture you need a social structure so that's why I am a great supporter of cultures  honestly I don't care about country what I like our culture those should survive because it's  important for the survival of humanity in the long term diversity of cultures is like diversity in  in biology so for ecosystem to survive you need biodiversity I think for human to survive  you need diversity of cultures I really hate to live in a world where everyone speak the same  language everyone eat the same food everyone wear the same dress it's just extremely boring  one reason I like mathematics is because of this diversity there are so many ideas of different kinds  I like music because I think of it of this diversity there are so many types of music so many ways  that you can enjoy and I think it's the same with with culture and the human life so that's why I try  to teach my kid as Danco Kurdish he learned Kurdish who now he speaks fluently from only one person  because there is no other Kurdish speaking person in the neighborhood so he learned it from just one  person so that also proves another point that you can teach a language by just your own okay I will stop here  you
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