India's Math Genius Manjul Bhargava talks to NDTV about his love for mathematics, and suggests that the teaching of math in India can be made fun and 'less robotic', using even magic tricks as teaching aids. He also touches on the mathematical nature of the tabla and other forms of music.
Here is the full transcript:
NDTV: Hello and welcome from me and from students all over India who are studying in the finest of colleges here in Delhi. We are all here together to do just one thing, to listen and learn from this bewildering genius Manjul Bhargava. Manjul is one of the greatest minds India has ever created. He has been awarded a prize, which I consider even greater than the Nobel Prize. Prof. Bhargava has recently won the Fields Medal in Mathematics. Why do I say its possibly even greater than the Nobel Prize, because this highest global award in Mathematics is given only once in every 4 years. How about a round of applause for this young gentleman and actually you will notice, as the evening goes on, that his majesty and simplicity is really truly Indian. Why do I call him a bewildering genus? Because of what he did to actually win that mathematics award. It's simple really. He won it for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bind the average rank of elliptic curves. Simple as that, you got it? Simple stuff. So what has he done? He has counted rings of small rank and to bound the average rank of elliptic curves. I don't think I would even ask you to explain that in English
Prof Bhargava: Thanks
NDTV: But in English, just basically what does it mean for an average viewer?
Prof Bhargava: Well the subject that I work in is the area of number theory.
NDTV: Number theory.
Prof Bhargava: So, number theory basically is the art of understanding the whole numbers, the numbers we use to count 1234 and 0 and 1 and 2. So these are the whole numbers and number theory is about the science and art of understanding those numbers, understanding the special sequences of those numbers, like square numbers, the prime numbers and finally it's about solving equations whose solutions are whole numbers.
NDTV: So it's like relationships between numbers?
Prof Bhargava: That's right.
NDTV: Basically its number theory
Prof Bhargava: Exactly. Simple
NDTV: Simple, all of you can do that, right. So based on that when you, I just want to get an idea of you in Princeton, sitting and roaming with a whole lot of other mathematicians. What do you talk about? I mean would any one of us understand anything?
Prof Bhargava: Well I mean a lot of the mathematics that goes on at Princeton is with the students. So students like all of you and so I think the audience here, since there are mostly mathematics students here, would understand.
NDTV: They would understand what you are talking about because I have listened to some of your speeches to mathematicians and you know, I did study maths to a certain level, but it's just with in 10 seconds, but I guess a lot of you here would understand, but there are many different levels.
Prof Bhargava: No doubt
NDTV: Yes, your Mother taught you maths. She was a mathematician herself.
Prof Bhargava: Yes.
NDTV: Yes still is, of course, and you used to get bored with other subjects and go into a room and chat with her about maths and stuff?
Prof Bhargava: Yes, I always liked mathematics since very, very small, maybe two or three years old, and I used to love doing little math puzzles and coming up to all maths questions and then I'd go and bother her and say..
NDTV: Is this the answer?
Prof Bhargava: Yes is this the answer? Can you tell me how to do it and her answer always was you should figure it out itself and then come tell me. And so, I used to just enjoy just playing around with mathematics and if I ever got stuck, my mother was there, as a resource, and that was something very useful.
NDTV: But obviously she did something in the way she taught you, the way she inspired you in maths that created your interest in it, and you've often said, that to some extent, why the Indians may not be good at maths is the teaching is a bit robotic. How should maths be taught? Because a lot of people say, "oh God, maths I can't stand it."
Prof Bhargava: Well, I sympathise with people who say that because I myself really didn't like mathematics class
NDTV: Class, oh really
Prof Bhargava: So I used to do anything I could to avoid going to mathematics class. I would skip out on any excuse I could find...
NDTV: This is in Canada?
Prof Bhargava: In the United States.
NDTV: In the United States.
Prof Bhargava: In New-York yes. So I used to do everything I could to avoid going to mathematics class. One thing I did was just take some several months out of school and come to Jaipur here in India, where I didn't have to go to school. In fact one time, my parents and grandparents put me in school here, but I dropped out after a couple of weeks
NDTV: Oh I see...
Prof Bhargava: But I knew I loved mathematics, but I didn't like the way mathematics was taught in school and so I used to find my own ways to make mathematics fun. I used to play around with mathematics, do puzzles, ask my Mom for nice suggestions that would be fun for me. My grandfather, who was a Sanskrit scholar, he had lots of mathematics textbooks on his shelf from Ancient India, so I used to read those. So, I had a very non-standard mathematics education and I really enjoyed it. I think that contributed a lot
NDTV: So enjoyment is the key...
Prof Bhargava: My suggestion for teaching maths in schools is really make mathematics fun because mathematics actually is fun. A lot of us really don't realise that when we go to grade school because it is taught in a robotic way. You're given a problem and you're asked to memorise steps to solve it and then you just blindly apply it and try to be careful so you don't make an error, but you don't really know why you're doing those steps. It shouldn't be like that. It should really about being creative; coming up with those steps on your own and everyone will come up with a different way to do it. Mathematics is great because there is always one answer, but there are many ways to come to that answer. And in school we are taught one way to come to that answer, so mathematics is about coming up with your own creative ways to come to that one right answer. There's not one path and everybody has their personal path that they can discover and that's what makes it fun. That's the adventurous part of mathematics, the creative part of mathematics and we miss that in the way mathematics is taught.
NDTV: So are you saying this teaching of mathematics slightly robotic around the world, worse in India or India is like the rest of the world, it's generally taught in a robotic way?
Prof Bhargava: It's pretty bad throughout the world, but in India, here it's even more about memorisation than it is in other parts of the world, so maybe it goes even further...
NDTV: It's fascinating that you hated maths class, you just did it yourself, bad lesson for all of you, maybe it's a bloody good lesson for all of you...
Prof Bhargava: If any questions now, we can start taking questions and then, you're from Rajasthan?
Student 1: First of all it's an honour to be speaking to you Professor, my question is that how do you think we can make maths classes more fun, because I know you have a class for your first year students in which you teach maths through magic tricks? So can you recommend some methods for the teachers here in India, you know, how do we make maths fun for people like me who hate it?
Prof Bhargava: It's a good question, one of the most common questions when I've been on tours for these past few months talking about mathematics. The most common question is-why is mathematics class so dry, so boring, so all about memorization and rote when we hear mathematics is an art and a creative subject, but why do we not see that in school? One thing that I have been doing at Princeton University for the past years, I developed a course, for freshmen, so first year, where we teach mathematics through poetry, classical music, classical Indian music, magic tricks like you said, and games; so those are the four ingredients of the course through which I get to teach fundamental mathematical concepts. So make classes begin with a card trick that's based on a mathematical concept and when you see this card trick, there's nothing you can do but want to know how it worked. And for the card tricks that I do or for the rope tricks or for the various other kinds of magic tricks that I do, there is a fundamental math concept that you have to learn in order to know how it works, and everyone is so immediately excited about knowing how did it work. And so, while they learn how it works and while they learn how to do the magic trick, they can't avoid but also learn in the process the fundamental mathematical concept. And when you learn it that way, there's no way that you'll ever forget it because you have that visual of the trick, the memory of the trick of how it worked and there's no way you'll forget the mathematical concept.
NDTV: So if they come and say how does it work, you say go figure it out yourself?
Prof Bhargava: Oh yes, so I teach in 3 hour seminars. I start with the trick, then I have everyone discuss, okay, what are the things that went into the trick? What are the things that could've been happening and then I give little hints and everyone has to think about it themselves, and then everyone has to sort of come up with their own way of understanding how it went. And by the end of the class, they know how to do the trick and they know the mathematical concept and since they discovered on their own, there's no way they'll ever forget it.
NDTV: Nice, exactly and as you say, it's a visual, cum curiosity, cum some practical, so you'll never forget that.
Prof Bhargava: And the same happens there with games, lots of fundamental games that have basic mathematic concepts embedded in them. If you know those math concepts, you can always win the game. So I have these people play games with each other, and eventually some people start winning because they start seeing what math concept will allow them to win and eventually, everyone figures it out, and by the end of the class they can go and play their friends who are not in that class and beat them, and the reason is because they figured out that math concept on their own during this class.
NDTV: That's why you're seen at Las Vegas all the time at the Black Jack table
Prof Bhargava: Actually, that's another common question I get when I've been giving lectures about this kind of way of teaching. Can this be used in Las Vegas? And the answer is yes, but I don't use it that way
NDTV: So the answer is yes, so that's even more worrying, the signals you're giving. I don't know what's going to happen to this serious bunch of students, any other questions?
Student 2: It's truly an honour to meet you in person. My question to you is that since you mentioned that as a student you hated maths classes, could you please tell us about your typical day in a classroom? Did you always prefer the first seat or you know, just like any other students, most of the students prefer the last bench, so most of the time where were you found?
Prof Bhargava: I preferred, I should probably not being say this, I preferred not going at all. When I did go, I would hide. I wouldn't go right to the back, but you know, I'd hide somewhere. I shouldn't say that about all my classes. There were many classes that I liked and I had some fantastic teachers, both in New York and in Jaipur, when I went to school here. And when I really did like the class, I'd want to sit in the front. So I was excited about that and when I was less excited about the class, I'd prefer to hide, so it really depended on the quality of the teaching and I think that's true about everyone. When you're excited you want to go sit up front and when you're less excited, but you have to go, then you try to hide. So a couple of the teachers that I had were actually really good and those were years when I did go to every single class, and I was excited about it and I'd sit up closer, but most years I tried to skip.
NDTV: Fall asleep while listening. I must say there are shows where, good and bad. When we had a show where we had doctors do live phone-ins and answering questions, we had one guy phone, who said he can't sleep, he can't sleep, he can't sleep, and so he was asking the doctor, what should he do, there's only one thing that puts me to sleep and that's when Prannoy Roy comes on the 9:00 news, live. And of course I have to play this again and again. So in the sense sometimes you fall asleep in class or nearly or look the other way and think of something else?
Prof Bhargava: I try not to do that, but I often do think about my own things. And another way to make Maths class, I mean when maths class is sometimes boring, you can make it fun by sometimes, instead of those doing those rote memorisation that you've been asked to do, try to come up with the solution on your own. Maybe just take hints by just taking quick peeks at some of the steps, but just really trying to figure them on your own, and often you'll find that you'll come up with different steps to lead but, of course, math only has one answer. So if you come up with steps logically, you'll always end up at the right answer, but since you came up with it yourself, you'll never forget it, and that's one way to make maths class more fun. Do it on your own.
NDTV: Are you all going to do that? You are also a musician, sorry before I ask you that, I wanted to ask you, when did you figure that you are actually quite good at this, that you are just outstanding? Which point was your turning point?
Prof Bhargava: I think I've never even thought in those terms. I knew I liked it and so, I would do it whenever I had the chance to. I went to a school that didn't really have that much math enrichment, it wasn't one of the top subjects at the public school that I went to, so I didn't really think in those terms. I would avoid math class like I said and I would do math on my own and I did well on all the exams. You know I always got a perfect score on all the exams but I didn't know what that meant. But when I really got excited about math and realized that's definitely what I want to do for a living, when I got to college at Harvard, and that was the first time when I met lots of students who loved mathematics, before it was just me, so that was a real eye-opening experience for me. I was at Harvard, doing mathematics with all the other students at Harvard and then I thought, maybe this is something I should because I am at the same level as the other students here.
Student 3: Leonardo Da Vinci quoted that we need to understand science of art and then art of science to excel in life. So is there something like mathematics of art and art of mathematics?
Prof Bhargava: Mathematics should be thought of as an art. Sometimes we don't see that when we do mathematics in grade school, but just like any art, music, painting, mathematics is a creative subject. Coming up to the theorems is an art, finding the way to understand why that theorem is true is an art, everyone comes up with a different answer to the same question and the reason is that there are different ways of understanding and ways of expressing yourselves, just like in any art. Mathematics is very much like that and one reason why I teach my course through poetry, through magic, these are all arts, through music, through games, because these are all different kinds of arts and mathematics closely connects to all of them. It should really be taught that way. Mathematics is often taught like a science but a lot of people don't know that its origins, especially in India, is in the arts, and we shouldn't forget that interesting aspect. We should be using both sides of the brain to understand mathematical problems.
NDTV: There is some mathematical basis to music as well., tabla, what is the connection? This is very tough for me to understand, maybe others do, but what are, what is the connection?
Prof Bhargava: Tabla. Tabla is all about rhythms, time cycles, trying to fit various pieces into a rhythm cycle and so, the arrangements that one practices as a tabla player uses a lot of mathematics. One example that I always start with in the class that I teach, just to get people to realise that mathematics is connected with poetry and music, is an example of Hemachandra. That is always one that I start with because it brings in tabla and poetry and mathematics right away. So, in Sanskrit poetry, there are two kinds of syllables, there is a notion of laghu syllable and guru syllable, how many people of heard of laghu and guru before?
NDTV: That's about 5 percent, 10 percent.
Prof Bhargava: So, yes, that's one thing I feel should be there in mathematics. The notion of laghu and guru is something that led to some of the most fundamental breakthroughs of mathematics, believe it or not, in ancient times in India. So this notion of a laghu syllable and a guru syllable, a short syllable and a long syllable, so in any kind, every kind of poetry in the world, there is a notion of stressed syllable or unstressed syllable. And you see poetry, some syllables are stressed and some are unstressed. In Sanskrit, it goes a step further. Stressed syllables are long and unstressed syllables are short and short syllables take one beat of time to say and a long syllable takes two beats of time to say. So what's peculiar about Sanskrit is that a long syllable takes exactly twice as long to say as a short syllable. So when you recite Sanskrit poetry, all the syllables will be like this, some will last one beat of time and some will last two beats of time. The short are one beat and the long are two beats, and so this is very peculiar about Sanskrit, and as a result of the set-up of Sanskrit poetry, lots of ancient poets considered lots of mathematical questions that related to this one-beat, two beat-up set-up of Sanskrit poetry. So one basic question that would come up, if you're writing poetry and you have 8 beats left in your stanza and you need to fill it with long and short syllables, where a long syllable takes two beats and a short syllable takes one beat, how many ways can you fill in 8 beats with long syllables and short syllables, where long syllables are two beats and short syllables are one?
NDTV: Don't give us the answer, does anyone know?
Prof Bhargava: What would be your guess?
NDTV: Oh wow, come on.
Audience: Communication combinations?
Prof Bhargava: Yes, it is about communication and combinations, but it's still beyond what you learned in school. What would be your guess, 8 beats filling it with longs and shorts, long two beats and short one beat?
NDTV: How many variations can you make?
Prof Bhargava: How many ways can you do it? So you could do long, long, long, long or you could do short, short, short, short, short, short.
NDTV: 8 times.
Prof Bhargava: Or you could do short, short, long, short, long, long, long, short, short, long, so I actually clap these rhythms with my class and we try to figure out how many there are.
NDTV: Sorry, say it again.
Student 4: 34 times
Prof Bhargava: Yes, so he knows the answer.
NDTV: So it just went straight above my head.
Prof Bhargava: So the answer is 34. So most people when they first hear this question, they think oh maybe there are 8 ways, 10 ways, the answer is actually 34, which is more than what most people expect it to be. And in this ancient Indian work of Hemachandra, which I read to the class because it's written in poetry, the answer, so it's a poetic question, it's a question about poetry and the answer is written in poetry. So it's something that really excites people, it excited me when I was a child so I like to share it, and it's really easy. So Hemachandra's answer was as follows: write down the numbers 1 and 2, and then every number you write down subsequently should be the sum of the previous two numbers that you wrote down. So 1, 2, then 1 plus 2 is 3, then 2 plus 3 is 5, then 3 plus 5 is 8, then 5 plus 8 is 13, then 8 plus 13 is 21 and then 13 plus 21 is 34 and so on. The 8th number that you write down will give you the number of rhythms that have 8 beats, which is 34.
NDTV: Wow, that's amazing actually.
Prof Bhargava: And this goes back to the year 1050, so these numbers may be familiar to many people, right. They are called the Fibonacci numbers in India. Even though in India they were discovered pre-Fibonacci, by Hemachandra in this work on poetry, which I find very amazing. So when we are taught Fibonacci numbers in school, maybe this is true in India as well, I've definitely seen it in some Indian schools, they teach it the way Fibonacci came up with it, which is about the problem about rabbits. This incestuous problem about rabbits where brothers and sisters are mating, and it's a very unnatural act, but the real place that it actually came up is in poetry, and the reason that it came up is a very natural one. You need to know the answer, if you want to know how many ways you can fill in the rest of the poem. So that's an example of the kind of way mathematics came up in poetry in ancient times and still comes up today. When people compose Marathi poetry or some Kannada poetry, this type of poetry is very similar in those languages as well.
NDTV: And it came in India a long time before this, right, so how important or how relative to other parts of the world? I know you have quoted maths, historically in many other parts of the world how important was India in developing some of these concepts in maths in ancient times?
Prof Bhargava: Oh very important. I mean in this example I just gave of course the fundamental, the fundamental concept, the Fibonacci numbers, the Hemachandra numbers as Sanskrit is called, it was important for the world of mathematics and science and art. So that's one example, but there are many. Pascal's Triangle we learned at school, with something that also came up in context of poetry, in the work of Pingle and by 2000 years before Pascal's
NDTV: Really?
Prof Bhargava: Yes, these were all the things really known in India, except that the Sanskrit is; so there are lots of contributions in India, mathematics is really a global subject. Every ancient of these nations have contributed
NDTV: Which is the other center that contributed?
Prof Bhargava: Egypt was a great center. Mesopotamia was a great center, China was a great centre and then Greece was the great centre
NDTV: So India is in context of equivalent to all of these, a little bit, like it's difficult to...
Prof Bhargava: Yes, all are equally important in development of mathematics. You know in India I have been seeing lots of debates, India contributed nothing to science versus India contributed everything to science. But the truth is that, I would say I have read a lot of mathematics work of India, the truth is India contributed really key ideas to geometry, lays some of the foundations of trigonometry, foundation of calculus were done in India in the Kerala school. So, all the major subjects of mathematics have lots of the key foundations from India, that's the true fact. It's not nothing it's not everything, but it's really important
NDTV: I am going to ask you something very pedantic. I mean being a pedantic person this connection between tabla and maths play 10 seconds of it and show him some connection
Prof Bhargava: I wished I could have a tabla here
NDTV: No, just use this to imagine they are tablas and just that kind of poetic connection.
Prof Bhargava: Long and short beats, all these things get translated when you are playing tabla also. So there are lots of compositions for tabla where you have, so when you are playing with a sitar player or something, you may be in a part of a piece with those jugalbandi like between long and short. So you're doing improvisation with each other, just passing back and forth, long and short combinations. That's why Hemachandra's idea was very important for tabla players. You are improvising, you have 8 beats of music left and you have to fill it with this number of beats of time, which is long, which is short. You need to know all those combinations and how they made so you can draw on them. So, there is mathematics, which is to know what you have for your disposal, just like a painter needs to know what kind of colours they have at disposal, but then there is the artistic aspect, which one should I choose from there, that will sound best at that moment, So that's the artistic aspect
.
NDTV: Just show the long and short beat for example
Prof Bhargava: So, one way in which tabla happens, dha tin dhina might be a long dhina, might be a short
NDTV: That's fantastic. Have you learned some of this from Zakir Hussain?
Prof Bhargava: Yes. Actually a lot ofthis dha tin dhina, I kind of realized that it can come up in these long and short kinds of things, learned it from him, Zakir Hussain ji
NDTV: But as you say...
Prof Bhargava: The whole time I used to play two different things, dina dha tin dhin, long and short that's all. It's amazing how just two things can be used to create an incredible complex pattern. And Hemachandra's numbers would tell you the number of patterns that are there, they go very quickly, the numbers and they tell you the number of patterns that you can make, has two motives can be...
NDTV: And how you put them together that's the art
.
Prof Bhargava: Yes that's the art
.
NDTV: That's your fan like at that moment
Prof Bhargava: Yes, you made the audience go that's wah wah, that's the good part of it
NDTV: Now the questions.
Student 5: Hello Sir, its good to meet you. You have been talking about how the mathematics is a sort of art. I wanted to know that like when faced with the question, do you need to be very creative, like you need some sort of genius intellect to jump to the answers, like during solving you make some un-extended jumps to the method of solving versus you can solve it in the mechanical manner? Do you believe that someone has an advantage or rather who does not have an intellect to solve?
Prof Bhargava: Just like any art some of the great artists create. It, what's needed is; inspiration is probably the most important. Your talent, some call it talent, some call it inspiration, you have to like it what you are doing and the rest is hardworking and practice and that's probably even bigger than the talent portion.
NDTV: The practice comes when you enjoy it also
Prof Bhargava: Yes, so your hard working and practice will be better if you will be enjoying it. And that's why I will say when students like mathematics they should go into mathematics instead of going into engineering, the closest thing it considers popular. If you do what you like, you're passionate about, that will lead to your best work. Because you're being inspired, you will be willing to work hard. So it's the combination of inspiration and talent because the best thing is hard work and practice. For tabla, for an art, for every thing, what you do worthy of those and mathematics is no exception
NDTV: So all of you are mathematicians, so just be honest, how many of you really love working with maths? Okay, that was good for a conclusion, okay any more questions?
Student 6: I want ask you, that apart from research and teaching, what are the future career options we can pursue only doing maths?
Prof Bhargava: So in the United States mathematics is very popular major. People do mathematics and then go to law because the kind of logical thinking that you learned doing mathematics. the argument you have to make in understanding mathematics is really useful in law. Some people go to finance, obviously mathematics is important in finance. They are going to companies for consultancy because the rational thinking you learn as a mathematician is useful in consulting in business, somehow in India that's common. First of all very few are there. It's wonderful that you all are doing mathematics. You guys will realise you are in a minority. I find in India you have to spread the world that mathematics is fun, there are many things you can do. Businesses, companies here need to learn it too, that it's really good to have mathematicians. They do a lot of good work because they have learned to work in a completely rational and logical way. Like deduction from a little bit of information, they will be able to make a complete deduction. That's the skill that is useful way beyond mathematics. So you know, it's very common to be a math major and do many things, not just going into mathematics research or be a maths teacher. Those are two average things you can do in mathematics. There is a great need for that obviously in this country. There are many new institutions that have science research that has been opened. There's a severe faculty shortage, so if you can produce really good mathematicians in this country, they really need it to fill this faculty shortage. There are more math teachers needed in this country in general, but even if you don't do mathematics teaching or research there are many things you can do. Those skills you have learned in mathematics are useful throughout.
NDTV: There are many economists who originally are mathematicians, so you can go into economics or you can go in other areas as well.
Prof Bhargava: There are many economists who think of themselves as mathematicians
NDTV: So I have got a hold of what they call rapid-fire questions from various emails, sms that we have got and they are just like one word or two word answers. So the first one is the other side of it. Do you like movies?
Prof Bhargava: I do, but honestly I don't get much of time to watch them
NDTV: So what kind of movie, if you had to watch one?
Prof Bhargava: You know I grew up liking Pixar movies and I still do, as I like movies about history. Gandhi was one of my favourite movies, about the stories of the figures who change the world, I really enjoy the movies, taking inspiration from that
.
NDTV: Somebody wants to know Bollywood in any corner of your life? No chance. What about sports, any interest there? Or no time really?
Prof Bhargava: I know. I grew up playing tennis, that's always my favourite and I am actually still a major tennis fan, never miss any of the slams. US Open every year.
NDTV: Oh really, wow
Prof Bhargava: From beginning to end
NDTV: Can you predict wins from the beginning with mathematical permutations?
.
Prof Bhargava: I have done pretty good
NDTV: Do you dream of maths at night?
Prof Bhargava: Yes, it's a good question. I don't know but I do for sure, many times I am thinking of a maths problem before I go to sleep and in the morning I figure out the answer
NDTV: Wow
Prof Bhargava: So I have to encourage that. I don't remember the process of thinking at night. But when I wake up it may be the process of mind clearing or something, but if you start anything, unless you do mathematics, you will sleep on it, You know its a phase. It works on mathematics too.
NDTV: So all of you read some maths problem before you go to sleep, last thing all right. If you were not a mathematician what would you be?
Prof Bhargava: I would be a musician.
NDTV: Musician
Prof Bhargava: Yes
NDTV: Wow, tabla?
Prof Bhargava: Tabla player, I am a kind of tabla player without....
NDTV: That would be your passion?
Prof Bhargava: Yes
NDTV: What's your favourite food?
Prof Bhargava: I think dosa is my favourite. Pizza is a close second
NDTV: So you like food. Somebody wants to know can you even fry an egg or make toast? Do you cook?
Prof Bhargava: Yes I do. I really do like food so I do like a lot of cooking .I don't get as much time as I like, but when I do at times I enjoy it
NDTV: Somebody says what happens if 5 mathematicians are locked in a room together? I know, that's like a nightmare
Prof Bhargava: I think its kind of amazing, mathematicians just love talking about maths, so they just talk about different topics after they have dinner with mathematicians and you know whenever the conversation turns about, talking about...
NDTV: Even at the dinner?
Prof Bhargava: Yes, even at the dinner
NDTV: What do you say to someone who says, that is quite common, I hate maths?
Prof Bhargava: That means he didn't learn in the right way
NDTV: Right, right...
Prof Bhargava: It's interesting that its okay in society to say that, because maths is so fundamental and yet people can be proudly saying oh I always hated mathematics. Can you imagine people saying I hated to learn, to read? People don't say that, right? I think that needs to change. You know maths is just fundamentals, reading, you shouldn't hate it. You should find the better way to learn it. Even being proud of illiterate, the same relates to being proud of not knowing maths. That's my feeling.
NDTV: And it is just the way of being taught the math or you are brought up on maths
Prof Bhargava: Yes I think so
NDTV: And you can change that?
Prof Bhargava: Yes
NDTV: Somebody wants to know, do you do weird things, like you automatically count the number of people in the audience? That's a strange question
Prof Bhargava: I have personally done, and I am sure there are mathematicians they do. I know mathematicians are known to be really quirky, they have their own tricks
NDTV: So they are kind of put them in bunches and put them in some theorem?
.
Prof Bhargava: For me the quick is, if I am working in some place I look at the floor tiles and analyse the geometry pattern
NDTV: Really? Wow
Prof Bhargava: That's a quirk which I had since I was a child.
NDTV: And do you kind watch were you step or you just make patterns out of it?
Prof Bhargava: Yes sometimes my step goes according to the geometric pattern
NDTV: Really, wow. Somebody wants to know what keeps you awake at night?
Prof Bhargava: I personally sleep really well. So nothing, nothing keeps me awake
NDTV: Not that, I haven't cracked that
Prof Bhargava: There have been nights where I was so engulfed by mathematics problems where I didn't, you know, there were nights I just stayed up all night. As it was such an exciting idea that I didn't want to do any thing around but work it out so I had those experiences, but only a few in my life, I can say
NDTV: So three more questions. What's the one thing you want to do in life from now onwards? One big thing
Prof Bhargava: For the last few months when I got this Fields Medal I guess life has a done a change. And I have realised that I suddenly have a passion to try to change education. So I think that's become certainly my main passion, to change the mathematics stuff, like a curriculum shift, that is exciting again
NDTV: Isn't it wonderful. I think it badly needs it. Two more questions I think. Because of all your records, your past, I just want to know how you are human? I just tied up the last question, do you cry?
Prof Bhargava: Not so much any more I guess. I only get sad about things I wish were different. And I use those as opportunities in that I think I am not different then anybody.
NDTV: So like you saying, many people here watching, could become good mathematicians like you, may be not as good as you, but if they're taught properly, given a ride, stimulated, it's not like you have to be super human to do that?
.
Prof Bhargava: Right and taking initiative on their own. If you are passionate about something, its not available in the school you are in, you do it on your own. You find the right book that teaches you in the way you like and just explore and develop the right way, because there is not any one way, which works for every body. So you have to discover it for yourself, figure out what you are passionate about and figure out the path that you want to take that you will enjoy the most and work hard on it. And then....
NDTV: Great. Questions?
Student 7: Hi Sir, some of the greatest mathematicians and scientists have done some of the best work in 20's and 30's. So how important would you say is starting early? How important starting early?
Prof Bhargava: Yes starting early is good but that doesn't mean that you have to decide what you're going to do early. You can be passionate about the many things starting early and then as you move forward, you can narrow it. It's not good to specialize too fast in my opinion and you can be good at many things. You don't have to specialise in one thing. But it's good to start early in many things, is what I'd say, as you figure out and narrow down your particular passions, you can do that as you get older...
NDTV: So actually one of the toughest things is finding your passion. I mean the whole process, because of this age, their age and your age about the same, that you got so many different things and signals, noise, you don't know whether what you're doing is what your parents or society wants you to do, you've got to find what you enjoy and what you are good at...
Prof Bhargava: Right. Right
NDTV: How do you do that?
Prof Bhargava: I think, you know, the right way I mean, there is, some how society does push people out, societal attitudes push people, mainly engineering, law, medicine, that's noise that you should try to keep out, you know that, that's there but keep it out. When you're working you know whether you are enjoying it or not. When you are doing a problem in math or whether you're reading a piece of poetry, you know whether you are enjoying it or not. That's what helps you narrow things down. As you are in school or even outside school, when you're doing things, you know those moments that are really memorable to you and you have to just focus on those and say what did I like about that? What are the other things that I like that'll give me the same experience and then learn those, be passionate about those. You don't need to specialise very quickly. Liberal arts, I think is a very wonderful concept, be good at many things that you like and you can specialize. As you do more of those things you will realize more, which things are even more memorable than the others, and eventually you can specialize. But be good at many things early on, figure out what you enjoy, pay attention when you enjoy something and seek out what are things like that that you can continue doing.
NDTV: But you, you did that plus also manage to keep out the noise and that you so you could become an IAS officer, whatever. How did you keep the noise out because that's a lot of pressure on kids?
Prof Bhargava: Yes, that requires a little discipline. You have to stick to your guns if you know you really like something. You make that clear to your family, I really like this, and I want to do this for a living, and your family will support you.
NDTV: And your family will support you. Well, coming the to last few questions, there is a question from Sahil from IIT?
Sahil: My question is that you know, you are highly inspired by the Vedic mathematics and you know their work and that is highly reflected in whatever you did until now. So how do you see it, you know, be a part of the mathematics that is being taught in school now, you know, given that an education system right now is very rudimentary mathematics until class 10 and then just takes a form in just two years, 11 and 12, and all the options that you have are either the main streams fields, you know, engineering, medicine, law, it's been like you know, you reach the age of 22 and you're still in the mainstream fields. Now, it's very late for you to decide, you know, it's very risky to go for mathematics now in this stage, so how do you look to revamp mathematics as a subject you know, a pragmatic, perceptive way? Because its not really possible to, you know, in school being taught like games and all of that because you have board examinations....
NDTV: That's the point, you should be taught like that, that's the big change that's needed.
Sahil: How do you really implement in the education system, Sir?
Prof Bhargava: You tell the teachers that this is how it should be, convince the teachers that this is how you should teach it, convince the parents, the students,
NDTV: That is how you got the best results...
Prof Bhargava: Right, so for example, I mean the way I started at Princeton, I didn't make that the curriculum for everybody right away. I taught it as an experimental course, as an experimental freshmen course. It got the highest evaluation of any mathematics course. Now many people are convinced in the United States and are adapting that syllabus. So the same thing, we bring it in gradually and if it's successful, we spread it further and eventually if it works very well, it will take over and then the Boards will change too. The boards will incorporate questions of that kind.
NDTV: Is your course or your lectures available on you-tube or on I-tunes?
Prof Bhargava: They are not yet. They probably will be
NDTV: It's great if they were. So, everyone knows about them. They are packed and everybody enjoys them.
Prof Bhargava: So eventually that is my goal. It was an experimental course the first time. I didn't put it online right away. I wanted to fine-tune it. Once I feel good about it, then I'll have it online for everybody to check. I am just joining this programme called Gyan which is this programme to bring scientists from all over the world to India and bring lots of students together to teach, to teach say mathematics or science in a more fun way, have the students inspired, record those and have it available on video for the entire country. So that's something that this particular course will help make into that format eventually.
NDTV: We have a last question, this young man in front of you wanting to ask a question.
Student 8: First of all, congratulations on winning the Fields Medal, I'm sure it's a very big thing and everyone around India is really proud of that achievement. Sir, I would like to ask you that currently, I hear that you are working on the BSD conjunction problem. Sir, can we expect another breakthrough from the genius himself in the coming future?
Prof Bhargava: I guess you read it that it is one of my favourite forms. The BSD Conjunction is one of the seven millennium problems at the Clay Mathematics Institute, we give the people one million dollar prizes for each of these
NDTV: I see
Prof Bhargava: That's now my motivation for working on it. It's never for the mathematicians. That is not the reason. It's just the point now that the seven points are really fundamental, that is one of my favourite ones. It's a number theory problem. It tells you how to solve cubic equations in whole numbers. So, in school we all learned how to solve cubical equations and the way we solve cubical equations, there is a general egestion that allows you to solve cubical equations in any number of variables. But for cubic equation it's no need to solve cubic equation in one variable once you have a cubic equation in two variables, Nobody know how to solve it in whole numbers, this way the conjecture tells you how to solve it. I think that's one of the fundamental problems, that's why its one of my favourites
NDTV: I have heard, talking about this earlier, I think just finally just to the role of intuition, in life intuition is very important for all of us. Is maths contrary to intuition or are they complementary? Does it remove intuition or does it help intuition?
Prof Bhargava: I think it's just like any other art. As if, I sort of feel that when mathematics starts, one of the goals should be to develop intuition about mathematics. And right now the way to start, you start the way of memorization, so the intuition is not developed. But if you discover the way to solve problems on your own you develop the intuition. So when the next problem comes and is not exactly the same kind as first, you will have an intuition to say, oh these are the changes I need to make in order to solve it. That development of intuition is very important, and is very important in my own mathematical research. Having developed intuition for many years in solving different kind of problems and if I just memorised this is how it will solve this problem and this is how it will solve this problem; so when a third kind of problem comes and those same steps don't work, it's a problem. If you will develop the intuition where you can make slight changes, just like when you are painting, you develop techniques, develop an intuition, how to express various emotions by this combination of colours, in the same way you develop an intuition for the kind of techniques and how to combine them to solve different problems when they come up.
NDTV: Oh that's fascinating. Thank you very, very much for taking out time and hope you succeed in your venture to change the way maths is taught
.
Prof Bhargava: Thanks every one for your support
NDTV: Thanks very much, that was fabulous
Here is the full transcript:
NDTV: Hello and welcome from me and from students all over India who are studying in the finest of colleges here in Delhi. We are all here together to do just one thing, to listen and learn from this bewildering genius Manjul Bhargava. Manjul is one of the greatest minds India has ever created. He has been awarded a prize, which I consider even greater than the Nobel Prize. Prof. Bhargava has recently won the Fields Medal in Mathematics. Why do I say its possibly even greater than the Nobel Prize, because this highest global award in Mathematics is given only once in every 4 years. How about a round of applause for this young gentleman and actually you will notice, as the evening goes on, that his majesty and simplicity is really truly Indian. Why do I call him a bewildering genus? Because of what he did to actually win that mathematics award. It's simple really. He won it for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bind the average rank of elliptic curves. Simple as that, you got it? Simple stuff. So what has he done? He has counted rings of small rank and to bound the average rank of elliptic curves. I don't think I would even ask you to explain that in English
Prof Bhargava: Thanks
NDTV: But in English, just basically what does it mean for an average viewer?
Prof Bhargava: Well the subject that I work in is the area of number theory.
NDTV: Number theory.
Prof Bhargava: So, number theory basically is the art of understanding the whole numbers, the numbers we use to count 1234 and 0 and 1 and 2. So these are the whole numbers and number theory is about the science and art of understanding those numbers, understanding the special sequences of those numbers, like square numbers, the prime numbers and finally it's about solving equations whose solutions are whole numbers.
NDTV: So it's like relationships between numbers?
Prof Bhargava: That's right.
NDTV: Basically its number theory
Prof Bhargava: Exactly. Simple
NDTV: Simple, all of you can do that, right. So based on that when you, I just want to get an idea of you in Princeton, sitting and roaming with a whole lot of other mathematicians. What do you talk about? I mean would any one of us understand anything?
Prof Bhargava: Well I mean a lot of the mathematics that goes on at Princeton is with the students. So students like all of you and so I think the audience here, since there are mostly mathematics students here, would understand.
NDTV: They would understand what you are talking about because I have listened to some of your speeches to mathematicians and you know, I did study maths to a certain level, but it's just with in 10 seconds, but I guess a lot of you here would understand, but there are many different levels.
Prof Bhargava: No doubt
NDTV: Yes, your Mother taught you maths. She was a mathematician herself.
Prof Bhargava: Yes.
NDTV: Yes still is, of course, and you used to get bored with other subjects and go into a room and chat with her about maths and stuff?
Prof Bhargava: Yes, I always liked mathematics since very, very small, maybe two or three years old, and I used to love doing little math puzzles and coming up to all maths questions and then I'd go and bother her and say..
NDTV: Is this the answer?
Prof Bhargava: Yes is this the answer? Can you tell me how to do it and her answer always was you should figure it out itself and then come tell me. And so, I used to just enjoy just playing around with mathematics and if I ever got stuck, my mother was there, as a resource, and that was something very useful.
NDTV: But obviously she did something in the way she taught you, the way she inspired you in maths that created your interest in it, and you've often said, that to some extent, why the Indians may not be good at maths is the teaching is a bit robotic. How should maths be taught? Because a lot of people say, "oh God, maths I can't stand it."
Prof Bhargava: Well, I sympathise with people who say that because I myself really didn't like mathematics class
NDTV: Class, oh really
Prof Bhargava: So I used to do anything I could to avoid going to mathematics class. I would skip out on any excuse I could find...
NDTV: This is in Canada?
Prof Bhargava: In the United States.
NDTV: In the United States.
Prof Bhargava: In New-York yes. So I used to do everything I could to avoid going to mathematics class. One thing I did was just take some several months out of school and come to Jaipur here in India, where I didn't have to go to school. In fact one time, my parents and grandparents put me in school here, but I dropped out after a couple of weeks
NDTV: Oh I see...
Prof Bhargava: But I knew I loved mathematics, but I didn't like the way mathematics was taught in school and so I used to find my own ways to make mathematics fun. I used to play around with mathematics, do puzzles, ask my Mom for nice suggestions that would be fun for me. My grandfather, who was a Sanskrit scholar, he had lots of mathematics textbooks on his shelf from Ancient India, so I used to read those. So, I had a very non-standard mathematics education and I really enjoyed it. I think that contributed a lot
NDTV: So enjoyment is the key...
Prof Bhargava: My suggestion for teaching maths in schools is really make mathematics fun because mathematics actually is fun. A lot of us really don't realise that when we go to grade school because it is taught in a robotic way. You're given a problem and you're asked to memorise steps to solve it and then you just blindly apply it and try to be careful so you don't make an error, but you don't really know why you're doing those steps. It shouldn't be like that. It should really about being creative; coming up with those steps on your own and everyone will come up with a different way to do it. Mathematics is great because there is always one answer, but there are many ways to come to that answer. And in school we are taught one way to come to that answer, so mathematics is about coming up with your own creative ways to come to that one right answer. There's not one path and everybody has their personal path that they can discover and that's what makes it fun. That's the adventurous part of mathematics, the creative part of mathematics and we miss that in the way mathematics is taught.
NDTV: So are you saying this teaching of mathematics slightly robotic around the world, worse in India or India is like the rest of the world, it's generally taught in a robotic way?
Prof Bhargava: It's pretty bad throughout the world, but in India, here it's even more about memorisation than it is in other parts of the world, so maybe it goes even further...
NDTV: It's fascinating that you hated maths class, you just did it yourself, bad lesson for all of you, maybe it's a bloody good lesson for all of you...
Prof Bhargava: If any questions now, we can start taking questions and then, you're from Rajasthan?
Student 1: First of all it's an honour to be speaking to you Professor, my question is that how do you think we can make maths classes more fun, because I know you have a class for your first year students in which you teach maths through magic tricks? So can you recommend some methods for the teachers here in India, you know, how do we make maths fun for people like me who hate it?
Prof Bhargava: It's a good question, one of the most common questions when I've been on tours for these past few months talking about mathematics. The most common question is-why is mathematics class so dry, so boring, so all about memorization and rote when we hear mathematics is an art and a creative subject, but why do we not see that in school? One thing that I have been doing at Princeton University for the past years, I developed a course, for freshmen, so first year, where we teach mathematics through poetry, classical music, classical Indian music, magic tricks like you said, and games; so those are the four ingredients of the course through which I get to teach fundamental mathematical concepts. So make classes begin with a card trick that's based on a mathematical concept and when you see this card trick, there's nothing you can do but want to know how it worked. And for the card tricks that I do or for the rope tricks or for the various other kinds of magic tricks that I do, there is a fundamental math concept that you have to learn in order to know how it works, and everyone is so immediately excited about knowing how did it work. And so, while they learn how it works and while they learn how to do the magic trick, they can't avoid but also learn in the process the fundamental mathematical concept. And when you learn it that way, there's no way that you'll ever forget it because you have that visual of the trick, the memory of the trick of how it worked and there's no way you'll forget the mathematical concept.
NDTV: So if they come and say how does it work, you say go figure it out yourself?
Prof Bhargava: Oh yes, so I teach in 3 hour seminars. I start with the trick, then I have everyone discuss, okay, what are the things that went into the trick? What are the things that could've been happening and then I give little hints and everyone has to think about it themselves, and then everyone has to sort of come up with their own way of understanding how it went. And by the end of the class, they know how to do the trick and they know the mathematical concept and since they discovered on their own, there's no way they'll ever forget it.
NDTV: Nice, exactly and as you say, it's a visual, cum curiosity, cum some practical, so you'll never forget that.
Prof Bhargava: And the same happens there with games, lots of fundamental games that have basic mathematic concepts embedded in them. If you know those math concepts, you can always win the game. So I have these people play games with each other, and eventually some people start winning because they start seeing what math concept will allow them to win and eventually, everyone figures it out, and by the end of the class they can go and play their friends who are not in that class and beat them, and the reason is because they figured out that math concept on their own during this class.
NDTV: That's why you're seen at Las Vegas all the time at the Black Jack table
Prof Bhargava: Actually, that's another common question I get when I've been giving lectures about this kind of way of teaching. Can this be used in Las Vegas? And the answer is yes, but I don't use it that way
NDTV: So the answer is yes, so that's even more worrying, the signals you're giving. I don't know what's going to happen to this serious bunch of students, any other questions?
Student 2: It's truly an honour to meet you in person. My question to you is that since you mentioned that as a student you hated maths classes, could you please tell us about your typical day in a classroom? Did you always prefer the first seat or you know, just like any other students, most of the students prefer the last bench, so most of the time where were you found?
Prof Bhargava: I preferred, I should probably not being say this, I preferred not going at all. When I did go, I would hide. I wouldn't go right to the back, but you know, I'd hide somewhere. I shouldn't say that about all my classes. There were many classes that I liked and I had some fantastic teachers, both in New York and in Jaipur, when I went to school here. And when I really did like the class, I'd want to sit in the front. So I was excited about that and when I was less excited about the class, I'd prefer to hide, so it really depended on the quality of the teaching and I think that's true about everyone. When you're excited you want to go sit up front and when you're less excited, but you have to go, then you try to hide. So a couple of the teachers that I had were actually really good and those were years when I did go to every single class, and I was excited about it and I'd sit up closer, but most years I tried to skip.
NDTV: Fall asleep while listening. I must say there are shows where, good and bad. When we had a show where we had doctors do live phone-ins and answering questions, we had one guy phone, who said he can't sleep, he can't sleep, he can't sleep, and so he was asking the doctor, what should he do, there's only one thing that puts me to sleep and that's when Prannoy Roy comes on the 9:00 news, live. And of course I have to play this again and again. So in the sense sometimes you fall asleep in class or nearly or look the other way and think of something else?
Prof Bhargava: I try not to do that, but I often do think about my own things. And another way to make Maths class, I mean when maths class is sometimes boring, you can make it fun by sometimes, instead of those doing those rote memorisation that you've been asked to do, try to come up with the solution on your own. Maybe just take hints by just taking quick peeks at some of the steps, but just really trying to figure them on your own, and often you'll find that you'll come up with different steps to lead but, of course, math only has one answer. So if you come up with steps logically, you'll always end up at the right answer, but since you came up with it yourself, you'll never forget it, and that's one way to make maths class more fun. Do it on your own.
NDTV: Are you all going to do that? You are also a musician, sorry before I ask you that, I wanted to ask you, when did you figure that you are actually quite good at this, that you are just outstanding? Which point was your turning point?
Prof Bhargava: I think I've never even thought in those terms. I knew I liked it and so, I would do it whenever I had the chance to. I went to a school that didn't really have that much math enrichment, it wasn't one of the top subjects at the public school that I went to, so I didn't really think in those terms. I would avoid math class like I said and I would do math on my own and I did well on all the exams. You know I always got a perfect score on all the exams but I didn't know what that meant. But when I really got excited about math and realized that's definitely what I want to do for a living, when I got to college at Harvard, and that was the first time when I met lots of students who loved mathematics, before it was just me, so that was a real eye-opening experience for me. I was at Harvard, doing mathematics with all the other students at Harvard and then I thought, maybe this is something I should because I am at the same level as the other students here.
Student 3: Leonardo Da Vinci quoted that we need to understand science of art and then art of science to excel in life. So is there something like mathematics of art and art of mathematics?
Prof Bhargava: Mathematics should be thought of as an art. Sometimes we don't see that when we do mathematics in grade school, but just like any art, music, painting, mathematics is a creative subject. Coming up to the theorems is an art, finding the way to understand why that theorem is true is an art, everyone comes up with a different answer to the same question and the reason is that there are different ways of understanding and ways of expressing yourselves, just like in any art. Mathematics is very much like that and one reason why I teach my course through poetry, through magic, these are all arts, through music, through games, because these are all different kinds of arts and mathematics closely connects to all of them. It should really be taught that way. Mathematics is often taught like a science but a lot of people don't know that its origins, especially in India, is in the arts, and we shouldn't forget that interesting aspect. We should be using both sides of the brain to understand mathematical problems.
NDTV: There is some mathematical basis to music as well., tabla, what is the connection? This is very tough for me to understand, maybe others do, but what are, what is the connection?
Prof Bhargava: Tabla. Tabla is all about rhythms, time cycles, trying to fit various pieces into a rhythm cycle and so, the arrangements that one practices as a tabla player uses a lot of mathematics. One example that I always start with in the class that I teach, just to get people to realise that mathematics is connected with poetry and music, is an example of Hemachandra. That is always one that I start with because it brings in tabla and poetry and mathematics right away. So, in Sanskrit poetry, there are two kinds of syllables, there is a notion of laghu syllable and guru syllable, how many people of heard of laghu and guru before?
NDTV: That's about 5 percent, 10 percent.
Prof Bhargava: So, yes, that's one thing I feel should be there in mathematics. The notion of laghu and guru is something that led to some of the most fundamental breakthroughs of mathematics, believe it or not, in ancient times in India. So this notion of a laghu syllable and a guru syllable, a short syllable and a long syllable, so in any kind, every kind of poetry in the world, there is a notion of stressed syllable or unstressed syllable. And you see poetry, some syllables are stressed and some are unstressed. In Sanskrit, it goes a step further. Stressed syllables are long and unstressed syllables are short and short syllables take one beat of time to say and a long syllable takes two beats of time to say. So what's peculiar about Sanskrit is that a long syllable takes exactly twice as long to say as a short syllable. So when you recite Sanskrit poetry, all the syllables will be like this, some will last one beat of time and some will last two beats of time. The short are one beat and the long are two beats, and so this is very peculiar about Sanskrit, and as a result of the set-up of Sanskrit poetry, lots of ancient poets considered lots of mathematical questions that related to this one-beat, two beat-up set-up of Sanskrit poetry. So one basic question that would come up, if you're writing poetry and you have 8 beats left in your stanza and you need to fill it with long and short syllables, where a long syllable takes two beats and a short syllable takes one beat, how many ways can you fill in 8 beats with long syllables and short syllables, where long syllables are two beats and short syllables are one?
NDTV: Don't give us the answer, does anyone know?
Prof Bhargava: What would be your guess?
NDTV: Oh wow, come on.
Audience: Communication combinations?
Prof Bhargava: Yes, it is about communication and combinations, but it's still beyond what you learned in school. What would be your guess, 8 beats filling it with longs and shorts, long two beats and short one beat?
NDTV: How many variations can you make?
Prof Bhargava: How many ways can you do it? So you could do long, long, long, long or you could do short, short, short, short, short, short.
NDTV: 8 times.
Prof Bhargava: Or you could do short, short, long, short, long, long, long, short, short, long, so I actually clap these rhythms with my class and we try to figure out how many there are.
NDTV: Sorry, say it again.
Student 4: 34 times
Prof Bhargava: Yes, so he knows the answer.
NDTV: So it just went straight above my head.
Prof Bhargava: So the answer is 34. So most people when they first hear this question, they think oh maybe there are 8 ways, 10 ways, the answer is actually 34, which is more than what most people expect it to be. And in this ancient Indian work of Hemachandra, which I read to the class because it's written in poetry, the answer, so it's a poetic question, it's a question about poetry and the answer is written in poetry. So it's something that really excites people, it excited me when I was a child so I like to share it, and it's really easy. So Hemachandra's answer was as follows: write down the numbers 1 and 2, and then every number you write down subsequently should be the sum of the previous two numbers that you wrote down. So 1, 2, then 1 plus 2 is 3, then 2 plus 3 is 5, then 3 plus 5 is 8, then 5 plus 8 is 13, then 8 plus 13 is 21 and then 13 plus 21 is 34 and so on. The 8th number that you write down will give you the number of rhythms that have 8 beats, which is 34.
NDTV: Wow, that's amazing actually.
Prof Bhargava: And this goes back to the year 1050, so these numbers may be familiar to many people, right. They are called the Fibonacci numbers in India. Even though in India they were discovered pre-Fibonacci, by Hemachandra in this work on poetry, which I find very amazing. So when we are taught Fibonacci numbers in school, maybe this is true in India as well, I've definitely seen it in some Indian schools, they teach it the way Fibonacci came up with it, which is about the problem about rabbits. This incestuous problem about rabbits where brothers and sisters are mating, and it's a very unnatural act, but the real place that it actually came up is in poetry, and the reason that it came up is a very natural one. You need to know the answer, if you want to know how many ways you can fill in the rest of the poem. So that's an example of the kind of way mathematics came up in poetry in ancient times and still comes up today. When people compose Marathi poetry or some Kannada poetry, this type of poetry is very similar in those languages as well.
NDTV: And it came in India a long time before this, right, so how important or how relative to other parts of the world? I know you have quoted maths, historically in many other parts of the world how important was India in developing some of these concepts in maths in ancient times?
Prof Bhargava: Oh very important. I mean in this example I just gave of course the fundamental, the fundamental concept, the Fibonacci numbers, the Hemachandra numbers as Sanskrit is called, it was important for the world of mathematics and science and art. So that's one example, but there are many. Pascal's Triangle we learned at school, with something that also came up in context of poetry, in the work of Pingle and by 2000 years before Pascal's
NDTV: Really?
Prof Bhargava: Yes, these were all the things really known in India, except that the Sanskrit is; so there are lots of contributions in India, mathematics is really a global subject. Every ancient of these nations have contributed
NDTV: Which is the other center that contributed?
Prof Bhargava: Egypt was a great center. Mesopotamia was a great center, China was a great centre and then Greece was the great centre
NDTV: So India is in context of equivalent to all of these, a little bit, like it's difficult to...
Prof Bhargava: Yes, all are equally important in development of mathematics. You know in India I have been seeing lots of debates, India contributed nothing to science versus India contributed everything to science. But the truth is that, I would say I have read a lot of mathematics work of India, the truth is India contributed really key ideas to geometry, lays some of the foundations of trigonometry, foundation of calculus were done in India in the Kerala school. So, all the major subjects of mathematics have lots of the key foundations from India, that's the true fact. It's not nothing it's not everything, but it's really important
NDTV: I am going to ask you something very pedantic. I mean being a pedantic person this connection between tabla and maths play 10 seconds of it and show him some connection
Prof Bhargava: I wished I could have a tabla here
NDTV: No, just use this to imagine they are tablas and just that kind of poetic connection.
Prof Bhargava: Long and short beats, all these things get translated when you are playing tabla also. So there are lots of compositions for tabla where you have, so when you are playing with a sitar player or something, you may be in a part of a piece with those jugalbandi like between long and short. So you're doing improvisation with each other, just passing back and forth, long and short combinations. That's why Hemachandra's idea was very important for tabla players. You are improvising, you have 8 beats of music left and you have to fill it with this number of beats of time, which is long, which is short. You need to know all those combinations and how they made so you can draw on them. So, there is mathematics, which is to know what you have for your disposal, just like a painter needs to know what kind of colours they have at disposal, but then there is the artistic aspect, which one should I choose from there, that will sound best at that moment, So that's the artistic aspect
.
NDTV: Just show the long and short beat for example
Prof Bhargava: So, one way in which tabla happens, dha tin dhina might be a long dhina, might be a short
NDTV: That's fantastic. Have you learned some of this from Zakir Hussain?
Prof Bhargava: Yes. Actually a lot ofthis dha tin dhina, I kind of realized that it can come up in these long and short kinds of things, learned it from him, Zakir Hussain ji
NDTV: But as you say...
Prof Bhargava: The whole time I used to play two different things, dina dha tin dhin, long and short that's all. It's amazing how just two things can be used to create an incredible complex pattern. And Hemachandra's numbers would tell you the number of patterns that are there, they go very quickly, the numbers and they tell you the number of patterns that you can make, has two motives can be...
NDTV: And how you put them together that's the art
.
Prof Bhargava: Yes that's the art
.
NDTV: That's your fan like at that moment
Prof Bhargava: Yes, you made the audience go that's wah wah, that's the good part of it
NDTV: Now the questions.
Student 5: Hello Sir, its good to meet you. You have been talking about how the mathematics is a sort of art. I wanted to know that like when faced with the question, do you need to be very creative, like you need some sort of genius intellect to jump to the answers, like during solving you make some un-extended jumps to the method of solving versus you can solve it in the mechanical manner? Do you believe that someone has an advantage or rather who does not have an intellect to solve?
Prof Bhargava: Just like any art some of the great artists create. It, what's needed is; inspiration is probably the most important. Your talent, some call it talent, some call it inspiration, you have to like it what you are doing and the rest is hardworking and practice and that's probably even bigger than the talent portion.
NDTV: The practice comes when you enjoy it also
Prof Bhargava: Yes, so your hard working and practice will be better if you will be enjoying it. And that's why I will say when students like mathematics they should go into mathematics instead of going into engineering, the closest thing it considers popular. If you do what you like, you're passionate about, that will lead to your best work. Because you're being inspired, you will be willing to work hard. So it's the combination of inspiration and talent because the best thing is hard work and practice. For tabla, for an art, for every thing, what you do worthy of those and mathematics is no exception
NDTV: So all of you are mathematicians, so just be honest, how many of you really love working with maths? Okay, that was good for a conclusion, okay any more questions?
Student 6: I want ask you, that apart from research and teaching, what are the future career options we can pursue only doing maths?
Prof Bhargava: So in the United States mathematics is very popular major. People do mathematics and then go to law because the kind of logical thinking that you learned doing mathematics. the argument you have to make in understanding mathematics is really useful in law. Some people go to finance, obviously mathematics is important in finance. They are going to companies for consultancy because the rational thinking you learn as a mathematician is useful in consulting in business, somehow in India that's common. First of all very few are there. It's wonderful that you all are doing mathematics. You guys will realise you are in a minority. I find in India you have to spread the world that mathematics is fun, there are many things you can do. Businesses, companies here need to learn it too, that it's really good to have mathematicians. They do a lot of good work because they have learned to work in a completely rational and logical way. Like deduction from a little bit of information, they will be able to make a complete deduction. That's the skill that is useful way beyond mathematics. So you know, it's very common to be a math major and do many things, not just going into mathematics research or be a maths teacher. Those are two average things you can do in mathematics. There is a great need for that obviously in this country. There are many new institutions that have science research that has been opened. There's a severe faculty shortage, so if you can produce really good mathematicians in this country, they really need it to fill this faculty shortage. There are more math teachers needed in this country in general, but even if you don't do mathematics teaching or research there are many things you can do. Those skills you have learned in mathematics are useful throughout.
NDTV: There are many economists who originally are mathematicians, so you can go into economics or you can go in other areas as well.
Prof Bhargava: There are many economists who think of themselves as mathematicians
NDTV: So I have got a hold of what they call rapid-fire questions from various emails, sms that we have got and they are just like one word or two word answers. So the first one is the other side of it. Do you like movies?
Prof Bhargava: I do, but honestly I don't get much of time to watch them
NDTV: So what kind of movie, if you had to watch one?
Prof Bhargava: You know I grew up liking Pixar movies and I still do, as I like movies about history. Gandhi was one of my favourite movies, about the stories of the figures who change the world, I really enjoy the movies, taking inspiration from that
.
NDTV: Somebody wants to know Bollywood in any corner of your life? No chance. What about sports, any interest there? Or no time really?
Prof Bhargava: I know. I grew up playing tennis, that's always my favourite and I am actually still a major tennis fan, never miss any of the slams. US Open every year.
NDTV: Oh really, wow
Prof Bhargava: From beginning to end
NDTV: Can you predict wins from the beginning with mathematical permutations?
.
Prof Bhargava: I have done pretty good
NDTV: Do you dream of maths at night?
Prof Bhargava: Yes, it's a good question. I don't know but I do for sure, many times I am thinking of a maths problem before I go to sleep and in the morning I figure out the answer
NDTV: Wow
Prof Bhargava: So I have to encourage that. I don't remember the process of thinking at night. But when I wake up it may be the process of mind clearing or something, but if you start anything, unless you do mathematics, you will sleep on it, You know its a phase. It works on mathematics too.
NDTV: So all of you read some maths problem before you go to sleep, last thing all right. If you were not a mathematician what would you be?
Prof Bhargava: I would be a musician.
NDTV: Musician
Prof Bhargava: Yes
NDTV: Wow, tabla?
Prof Bhargava: Tabla player, I am a kind of tabla player without....
NDTV: That would be your passion?
Prof Bhargava: Yes
NDTV: What's your favourite food?
Prof Bhargava: I think dosa is my favourite. Pizza is a close second
NDTV: So you like food. Somebody wants to know can you even fry an egg or make toast? Do you cook?
Prof Bhargava: Yes I do. I really do like food so I do like a lot of cooking .I don't get as much time as I like, but when I do at times I enjoy it
NDTV: Somebody says what happens if 5 mathematicians are locked in a room together? I know, that's like a nightmare
Prof Bhargava: I think its kind of amazing, mathematicians just love talking about maths, so they just talk about different topics after they have dinner with mathematicians and you know whenever the conversation turns about, talking about...
NDTV: Even at the dinner?
Prof Bhargava: Yes, even at the dinner
NDTV: What do you say to someone who says, that is quite common, I hate maths?
Prof Bhargava: That means he didn't learn in the right way
NDTV: Right, right...
Prof Bhargava: It's interesting that its okay in society to say that, because maths is so fundamental and yet people can be proudly saying oh I always hated mathematics. Can you imagine people saying I hated to learn, to read? People don't say that, right? I think that needs to change. You know maths is just fundamentals, reading, you shouldn't hate it. You should find the better way to learn it. Even being proud of illiterate, the same relates to being proud of not knowing maths. That's my feeling.
NDTV: And it is just the way of being taught the math or you are brought up on maths
Prof Bhargava: Yes I think so
NDTV: And you can change that?
Prof Bhargava: Yes
NDTV: Somebody wants to know, do you do weird things, like you automatically count the number of people in the audience? That's a strange question
Prof Bhargava: I have personally done, and I am sure there are mathematicians they do. I know mathematicians are known to be really quirky, they have their own tricks
NDTV: So they are kind of put them in bunches and put them in some theorem?
.
Prof Bhargava: For me the quick is, if I am working in some place I look at the floor tiles and analyse the geometry pattern
NDTV: Really? Wow
Prof Bhargava: That's a quirk which I had since I was a child.
NDTV: And do you kind watch were you step or you just make patterns out of it?
Prof Bhargava: Yes sometimes my step goes according to the geometric pattern
NDTV: Really, wow. Somebody wants to know what keeps you awake at night?
Prof Bhargava: I personally sleep really well. So nothing, nothing keeps me awake
NDTV: Not that, I haven't cracked that
Prof Bhargava: There have been nights where I was so engulfed by mathematics problems where I didn't, you know, there were nights I just stayed up all night. As it was such an exciting idea that I didn't want to do any thing around but work it out so I had those experiences, but only a few in my life, I can say
NDTV: So three more questions. What's the one thing you want to do in life from now onwards? One big thing
Prof Bhargava: For the last few months when I got this Fields Medal I guess life has a done a change. And I have realised that I suddenly have a passion to try to change education. So I think that's become certainly my main passion, to change the mathematics stuff, like a curriculum shift, that is exciting again
NDTV: Isn't it wonderful. I think it badly needs it. Two more questions I think. Because of all your records, your past, I just want to know how you are human? I just tied up the last question, do you cry?
Prof Bhargava: Not so much any more I guess. I only get sad about things I wish were different. And I use those as opportunities in that I think I am not different then anybody.
NDTV: So like you saying, many people here watching, could become good mathematicians like you, may be not as good as you, but if they're taught properly, given a ride, stimulated, it's not like you have to be super human to do that?
.
Prof Bhargava: Right and taking initiative on their own. If you are passionate about something, its not available in the school you are in, you do it on your own. You find the right book that teaches you in the way you like and just explore and develop the right way, because there is not any one way, which works for every body. So you have to discover it for yourself, figure out what you are passionate about and figure out the path that you want to take that you will enjoy the most and work hard on it. And then....
NDTV: Great. Questions?
Student 7: Hi Sir, some of the greatest mathematicians and scientists have done some of the best work in 20's and 30's. So how important would you say is starting early? How important starting early?
Prof Bhargava: Yes starting early is good but that doesn't mean that you have to decide what you're going to do early. You can be passionate about the many things starting early and then as you move forward, you can narrow it. It's not good to specialize too fast in my opinion and you can be good at many things. You don't have to specialise in one thing. But it's good to start early in many things, is what I'd say, as you figure out and narrow down your particular passions, you can do that as you get older...
NDTV: So actually one of the toughest things is finding your passion. I mean the whole process, because of this age, their age and your age about the same, that you got so many different things and signals, noise, you don't know whether what you're doing is what your parents or society wants you to do, you've got to find what you enjoy and what you are good at...
Prof Bhargava: Right. Right
NDTV: How do you do that?
Prof Bhargava: I think, you know, the right way I mean, there is, some how society does push people out, societal attitudes push people, mainly engineering, law, medicine, that's noise that you should try to keep out, you know that, that's there but keep it out. When you're working you know whether you are enjoying it or not. When you are doing a problem in math or whether you're reading a piece of poetry, you know whether you are enjoying it or not. That's what helps you narrow things down. As you are in school or even outside school, when you're doing things, you know those moments that are really memorable to you and you have to just focus on those and say what did I like about that? What are the other things that I like that'll give me the same experience and then learn those, be passionate about those. You don't need to specialise very quickly. Liberal arts, I think is a very wonderful concept, be good at many things that you like and you can specialize. As you do more of those things you will realize more, which things are even more memorable than the others, and eventually you can specialize. But be good at many things early on, figure out what you enjoy, pay attention when you enjoy something and seek out what are things like that that you can continue doing.
NDTV: But you, you did that plus also manage to keep out the noise and that you so you could become an IAS officer, whatever. How did you keep the noise out because that's a lot of pressure on kids?
Prof Bhargava: Yes, that requires a little discipline. You have to stick to your guns if you know you really like something. You make that clear to your family, I really like this, and I want to do this for a living, and your family will support you.
NDTV: And your family will support you. Well, coming the to last few questions, there is a question from Sahil from IIT?
Sahil: My question is that you know, you are highly inspired by the Vedic mathematics and you know their work and that is highly reflected in whatever you did until now. So how do you see it, you know, be a part of the mathematics that is being taught in school now, you know, given that an education system right now is very rudimentary mathematics until class 10 and then just takes a form in just two years, 11 and 12, and all the options that you have are either the main streams fields, you know, engineering, medicine, law, it's been like you know, you reach the age of 22 and you're still in the mainstream fields. Now, it's very late for you to decide, you know, it's very risky to go for mathematics now in this stage, so how do you look to revamp mathematics as a subject you know, a pragmatic, perceptive way? Because its not really possible to, you know, in school being taught like games and all of that because you have board examinations....
NDTV: That's the point, you should be taught like that, that's the big change that's needed.
Sahil: How do you really implement in the education system, Sir?
Prof Bhargava: You tell the teachers that this is how it should be, convince the teachers that this is how you should teach it, convince the parents, the students,
NDTV: That is how you got the best results...
Prof Bhargava: Right, so for example, I mean the way I started at Princeton, I didn't make that the curriculum for everybody right away. I taught it as an experimental course, as an experimental freshmen course. It got the highest evaluation of any mathematics course. Now many people are convinced in the United States and are adapting that syllabus. So the same thing, we bring it in gradually and if it's successful, we spread it further and eventually if it works very well, it will take over and then the Boards will change too. The boards will incorporate questions of that kind.
NDTV: Is your course or your lectures available on you-tube or on I-tunes?
Prof Bhargava: They are not yet. They probably will be
NDTV: It's great if they were. So, everyone knows about them. They are packed and everybody enjoys them.
Prof Bhargava: So eventually that is my goal. It was an experimental course the first time. I didn't put it online right away. I wanted to fine-tune it. Once I feel good about it, then I'll have it online for everybody to check. I am just joining this programme called Gyan which is this programme to bring scientists from all over the world to India and bring lots of students together to teach, to teach say mathematics or science in a more fun way, have the students inspired, record those and have it available on video for the entire country. So that's something that this particular course will help make into that format eventually.
NDTV: We have a last question, this young man in front of you wanting to ask a question.
Student 8: First of all, congratulations on winning the Fields Medal, I'm sure it's a very big thing and everyone around India is really proud of that achievement. Sir, I would like to ask you that currently, I hear that you are working on the BSD conjunction problem. Sir, can we expect another breakthrough from the genius himself in the coming future?
Prof Bhargava: I guess you read it that it is one of my favourite forms. The BSD Conjunction is one of the seven millennium problems at the Clay Mathematics Institute, we give the people one million dollar prizes for each of these
NDTV: I see
Prof Bhargava: That's now my motivation for working on it. It's never for the mathematicians. That is not the reason. It's just the point now that the seven points are really fundamental, that is one of my favourite ones. It's a number theory problem. It tells you how to solve cubic equations in whole numbers. So, in school we all learned how to solve cubical equations and the way we solve cubical equations, there is a general egestion that allows you to solve cubical equations in any number of variables. But for cubic equation it's no need to solve cubic equation in one variable once you have a cubic equation in two variables, Nobody know how to solve it in whole numbers, this way the conjecture tells you how to solve it. I think that's one of the fundamental problems, that's why its one of my favourites
NDTV: I have heard, talking about this earlier, I think just finally just to the role of intuition, in life intuition is very important for all of us. Is maths contrary to intuition or are they complementary? Does it remove intuition or does it help intuition?
Prof Bhargava: I think it's just like any other art. As if, I sort of feel that when mathematics starts, one of the goals should be to develop intuition about mathematics. And right now the way to start, you start the way of memorization, so the intuition is not developed. But if you discover the way to solve problems on your own you develop the intuition. So when the next problem comes and is not exactly the same kind as first, you will have an intuition to say, oh these are the changes I need to make in order to solve it. That development of intuition is very important, and is very important in my own mathematical research. Having developed intuition for many years in solving different kind of problems and if I just memorised this is how it will solve this problem and this is how it will solve this problem; so when a third kind of problem comes and those same steps don't work, it's a problem. If you will develop the intuition where you can make slight changes, just like when you are painting, you develop techniques, develop an intuition, how to express various emotions by this combination of colours, in the same way you develop an intuition for the kind of techniques and how to combine them to solve different problems when they come up.
NDTV: Oh that's fascinating. Thank you very, very much for taking out time and hope you succeed in your venture to change the way maths is taught
.
Prof Bhargava: Thanks every one for your support
NDTV: Thanks very much, that was fabulous
Track Latest News Live on NDTV.com and get news updates from India and around the world
