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 it’s 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 modesty and simplicity is really truly Indian. Why do

I call him a bewildering genius? Because of what he did to actually win that mathematics award. It’s simple really. He won it for and I quote developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptical curves. Simple as that right? You got it? Simple stuff. So what has he done? He has counted rings

of small rank and bound the average rank of elliptical 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 that’s 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 within 10 seconds I was out of it, but I guess a lot of you here would understand. Prof Bhargava: There are many different levels. NDTV: Of course, yeah. Yes, your Mother taught you maths. She was a mathematician herself.

Prof Bhargava: And is. Yeah. 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 yourself 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, while Indians may be good at maths but 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… 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 mathematics classes 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, and 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 and 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 to an even further extent.

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 actually…

If any questions now, we can start taking questions and then… you’re from Rajasthan? Student 1: Yeah… 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 I get when I’ve been on tours for these past few months talking about mathematics. The most common question is – why is mathematics class always so dry, so boring, so all about memorisation 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 three years – I developed a course, for freshmen, for first years, where we teach mathematics through poetry, classical

music, classical Indian music, magic tricks as you said, and games; so those are the

four ingredients of the course through which I get to teach fundamental mathematical concepts.

So most 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 it on their own, there’s no way they’ll ever forget it.

NDTV: Right, exactly and as you say, it’s a visual cum curiosity cum something practical, so you’ll never forget that. Rather than just on a black board. 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 lectured tours 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 student, 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 because I was so 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 math 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 escape. NDTV: Fall asleep kind of thing. 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 phoned in and said, ‘I have a terrible sleep problem. I can’t sleep. I’ve tried every pill’ asking the doctor, ‘what should I 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, our producers 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 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 try to fill it in on your own,

and often you’ll find that you’ll come up with different steps that lead but, of course,

math only has one answer. So if you come up with steps that are correct logically, you’ll always end up with 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 actually figure out 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 avoided math class as I said

and I would do math on my own and I did well in all the exams. You know I always got a

perfect score on all the exams but I didn’t know what that meant in particular. 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 do because I can do it at the same level as the other students here. NDTV: Yes young man. 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: Definitely. 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 with 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 things, different 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 art and mathematics closely connects

to all of them. It should really be taught that way in my opinion. 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 artistic aspect. We should be using both sides of the

brain to understand mathematical problems. NDTV: You have said that there is some mathematical basis to music as well, tabla for example, what is the connection? This is very tough for me to understand, maybe

others do, but 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 have 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 in 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 and unstressed syllable. When you say 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 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: Permutations and combinations? Prof Bhargava: Yes, it is about permutations 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? Student: 4 short beats and 2 long beats. 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, 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: 8th Fibonacci number. 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 excites students. 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 where it came up was actually 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 if you have a certain number of beats left. 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 Kannada poetry, the set up of poetry is very similar in those languages as well.

Why this man not in India…?

Beautify mind

Perfect person

Well rather than asking about the possible breakthrough through his work or what concepts helped him in achieving that or how his work can be applied in future were not at all asked… instead some petty questions summed up the whole show where the anchor who for the sake of getting the publicity just turned up with having the minimal knowledge about the subject!

Lol michel gonna get extradited soon.

He is absolutely right , the way mathematics taught now a days is rubbish

how can I use mathematic to made machine , that is most different than our modern machine?

SIR CAN I DO MSC IN PURE MATHEMATICS AFTER BE ELECTRICAL ENGINEERING

๐ช๐ช๐ช๐ช๐๐๐ฃ๐ฃ๐ต๐ต๐ฑ๐ฑ๐ค๐ค๐ ๐ ๐ก๐ก๐ก๐ก๐ ๐ ๐ฟ๐ฟ๐ฟ๐๐๐

india gov. should help the poor smart kids to make India a power nation.

Every maths genius… I like maths but i dont like the way maths taught.

"I memorised maths even though it was fun to me I was afraid to become a mathematican !!!"

Blunder

By this mathematician

-1 -2 are not whole numbers .

If i m not mistaken

2:12

Michael Jackson

I solved pi.

"1/3".

Your welcome.

Im taking your fun way of learning and will apply it to Children soldiers.

I don't want them to hate blood. guts n brain splatter, we're going for art here at the academy.

Amazing!

Just realized this is an NDTV expose. Check out the comments that spew vitriol against the Indian in Manjul. These assholes take no time to discredit India and Indians around the world. I donno the satisfaction that comes when you hate yourselves. I really don't. You guys should grow up and start loving your country. Every step you take in trying to cause self hatred in Indians is going to be your downfall too. You do not have identity or job. So you slander and disparage someone who actually believes in his roots, his Indian identity, and his ancient wisdom. He talked about Hemachandra, his mother, his grandfather who are clearly Indian. He talked about Indian classical music, clearly Indian. He talked about so many things that inspired him were Indian. He did criticize the way math was taught in India. Guess whose fault that is, yes, those who created the education system in India, the Gandhi's and Nehru's of the world, leftist vermin and their ilk. So blame your self hatred on them and not on India. Grow up losers. Get a life and a real job

He studied in USA and Canada but know Sanskrit to such depth and we disregard Sanskrit as unuseful.

Stupid asses don't know wen to applause !!!!Indians obviously

we are loosing all the best minds to foreign countries. Most of the people blame the reservation system in india and corrupt politicians. we send them away everyday and then interview them for their genius one day.

Simplicity is truly Indian it is a joke ๐ he is an exception,

Goooooooooood ๐๐

did he say sequence of prime numbers….well i disagree at 2:20

He isnt created by India

I hate math…

I give credit to the maths teacher , who raised him.

from algeria : you should be New Ramanujan, thanks

I spend whole life to learn mathematics

But I always make blunder

One of my friend open whole sheet in mathemaics

I scored well

But i teacher mentioned you cannot score well in mathematics

But my father said you will be grand master one day

Because Anand born in 1969

I learnt three thing

Determination dedication devotion

I played chess in state tradition corporation

Scored 5.5

But i was not sarisfied

I joined russian chess club in cp

But i played very good match with delhi engineering college student

But some how they are very clever leant our stragies

I lost the match

But I again analyse the game I was inquiring ing postion

That was explained my friend my bihari dost

But when I was fully prepared for chess my chemistry told either play chess or chemistry

I opted for chemistry pratical rather then chess when my I was in college

But i make silly in mathematics……still big 0

Indian school teachers = POTTY.

It is Vedic genes which inherently got by everybody born in the Indian subcontinent. because once all used to be Vedic follower in this subcontinent. Slowly Buddism took it to China, Japan and Korea. study original Vedas in Sanskrit, not the English translated version. My fellow Indian hybrid generation, you have to learn a lot yet.

I was expecting him to have an Indian accent. Plus he's dressed like an Indian. I totally agree with him, that there are multiple ways u can come up with your answer to a problem. Shouldn't be force fed to u to how u should come up with it, as long as it's right.

got one of the greatest mind out their and asked stupid question like where you a back bencher.

He just showed the knowledge of Vedic Mathematics.

as a mathematics lover, I highly agree with MANJUL BHARGAVA …

Mr.Prannoy Roy thank is also due to you for presenting Manjul Bhargava no doubt he is a great mind and I don"t find you any less. I am senior citizen but I still have curiosity of a cat.Thanks again.

This is just the presenter going, โHi Siriโ.

But Manjul seems like a meetha

Nice introduction of a genius in mathematics.

he isnt an indian creation ……. he is a canadian creation…..

A brilliant young mind

Presenter is fucking irritating

Shriniwas Ramanujan was the most genius indian mathematician….

same here in Pakistan, every thing we do is to memorize and memorize

The Moment teachers will teach maths for its sheer thinking ability and problem-solving approach not to get good marks in the board, you'll have great mathematicians.

simple as thatMaths is used allot in witchcraft and witchcraft makes a mirage which u been taught today and use to create gizmo ,games and literally magic

And here's a harsh truth for u , we live in a physical realm and everything in this realm is fake cuz we live in a matrix where mechanics starts from spiritual realm and we can't get there but……. we r there controling our body from ,maths is just a waste of time(time is not what science and Ur daily routine and social people tell u) zooming an infinity loop of this physical realm…good at math doesn't make u genius,this world rulers want u to be look cuz they know real math ain't trigonometry ,what we learn in high school is witchcraft

Interviewer is an idiot

Those who have disliked this video god bless them

Maths is the most easy and fun subject,

Dont worry Failure because Mathematics Genius also made mistakes by saying -2,-1 is whole number which is not.

I asking one question for you tell me now answer,

Manjul Bhargava looks like Shashi Tharoor

Pure adventure comes from mathematics..

Too complicated for porkies whose only aim in life is to raise terrorists and destroy

Whole numbers are {0,1,2,3…..}, right?

He says -1 and -2 as well, is that true?[at 2:10]

(I'm not trying to prove him wrong in any way. I just wanna know if it's some different theory.)

He is a true genius

Henry sir

Basically this is the tutorial on how to hate Math

Indian politics never encourage any genius because they are busy at making black money so our geniuses migrate foriegn they become success in their field,like S Ramanujan,sir CVRaman,jc bose,……..

Brilliant interview. Indian youth should be exposed to more such content.

13:10 is what freaks kids out…

thats the way of learning -thanks for this video

I am glad he didn't study in india as then he never would have won the fields medal and that is a certainity.

NOBODY –

LITERALLY NOBODY –

MANJUL BHARGAVA –

chucklesI felt through out my college days the same as what he said at 5:50, mug up formulas and just apply it. No one explained me why i have to apply that, if i ask they say just remember formula and apply. Then i quit maths altogether. I wish there must be maths teachers who explain the things so maths will be more fun.

I didn't know Stevie T was great at math too

He speaks quality.

did he just say that -1,-2,-3 and other negative nos. are whole nos. . I am confused now, my life was simple before

anyone in 2019?

This video has been in my recommendation since years….finally.

Great

first NDTV video i liked

2:10 – 2:14 I'm sorry, what?

are you discuss with me about the yantra mistry according to modern mathematicsโโโโ

mathematics become magic with the help of data collected from students itself๐๐๐๐

Loved his spirit and every word from his mouth …….Thank you so much NDTV India for bringing this hero on board๐น๐น๐๐๐๐

Sir do u know vashisht narayan he is also a great mathematician. Plz u have to or every one knwon about him. If possible plz speak few words for him it will really appreciate the new mathematician

i think sirinivasa ramanujan is the greatest mind India has ever created

2:04 "The art of understanding whole numbers, 1,2,3,4 and 0 and -1, -2," I don't think he even knows the definition of whole numbers.

Mathametics is a language of science. Important thing to understand is … it is a language