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Video tags
Subtitles
Russian
00:00:07
our journey leaves behind the00:00:09
vast Egyptian desert00:00:13
we witnessed how mathematics00:00:17
played a key role in the emergence of00:00:19
civilization00:00:20
[music]00:00:24
and two millennia later It received a00:00:27
New Start on the Greek islands00:00:32
where men and women learned to00:00:34
debate logically mathematics was00:00:38
their weapon of choice in ancient00:00:41
Greece mathematics filled with a new00:00:43
spirit00:00:46
this series takes us to another country00:00:49
further east00:00:51
[music]00:00:57
where the greatest revolution in00:01:01
mathematics took place00:01:10
[music]00:01:28
[music]00:01:46
[music]00:02:10
mathematics and the rise of civilization00:02:13
[music]00:02:27
it exists But it doesn’t mean anything00:02:46
if you think about it it would be more natural00:02:49
if this did not exist00:03:03
in this country buildings have a zero floor00:03:06
This is truly the home of the number zero00:03:14
How and why the number 0 was created let00:03:18
's travel through time in search of its00:03:20
origins episode 3 the00:03:23
divinity of numbers00:03:44
this area is full of noise and energy all of00:03:49
modern India looks like this00:03:56
[applause]00:04:00
people are sprinkled with paint but no one is00:04:04
angry00:04:05
[applause]00:04:08
[music]00:04:11
I myself can’t avoid it00:04:16
This man goes to the city and00:04:19
covers my whole face with paint00:04:29
Krishna, one of the main gods of India, has a00:04:32
blue face00:04:37
today they paint each other’s faces00:04:40
in Tribute to God Krishna people celebrate00:04:43
holly day festival of colors the biggest00:04:45
festival in india00:04:46
[music] the00:04:49
road to the temple at madhura in the north00:04:52
indian state near tarpradesh is always00:04:54
crowded with people during holly celebrations00:04:57
we were stuck here for about half an hour00:05:00
although the shrine is just around the corner00:05:07
this hindu temple is recognized as the00:05:10
birthplace of god Krishna is an00:05:24
amazing sight, festival guests have been00:05:26
praying like this for 3 hours,00:05:35
the priest distributes the food offered to Krishna,00:05:41
sharing food with this God, they feel00:05:45
one with him,00:05:55
deities play a central role in the life of00:05:58
Indians00:05:59
[applause]00:06:00
gods and people live together. To00:06:12
outsiders, this scene may seem00:06:15
alien and new how such a deep Faith00:06:18
exists in the scientific world is00:06:20
truly amazing00:06:25
but For over a billion people in00:06:27
India it is as natural as food and00:06:30
water00:06:33
[applause]00:06:36
Holly falls on the last full moon00:06:39
of the lunar calendar when00:06:42
this festival arrives spring begins00:06:45
[applause]00:06:56
the festival reaches its climax at night people00:06:59
light bonfires and praise the god Krishna00:07:02
Holly begins on the last winter day of the00:07:05
full moon in India, what the gods have00:07:08
ready is manifested in the sky and people00:07:11
must understand the will of heaven00:07:13
[music]00:07:16
this is the canon of the festival, bonfires are not lit00:07:20
until the full moon appears00:07:30
[applause]00:07:33
people pray that to banish any bad luck00:07:36
they do this by burning an effigy of holika00:07:39
symbols By00:07:44
watching such festivals children00:07:47
grow up feeling Closeness to their gods00:07:49
serving good gods and punishing00:07:51
bad gods are integral parts of Indian00:07:54
life00:07:58
[music]00:08:09
holika falls the00:08:11
coming year will be abundant00:08:15
[music]00:08:20
every day throughout the year in different00:08:23
parts of India, festivals are held these00:08:26
holidays are a form of communication with the gods00:08:28
definition The dates of the festival were the beginning of00:08:31
mathematics in India00:08:48
11 o'clock we were driving a car products the00:08:51
capital of India wujain is a00:09:02
small city located in00:09:04
Central India00:09:06
but when in the seventh century AD00:09:09
Brahmagupta was appointed head of00:09:12
the city observatory this place is very strong00:09:13
was different from what we see today00:09:15
in those days the Jains were the center of00:09:17
Indian astronomy and to be the center of00:09:21
astronomy is to be the center of00:09:24
mathematics00:09:30
[music]00:09:34
Brahmagupta who was from Phinmal state of00:09:37
Rajasthan in northwestern India took a long time00:09:40
to get to the Jain DOU from the Indian00:09:42
region of Malava00:09:44
he was the most respected scientist of his00:09:47
time His appointment as head of00:09:50
the observatory was proof of his00:09:52
high status00:09:54
[music]00:10:05
in those days Indian astronomy was00:10:08
much more developed than Western00:10:14
people in India already knew that the Earth was round00:10:17
they were even able to calculate its circumference00:10:21
with relative accuracy00:10:25
they were only off by a hundred kilometers00:10:28
Brahmagupta had just come to the00:10:31
forefront of science00:10:39
Although he was in charge of an observatory he was in00:10:42
love with mathematics00:10:45
But at that time mathematics was relegated to a00:10:47
secondary role to astronomy00:10:50
[music]00:10:52
being in ujan the concerns of the brahmagubians00:10:55
ended up focusing00:10:57
solely on mathematics00:10:59
[music]00:11:15
as astronomy developed along with it,00:11:17
mathematics developed in India, yes,00:11:22
mathematics was not just for calculating00:11:24
large numbers in astronomy, thanks to00:11:27
Indian mathematicians, we can perform00:11:29
small calculations important for00:11:31
everyday life, the00:11:35
ancient people of the East were more00:11:37
skillful in calculating numbers than in00:11:40
geometry, in particular, some special00:11:43
calculations were presented in Indian00:11:46
sacred books, for example, such as these00:12:01
94 by 97, this is how the Indians solved complex problems00:12:06
many centuries ago,00:12:12
better than 94 from 100 and subtract 97 from 100,00:12:19
add each resulting value 6.3 and00:12:22
subtract it from 100 answer00:12:25
9100:12:27
now multiply 6 really00:12:49
Indian sacred scriptures presented00:12:52
such unique calculations on many00:12:54
different pages the00:12:56
amazing magic of Indian mathematics00:12:59
played a major role in observing the00:13:01
movement of the sun the moon and stars00:13:10
on the summer solstice the sun00:13:13
passes straight through the center for a jain00:13:15
latitude for a jain 23 degrees north00:13:18
latitude known as the tropic of cancer00:13:24
similar to the greenwich observatory for the00:13:27
british the Jainas were the center of the world for the00:13:30
Indians00:13:32
They were able to calculate the length of00:13:34
one year to within a few00:13:36
seconds00:13:40
They discovered another important00:13:42
mathematical method00:13:50
Today it is known as00:14:03
trigonometry is especially useful for00:14:05
determining the length of an object that is00:14:07
too high or far away00:14:09
to measure in person for example00:14:11
suppose that we need to use a00:14:13
tree trunk as a column the00:14:19
top of the tree is too high to00:14:21
measure I need to find a point that00:14:24
makes a 45 degree angle with the top00:14:36
it's too close let's move a little00:14:39
further00:14:48
I found a point 45 degrees from the top of the00:14:52
tree the00:14:56
angle on my side00:15:00
is 45 degrees and opposite00:15:04
it is the same00:15:07
when two corners are the same size, the length of the00:15:10
opposite side of each corner is00:15:12
also the same Therefore, the height of the00:15:14
tree is the same as the The distance that00:15:16
I walked00:15:20
I walked 15 meters means the height of the tree is00:15:23
about 15 meters00:15:26
If I go further the angle Where I am will00:15:29
accordingly become smaller and00:15:33
naturally change and the length of the00:15:35
corresponding sides of the00:15:39
angle closest to me becomes smaller00:15:42
And the hypotenuse is longer00:15:46
when the angle closest to me becomes equal to00:15:49
30 degrees the hypotenuse will be 30 m at00:15:52
this moment the ratio of the height of the hypotenuse00:15:54
is 1:2 this is the value of the sine of 3000:15:58
degrees00:16:07
[music]00:16:08
the basic concepts of trigonometry originate00:16:11
from Greek mathematician00:16:13
Ptolemy but the Greeks only knew the value of sine00:16:16
for a few angles00:16:19
[music] the00:16:26
Indians knew more about trigonometry they00:16:30
made tables representing the00:16:32
value of sine and cosine from 0 to 9000:16:35
degrees00:16:38
the tables correspond almost exactly to the00:16:40
values of trigonometry we know00:16:42
today India Truly was the birthplace of00:16:45
modern trigonometry00:16:47
[ music]00:17:01
this is Mount Everest00:17:05
in 1856 a century before people00:17:09
climbed the dizzying peak of00:17:12
Everest its height was determined00:17:15
using trigonometry and was 884000:17:18
meters but with the help of trigonometry00:17:20
the Indians could measure something even greater00:17:22
than that it00:17:24
was the distance to the sun00:17:29
during a full moon The Earth and the Sun00:17:31
form an almost perfect right angle00:17:34
relative to the position of the Moon00:17:36
and the angle formed by the Earth is 86 and00:17:40
6-7 degrees.00:17:48
This is the same type of calculation that we00:17:50
used to measure the height of a tree. The00:17:52
angle at the point of the sun is only 1/700:17:55
degree since the Indians knew the value of00:17:58
sine They used the numbers sine of 1/700:18:02
degree is equal to 1.400:18:07
They knew this means that the Sun00:18:09
is 400 times further away from the Moon00:18:28
this city is not much different from what00:18:30
it looked like back in the day00:18:33
[music] a00:18:36
particularly attractive place for00:18:39
tourists00:18:43
India is home to over a billion00:18:46
people and more than 300 million gods00:18:50
in iranas includes almost all00:18:52
the elements of india but the potential of a country is not00:18:55
always determined by the number of people00:18:57
or gods00:19:00
tourists in india want to visit varanasi00:19:05
and those who are here want to00:19:08
see the durgyi temple00:19:11
in this temple there is something interesting00:19:20
and related This with the end of the world00:19:23
[music]00:19:25
in this temple in the pond there are two00:19:27
pillars on one pillar 64 round00:19:31
plates the00:19:40
end will come when all the round00:19:43
plates move to the right pillar00:19:46
But there is one condition when moving the00:19:49
larger of the plates cannot be placed on top of the00:19:53
smaller one00:19:56
and therefore there is an additional pillar00:19:59
which will help with solving this problem00:20:02
So How many moves are needed to00:20:05
move all 64 plates00:20:08
Let's first try to move00:20:11
one of them, one00:20:15
move is enough to move00:20:18
one plate What about two00:20:27
one00:20:29
two00:20:31
But this is against the rules a large00:20:35
plate cannot be placed on top of a smaller one 100:20:38
2 300:20:42
now I'll try to move it three plates00:20:46
How many moves will it take me00:20:51
one two three four five six seven It00:20:59
took me 7 moves to00:21:01
move all three plates00:21:06
three moves00:21:10
Can I know the answer only after I00:21:13
have moved all 64 plates00:21:22
one plate in one move00:21:25
two plates in three moves00:21:29
three plates in 7 moves00:21:32
What pattern or formula is hidden00:21:35
here00:21:41
raise the number 2 to the power equal to the00:21:44
number of plates then subtract00:21:46
one00:21:49
if we move 4 plates multiply 400:21:52
twos and subtract one it will00:21:56
take 15 moves00:22:02
This means that in order to00:22:04
move 64 plates you must00:22:07
multiply 64 twos and then subtract00:22:10
one what we end up with00:22:12
[music]00:22:28
the answer is 18 quintillion 446 quadrillion00:22:33
744 trillion 73 billion 709 million00:22:38
551615 if I move one00:22:42
plate every second It will take00:22:45
584.9 billion years00:22:53
almost 18.5 quintillion movements which00:22:57
takes 585 billion years,00:23:06
Indians have been aiming for very large00:23:09
numbers,00:23:17
but no one sees the end of an infinite00:23:21
number00:23:24
[music]00:23:34
such extreme numbers personified the00:23:37
desire for eternity,00:23:39
Indians believe that life does not end with00:23:42
death, but repeats itself endlessly00:23:45
[music]00:23:51
this life is just a short moment among an00:23:53
infinite number of lives00:23:56
Therefore, many people care little about00:23:59
how they look00:24:01
[music]00:24:06
Indians believe that at least once in their life00:24:09
they should take a bath in this river00:24:14
they care more about their spirit00:24:27
[music] the00:24:31
desire for large numbers led to00:24:34
unexpectedly huge numbers that00:24:35
represented unimaginable numbers00:24:47
to see how huge00:24:50
it was unique number moving the00:24:52
plates we must compare it with00:24:54
numbers in other cultures00:25:01
we know that in this part of the Earth00:25:03
one of the oldest00:25:05
number systems in human civilization was created00:25:10
they depicted numbers in the form of beautiful00:25:13
hieroglyphs00:25:17
just like we give names to new00:25:20
objects We also designated new numbers00:25:23
[music]00:25:27
one was a stick00:25:30
2 Two sticks numbers up to 9 were expressed00:25:34
using sticks00:25:35
[music]00:25:37
10-100 and 1000 were expressed in different numbers and00:25:43
fractions also appeared00:25:51
Roman civilization arose00:25:54
Thousands of years after Egypt But their culture00:25:56
had a lot in common00:25:59
Roman numerals can be a little more complex00:26:02
[music]00:26:06
Here they are Roman numerals these Shiny00:26:10
letters mean one thousand 82800:26:13
Roman civilization created numbers in00:26:16
blocks of 500:26:19
100:26:20
5 10 50 100 50000:26:27
[music]00:26:36
Mesopotamian numerals00:26:40
Mayan numbers00:26:46
Chinese numbers that even include00:26:48
negative numbers all these ancient00:26:51
peoples created new numbers when necessary00:27:08
natural numbers and fractions Found in00:27:10
every ancient civilization And the Chinese00:27:12
even created negative numbers00:27:14
Human civilization00:27:16
has been expanding its mathematical horizons for a very long time00:27:18
But this innovation was the last Although00:27:21
perhaps the most important of all it is00:27:25
right in front of you - a00:27:36
fort built about 12 hundred years00:27:39
ago00:27:43
among hundreds of temples Fort gabaliora this00:27:46
gate is the only one with a lock00:27:52
[music]00:28:01
this temple is dedicated to God krishna00:28:04
[music]00:28:11
on the wall in this temple we find exactly00:28:14
what I am looking for00:28:18
in this passage the offering00:28:22
given at the time of the dedication of the temple is recorded00:28:27
among the numbers representing their offering00:28:34
27000:28:35
I came to look for zero00:28:41
this zero is the first zero recorded in the00:28:45
history of mankind00:28:46
[music]00:28:52
[music]00:28:56
Let's take a trip down00:28:59
memory lane00:29:04
we master basic numbers at the age of00:29:07
6-7 years00:29:10
the history of mathematics is reminiscent of the history of00:29:12
human development00:29:17
numbers appeared at an early stage in the history of00:29:20
mathematics and we learn numbers at an early age00:29:23
age,00:29:26
we asked this child to write 232,00:29:45
he writes it like this.00:29:49
Perhaps we forgot about it, but we ourselves00:29:52
wrote our numbers like him.00:29:56
To understand numbers in the form in which00:29:59
we use them now we need a lot of00:30:01
practice. Little children first00:30:03
write 200 then 30 and then and two00:30:19
on the left and two on the right look the same but00:30:22
have different meanings This is a complex00:30:25
concept00:30:26
those who first accepted it faced00:30:30
difficulties00:30:38
modern numbers appeared in India the00:30:44
numbers that we call Arabic00:30:46
were actually invented by the Indians and the00:30:49
number system with our current00:30:51
numbers was invented by the Indians00:31:00
Brahmagupta was mathematician in the country00:31:02
that revolved around this system00:31:08
The difference is that in India00:31:10
different symbols were used for each number00:31:14
what was amazing about the Indian00:31:16
numbering system was the way of00:31:18
expressing the next number00:31:22
instead of creating new00:31:24
symbols for the next number they00:31:26
reused the numbers that already00:31:28
existed that the number on the right is similar00:31:31
to the one on the left but they are different in00:31:33
meaning00:31:36
and all this is because of the zero following the00:31:40
one00:31:47
Now when other numbers are followed by00:31:50
zeros the numbers can expand to00:31:52
infinity00:31:54
this was a revolution in numbering00:32:06
[music] the00:32:17
Indian numbering system00:32:19
spread to Europe through Arab00:32:21
world That's why they are called Arabic00:32:23
numerals Indians have lost ownership of00:32:26
their greatest intellectual00:32:28
property00:32:30
this is a banknote used in the African00:32:34
country of Zimbabwe is worth 100 trillion00:32:37
dollars00:32:40
the face value of the banknote contains 14 zeros how00:32:44
could we express 100 trillion without00:32:46
the existence of zero our life is impossible without it00:32:53
[music]00:32:57
many things can be described as sand on00:33:00
the beach00:33:02
but now we can express such things00:33:05
as numbers00:33:06
[music]00:33:10
these grains of sand red blood cells or00:33:14
stars in the sky00:33:19
having numbers to represent these objects00:33:22
we can move forward More00:33:24
and more00:33:31
[music] it00:33:33
is paradoxical that we we can express00:33:35
huge numbers by inventing the smallest00:33:37
equal to 000:33:39
[music]00:33:52
zero means nothing nothing00:33:55
is expressed00:33:56
[music]00:33:58
this is a number created by people who00:34:00
perceived emptiness as something that's what00:34:04
zero is00:34:10
[music]00:34:26
this00:34:29
Brahmagupta Ashram conducted a study00:34:31
discussion with his students00:34:36
while working as the head of the observatory He00:34:38
fell in love with numbers00:34:41
He tried to calculate all the possible00:34:43
numerical results of addition, subtraction and00:34:46
division But for everyday life it00:34:49
was not very practical00:34:53
so that Rahmagupta Indian mathematics00:34:55
was a minor practical00:34:57
subject a simple tool to00:34:59
help astronomers and architects but00:35:02
Brahmagupta began to study mathematics as an00:35:05
independent field and this led to00:35:07
what he made The greatest discovery in00:35:11
the history of mathematics in00:35:17
628 AD brahmagupta wrote00:35:20
a book while working as the head of an observatory a00:35:27
book on astronomy called brama00:35:30
puta shedanta this means the correctly00:35:32
established doctrine of brahma two chapters of00:35:36
this book were devoted to mathematics in00:35:38
which he wrote the four basic00:35:39
arithmetic operations performed with00:35:43
positive or negative00:35:44
numbers00:35:46
in his number world positive00:35:49
numbers were assets and negative00:35:52
debts00:35:58
assume these blue bins00:36:00
represent assets and brown debts00:36:04
add more assets to existing00:36:07
assets the entire set of assets increases00:36:12
when more debt is added to existing debt00:36:15
even more debt is created00:36:20
[music]00:36:22
But what will happen if you combine assets and00:36:26
debts,00:36:31
if the assets are greater than the debts, you get00:36:34
the remainder00:36:36
What to do if the sum of assets and the sum of00:36:40
Debts are equal,00:36:43
nothing will remain00:36:46
Yes Brahmagupta, every mathematician00:36:48
completed his studies at this stage00:36:54
decided to call00:36:57
[music]00:36:59
thus 0 took his first steps in the00:37:03
world mathematics00:37:04
[music]00:37:12
brahmagupta was the first mathematician00:37:14
to introduce 0 into calculations00:37:18
other people did not understand mathematical00:37:20
formulas using zero they believed00:37:23
that zero does not play any role in00:37:25
calculations because it does not change the00:37:27
results When you add it or00:37:30
you read it, it is00:37:38
difficult for us to understand why it included zero00:37:41
in his calculations00:37:46
he knew well the nature of mathematics00:37:54
that is, to find the principles underlying00:37:57
objects and not just their use in00:37:59
everyday life00:38:04
0 like the one we find in00:38:07
201200:38:10
Brahmagupta's00:38:13
country really existed zero began to be used00:38:16
independently when he was part of the00:38:19
calculations00:38:23
brahmagupta knew the hidden meaning of zero00:38:26
which was crucial to these00:38:28
calculations its power comes from the equations00:38:38
I will show you what the equation can do00:38:44
imagine a farmer who00:38:47
raises cows and chickens00:38:53
the total number of these two animals00:38:55
is 19 the00:38:57
total number of legs is 6200:39:01
[music]00:39:04
So how many cows and chickens are there from00:39:08
the farmer00:39:11
If you keep trying number00:39:14
combinations one after another eventually00:39:16
you will find the answer00:39:19
but with the advent there is a way to quickly and00:39:23
easily find the answer00:39:32
[music]00:39:33
cows and chickens together make 1900:39:36
animals00:39:38
cows have four legs and chickens have two for a00:39:43
total of 62 legs00:39:49
let's imagine cows and chickens as X and Y,00:39:52
respectively,00:39:55
now we remove Y from each side of the00:39:58
upper equation,00:40:07
we get 000:40:09
without this it is impossible to make00:40:11
further calculations00:40:18
now Insert the value of X into the lower00:40:20
equation00:40:25
[music]00:40:33
the number of cows is 12 and the number of chickens is 700:40:37
[music]00:40:52
many have strived for eternal peace00:40:56
to achieve such a world could only be00:40:59
philosophers who thoroughly realized its00:41:01
emptiness00:41:02
[music]00:41:09
this Realization could be expressed in00:41:13
human language using mathematics00:41:15
[music]00:41:32
it was the greatest innovation in00:41:35
the history of mathematics zero traveled a long00:41:37
way to the west through Arabia it00:41:43
took Western cultures 8 centuries00:41:46
to assimilate zero00:42:02
In the summer of 2010 mathematicians from all over the world00:42:06
gathered in India00:42:15
They are here at the international congress of00:42:18
mathematicians events which is00:42:20
held every 4 years00:42:23
about 5000 world-class mathematicians are invited00:42:28
in the spotlight of the world winner of the00:42:30
filts medal international medal for00:42:33
outstanding discoveries in the field of mathematics00:42:35
awarded at this congress It is00:42:37
known as the Nobel Prize in00:42:39
mathematics is awarded to young00:42:41
mathematicians under the age of 4000:42:43
thanks to this event we can00:42:45
see How the current state of mathematics is changing00:42:54
on stage the president of India00:43:09
the head of state of the host country00:43:11
traditionally welcomes all00:43:13
mathematicians00:43:17
this is an indicator of how important this00:43:20
congress is the00:43:31
first recipient of the Fields Medal this00:43:34
year was Elon Lindenstrauss from Israel00:43:39
his achievements lie in the field of00:43:41
organic theory and its applications in00:43:44
number theory00:43:47
he used an equation to00:43:49
prove his theory in his00:43:51
dissertation these awards are of particular00:43:53
importance because they are awarded in India to00:43:55
the country that discovered zero, there are00:44:04
also winners from Vietnam Russia00:44:07
and France the00:44:10
country with the largest number of00:44:12
Fields Medal winners the highest honors in00:44:15
mathematics is the USA00:44:18
this tells us about the influence of mathematics00:44:22
throughout the world the00:44:29
next international congress of00:44:31
mathematicians in 2014 will be held in00:44:34
Seoul South Korea we expect a00:44:37
new revolution in mathematics there00:44:39
[applause]00:44:47
[music]00:44:58
[music]00:45:09
[music]00:45:21
[music]00:45:38
[music]00:45:40
commissioned by CLS Media in 202100:45:48
[music]Description:
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