History & Development of Ganita - Ancient to Modern | Prof Somesh Kumar | IIT KGP | #SangamTalks

Estimated read time: 1:20

Summary

This talk, delivered by Professor Soumesh Kumar of IIT Kharagpur at Sangam Talks, explores the rich history and continuous development of Ganita (mathematics) in Indian civilization. Tracing its roots from the Harappan civilization to modern times, the talk highlights the advanced mathematical practices and continuity of knowledge in Indian mathematics. Professor Kumar emphasizes the indigenous origin of the decimal system and place value system, crafted through diverse regional practices and preserved in myriad historical records, challenging the misconception of limited Indian scientific heritage.

Highlights

Professor Soumesh Kumar emphasizes India's deep-rooted mathematical tradition that started as early as the Harappan civilization! 🕰️
He highlights the advanced mathematical practices used in ancient Indian architecture and urban planning! 🏛️
India's invention of the decimal system and positional value system paved the way for modern mathematics! 🔢
Historical accounts and scholarly writings affirm India's influential role in global mathematics! 🌍
Despite the colonial narrative, Indian mathematical progress witnessed continuity and innovation over millennia! 📜

Key Takeaways

Math in India dates back to Harappan times with advanced use and knowledge! 🏺
Continuous tradition of mathematical development from ancient to modern India! 🔄
The decimal and place value systems originated in India! 🇮🇳
Evidence from history debunks myths of India's delayed scientific progress! 📚
Profound influence of Indian numerals on modern global mathematics! 🌐

Overview

Mathematics, or Ganita, holds a prestigious position in the Indian tradition, as highlighted in Professor Soumesh Kumar's engaging talk. He traces its origin back to ancient times, especially emphasizing structures from the Harappan period that reveal advanced use of ratios and measurements in their urban planning. He presents this as evidence of a longstanding and sophisticated tradition in Indian civilization's mathematical practices.

The discussion extends to the origin and global influence of the decimal system and the place value system, both attributed to Indian mathematicians. Professor Kumar clears misconceptions fueled by colonial narratives, illustrating continuous mathematical innovation within India, contrary to beliefs of stagnation post the 12th century.

Professor Kumar also discusses the widespread use and adaptation of mathematical systems across regions, with varied traditional numeral representations. This tradition underscores the legacy and impact of Indian mathematical concepts, offering insights into its profound contributions that shaped modern global mathematics.

Chapters

00:00 - 02:30: Introduction and Background The chapter introduces Professor Soumesh Kumar, a mathematics professor at the Indian Institute of Technology, Kharagpur. His talk focuses on the coherent presentation of knowledge and ideas, their applications, and future directions. His research interests include statistical decision theory and inference.
02:30 - 45:00: Ancient Mathematics in India The chapter delves into the historical contributions to mathematics in India. It highlights the works of a prominent mathematician with over 100 research publications, who is also associated with prestigious organizations like the International Statistical Institute and the National Academy of Sciences in India.
45:00 - 80:00: Weights, Measures, and Numeral System The chapter titled 'Weights, Measures, and Numeral System' involves discussions around the state of statistics in 2022. It highlights the popularity of certain educational video courses on probability and statistics. Additionally, it mentions the extensive outreach of the subject presenter, who has delivered over 150 invited lectures at national and international events.
80:00 - 105:00: Mathematical Continuity and Evidence This chapter begins with an introduction that includes a shloka, which the speaker attempts to recite, suggesting someone else (Maheshji) might sing it better. The introductory verse emphasizes the supreme importance of mathematics among sciences, likening it to the crest among peacocks and the jewel among serpents.
105:00 - 120:00: Interpretations of Indian Mathematical Achievements The chapter discusses the high regard for mathematics within the context of Indian Vedic and scientific traditions. It challenges the stereotype that Indian achievements were limited to philosophy, religion, and social sciences by asserting the historical competence in scientific fields, particularly mathematics. The speaker aims to address and correct this misimpression, supporting their points with existing evidence of India's contributions to science.
120:00 - 143:00: Challenges and Future Perspectives The chapter discusses the continuity of mathematical traditions in Indian civilization from ancient to modern times. It highlights the existence of shlokas (verses) that signify the rich heritage and continuous development of mathematics in India. The mention of these shlokas indicates the significance and reverence of mathematics throughout Indian history.

History & Development of Ganita - Ancient to Modern | Prof Somesh Kumar | IIT KGP | #SangamTalks Transcription

00:00 - 00:30 We have Professor Soumesh Kumar with us. Professor Soumesh Kumar is a professor of mathematics in Indian Institute of Technology, Kharagpur. He will be speaking on the cogent statement of knowledge and ideas, applications, and way forward. Let me introduce him. Professor Soumesh Kumar has research interests in the area of statistical decision theory and inference.
00:30 - 01:00 He has published more than 100 research papers in international journals. He is an elected member of the International Statistical Institute, Netherlands, National Academy of Sciences, India. He received the Platinum Jubilee Lecture Award of the Indian Science Congress Association in 2016. He also received Professor K.S. Bose Best Researcher Award from Indian Society for Probability and
01:00 - 01:30 Statistics in 2022. His video courses on probability and statistics are very popular. He has delivered more than 150 invited lectures, talks in various national and international conferences, symposia, and workshops. Over to you, sir. Thank you, Maheshji, for giving a very generous
01:30 - 02:00 introduction of mine. I will start with a shloka. Maybe Maheshji can sing it better. But anyway, let me just say, yatha shikha mayuranam naganam maniyo yatha tad vedang shastranam ganitam murdhani vartate jaise moron mein shikha ka aur nagon mein mani ka sthan sabse upar hai,
02:00 - 02:30 waise hi vedang aur shastron mein ganit ka sthan sabse upar hai. Actually, my topic is mathematics today. And what I just wanted to convey, I mean, there has been some sort of impression that, okay, we were good in philosophy, we were good in religion, we were good in many other areas which are of social sciences, but probably not so good in sciences, although now we have enough evidence about those things.
02:30 - 03:00 So, let me, my title I have written, From Ancient to Modern. It means I want to convey some continuity of mathematics tradition in Indian civilization, starting from the very early times. And the fact that we have a shloka devoted to this, it means that, yes, it is not just that there are some snippets
03:00 - 03:30 here and there. There is a substantial body of work which continued. So, I will give my perspective as well as the details. Since I am from analytic side, I generally speak with the evidence rather than saying something. So, evidence of usage of ratios in construction of bricks, walls, yajna vedis, etc., they are available in ancient texts. And we find that excavations from Harappan as
03:30 - 04:00 well as Hindu Saraswati era, they show that urban architecture used various ratios and measurements indicating mathematical abilities. So, now these evidences I have taken from the work by Michel Danino, and there are many archaeologists as well as people who worked in excavations generally.
04:00 - 04:30 And this included lot of European scientists or you can say excavators who visited India during 18th, 19th and 20th century and they have discovered various things. And now that information or knowledge has been compiled. So, I recently read the book of Michel Danino, The Lost River, that is on Saraswati. And I have collected certain mathematical contents from
04:30 - 05:00 there. So, what is striking there? So, I mean like they have now given lot of diagrams or you can say graphs where they are showing the architecture of the city planning, the town planning, the houses, the palaces, the temples and so on. What is remarkable there is that they are mostly following certain standard ratios. Now, if there is a knowledge of ratios that means there is some sort of counting
05:00 - 05:30 system even in that civilization. So, I am starting from the Harappan civilization what we call Harappa, Mohan, Jodhro. So, that is now dated to something like 5000 to 7000 BC. So, that is the timeline that has been now improved upon. Earlier it was said 3000 BC and so on. But now with advanced features, I mean advanced methods of study, it has been now dated back, much dated back.
05:30 - 06:00 So, for example, street widths in Kalibangan have been found to have been arranged in arithmetic or geometric progression. You can consider it like 1.8 meter, 3.6 meter, 5.4 meter, 7.2 meter. Here I have written in the terms of meters. So, actually they are not in the meter. So, I will tell you later on that what is that corresponding to. But in today's measurements if we measure it is coming to something like this 1.8 meters, 3.6 meter and so on. So, which is almost you can consider it
06:00 - 06:30 as a arithmetic or a geometric progression which is in the ratio of 1 is to 2 is to 3 is to 4. Similarly, now you come to far different place. This is Kaushambi. So, that is here in UP. And here they are saying a road of width 2.44 meter it is further broadened and it has been doubled to 4.88 meter. So, that means doubling concept is there. So, ratio 2 is to 1. And then if you look at Arthashastra, Arthashastra
06:30 - 07:00 is dated something like 300 BC kind of thing, 350 BC. So, there is lot of gap between the Harappan civilization and this one. But here if you look at the widths of streets, they are described in the unit of danda. So, what is the unit of danda? Danda is usually something like a 6 feet or 1.8 meter kind of thing. And they are considering widths of 2 danda,
07:00 - 07:30 4 danda, 8 danda and so on. So, again it is in certain ratios. Again let us go back to Harappan phase. And in the early Harappan phase, one Harappan city which was discovered in 1970s in, which is actually in Haryana, present day Haryana in Fatehabad district. And the earliest bricks that are found there, they are in the ratios 1 is to 2 is to 3. And then there is a latter phase there.
07:30 - 08:00 That means there are certain houses which are dated slightly later. In the same settlement, they have found two types of houses. So, some constructions they are dating little early. And there the ratios of the bricks are the length and the width and the height, 1 is to 2 is to 3. Whereas, in the latter phase, they are in the ratio 1 is to 2 is to 4. And there is another layout which is probably of a mature phase.
08:00 - 08:30 It is of a trapezoidal shape. And there is an acropolis there which is semi-elliptical. So, that means the knowledge of the structure and the stability of that, that the semi -elliptical structure will actually stay. So, that is there. The street arrangement in these places which has been discovered and they have been found to be mostly in the right angles.
08:30 - 09:00 And also some of them are considered oriented in the north-south axis. And there is another small building which has been discovered there. It is having semi-elliptical shape. And inside that, so this semi-elliptical shape is not a coincident. Actually, inside there is a fire altar. And that is actually also having similar shape. So, that means there is a thinking behind that kind of thing. And many other structures are seen to be
09:00 - 09:30 in fixed ratio. So, I have just given certain examples. Actually, the archaeologists who have studied it in detail, they have given for each building the ratios and all. I have just taken certain examples here. So, for example, in the Mohan Jodhro, one acropolis is found. It is having ratios approximately 200 meter into 400 meter. That is the length and the width. And a similar thing if you note here in Kalibangan, which is far off from Mohan
09:30 - 10:00 Jodhro, this is 120 meter by 240. So, 1 is to 2 ratio has been maintained there. There is another lower town acropolis in Kalibangan which is found to have 3 is to 2. That is 360 by 240. So, that means there is some sort of continuity of proportions in various structures. Like if you consider the Hindu Saraswati civilization and then the latter civilization which you can call Indo-Gangetic civilization, there is a continuity
10:00 - 10:30 of the thing. So, this also of course is against the Vedic, the Aryan invasion theory. Because if there was Aryan invasion, then all this thing would not have been possible. There is a continuity of the tradition. So, there is no foreign invasion or that kind of thing. That means the Aryans came from outside and so on. So, if you look at the designs of pillars, temples, etc., in the latter day Pataliputra, there have been some excavations near Agra, in
10:30 - 11:00 Prayagraj, etc. And they are generally found to be in the ratios 5 is to 4, 10 is to 8 and so on. And the buildings are mostly in the parallelogram, square or rectangular shapes. See, if mathematical knowledge was not there, then they would have simply gone with the circle and the square. Because that is the simplest thing. I mean you don't need mathematical knowledge to do that thing. The square and the circle can be done by any common person who is not having any scientific understanding.
11:00 - 11:30 But they have used various shapes, that is parallelogram, the rectangular and that too following certain ratios, it shows a well-developed mathematical thinking. So, I have given here one table which is actually work of Michel Danino as well as R. S. Bist, etc. And they have given various ratios which are used in Dholavira. And I have given the margin of error. Because we are measuring in the present day
11:30 - 12:00 meters or the feet. But that time they would not have used meter and feet because that was not there. So, I will tell you what they actually used. So, if you look at the ratios of the inner castle, that is 5 is to 4. And here they have found the error margin to be less than 1 percent. It is just 0.9 percent. And outer castle if you look at, that is also in the ratio 5 is to 4 with a margin of error 2.4 percent. Then similarly you can see, Delhi it is 1 is to 1 with margin of error
12:00 - 12:30 0 percent. Middle town 7 is to 6, half percent. Ceremonial ground 6 is to 1, 0.7 percent and so on. So, these you can see and if you look at this right column, in the right column you can see that the error margins are, except one place, it is always less than 1 percent. A length of the middle town and so on. Similarly in the Lothal also, the Lothal town itself, it is observed to be 280 meter
12:30 - 13:00 to 225 meter. And there are other structures there which are also. Similarly, a granary found in Harappa, that is 5 is to 4. So, 50 meter by 40 meter. Another major building in Mohenjo-daro, it is seen to have 18.9 meter into 15 .2 meter, which is approximately 1.25, which is 5 is to 4. Now it is possible that the ratios which are used in the Indus Saraswati civilizations, they
13:00 - 13:30 may have followed religious, aesthetic or cosmological considerations, but they have been carried over in Vedic, Indo-Gangetic civilization showing continuity of the mathematical tradition. In fact, if you see Shatpad Brahman and you look at the construction of Mahavedi described there, that is also using 5 is to 4 in rectangular dimensions. So, Shatpad Brahman is much later compared to the Harappan civilization. Almost 3-4 thousand years later.
13:30 - 14:00 And again, if you see a slightly later, that is Shulva Sutras, and there they have considered the construction of multi-layered altars. And again, they use the similar thing. I have not presented here various geometrical concepts. Actually, there is a beautiful PhD thesis from Banaras Indian University, that is Saraswati Amma. And if you read that one, they have given the geometrical arguments about various shapes like
14:00 - 14:30 squaring of a circle and all those problems which are studied in the modern Europe. But many of those problems are mentioned there. For example, bisecting angle, trisecting and many other kind of problems they have discussed there. If you look at Mahabharata Kaal, in Mahabharata Kaal you had famous King Drupada, that is the father of Draupadi. So, again in 1900 etc., so there was
14:30 - 15:00 an excavation. It's in a town called Farookabad in UP. It is on the banks of river Ganges. So, the place is called Kampilya which is mentioned in Mahabharata. So, there is a palace type of structure which is said to be palace of the King Drupada. It is called Drupada Kila. And again, the dimensions of that are also in the ratios 5 is to 4, 7 is to 6 and so on.
15:00 - 15:30 So, we can just say that there is a continuous tradition. So, this is about the geometrical things. Let us come to the weights and measures. Now, if you look at the weights and measures in the Harappan system, they have used cubes, some truncated spheres and many kind of things. And the lowest ones are below 1 gram and they have something like 14 different weights and they go up to beyond 10 kg. The units either they are in the geometric
15:30 - 16:00 progression or they are following certain arithmetic geometric progression. So, like it is 1 is to 4, 2, 4, 8, 16, 32 and so on or it is arithmetic geometric 200, 320, 640 and so on. This similar series are observed in Arthashastra and many later texts. Now, one can say that many of these could have come from the say European civilization or anywhere. But if I remember correctly, I mean like
16:00 - 16:30 even when we were children in village, see some village old person who is sort of uneducated person, but they will give us a puzzle to solve. And they will say that divide the number, I mean like you should have weights in such a way that you can measure every integer unit between 1 to 100 kg using only 5 weights or 7 weights and we used to solve that thing. And the solution was actually arithmetic like we
16:30 - 17:00 say geometric progression. So, 1, 2, 4, 8, 16, 32 and similarly we had for the 3, 1, 3, 9, 27 and 81. So, we used to have this. So, this cannot come like that those persons would have known European mathematics or something. It is coming from indigenous thing and which is because of this. So, I am again showing the continuity between
17:00 - 17:30 the Harappan civilization and the traditional Indian system and we find amazing similarities. If you look at the Harappan weights, I have written on the left hand column it is showing the units during the Harappan weights and if you compare them with the corresponding value in the grams. So, that is the second column here and you look at the corresponding thing in the traditional Indian weights which was used till very recently. In fact, till 30 to 40 years back these things were used because I have actually
17:30 - 18:00 lived in village till my class 12 and there in the village shopkeepers they used to have this thing, I mean different units. This is called Raktis and Karshas and here you compare these numbers. So, 0.8525, this is 0.8375, this is 0.1705, this is 1.675, this is 3.41, this is 3.35. So, that means except for certain correction you can
18:00 - 18:30 say the numbers are almost the same. So, this is again now let us come to that what basic unit of measurement like you said today you use centimeter or millimeter and in grams you use. So, what they could have, how did they come up with these measurements that means the ratios and so on. So, probably the human angle, I mean the length of the finger probably that is most common unit of measurement and a human angle
18:30 - 19:00 actually measures between 1.6 to 1.9 centimeter. So, if you look at that so if I take some sort of average value 1 .76 into 108 that is 190. So, that is probably 1.9 meter why that is occurring so often why not 2 meter or why not 1 meter or why not 1.5 meter something which is coming very regularly that is in the measurements of 1.9 meter. So, this calculation has been shown that it
19:00 - 19:30 is 108 times 1.76 and then again 108 angulas are equal to 1 dhanu. So, that is the bow length actually. So, this is present both in the Lothal Kalibangan tradition as well as in the Arthashastra. So, that means there is a gap of 3-4 thousand years and still the same things are being used. Now, again another question is about 108, what is this number 108?
19:30 - 20:00 We usually associate with the religious connotation but actually it need not be religious actually if you look at the distance between the sun and earth and if you divide by the sun's diameter so that is actually 108. Now, the thing is that how you can measure does it need very advanced tools? No. Actually you don't need very big things here you can actually just proceed with say some simple geometric experiment which was done even in
20:00 - 20:30 by Euclid or by Archimedes and so on. That means you just put a stick in the sunlight and then from there you can just measure. So, it is 108 times there. So, it does not require very very great scientific things. So, that means they have used this based on a scientific principle not based on some religious principle. Later on it has been connected with the religious things like you have 108 Upanishads and so on. Now, you come back to even later time
20:30 - 21:00 that is Iron Pillar in Delhi and R. Bala Subramaniam of IIT Kanpur he was professor in meteorology he did very extensive work on that. He checked what is the metal and so on and he did the dimensions also. So, there if you look at the total length is 4 Dhanus. The pillars diameters they are 36 Angulas at the bottom. On the ground it is 24 Angulas and actually it is some part is below the
21:00 - 21:30 ground and then so at the bottom it is 36 Angulas then 24 Angulas at the ground 12 Angulas at the top. So, again you can see the ratios are there and if you look at the ratio of the pillars total length to the portion above the ground that is 5 is to 4. So, these are all very very very interesting. And then there are studies in the some construction some constructions in Nepal especially in Kathmandu
21:30 - 22:00 some ancient constructions are there and there also so I think I will just complete this part here that I am talking about the one type of mathematics so that means ratios which are used in the geometrical construction. So, that means the ancient constructions followed geometrical principles using mathematical ratios. So, that is one very important thing I think one should notice here.
22:00 - 22:30 Now, I come to another gift of India to civilization that is the origin of modern numerals. So, we are establishing that the present numeral system decimal and place value system actually originated in India. In fact, the present development in modern science is based on the current numeral system that we use the numbers 1 to 9 and 0 and the decimal place value system. Now, it is important to note that this number system in which every number has an
22:30 - 23:00 absolute value as well as positional value it evolved in India. In fact, substantial achievements in modern physics, mathematics and technology in Europe it is started only after the Indian number system reached Europe through Arabs starting late first millennium. However, due to effect of colonization of Indian subcontinent during 18th, 19th century an impression was created that the Indian civilization lagged in scientific development more so in mathematical sciences.
23:00 - 23:30 However, now there is a rich catalog of findings which is stored in inscriptions, stone carvings, plates, stamps, seals, charters, tablets, manuscripts in various parts of the country. So, and another thing is that again the second impression that was created is that probably that after Bhaskaracharya and Madhava again there is a gap that means after 12th, 13th century again there is no development.
23:30 - 24:00 So, again I will show that this is also a false statement. Actually there is a continued tradition which continues till now. Okay. I will just put, show one word at the bottom which is written. It can be put equivalent to the discovery of fire and wheel in the evolution of human race. The discovery of the or you can say setting up of the numeral system.
24:00 - 24:30 And we will also show that the decimal place value system refer to the unique numbers. It is observed that the ancient Indians used very high that is 10 is to the power 421 as well as very small that is 7 to the power minus 10 numbers. And here I will like to present some controversial things also. One is that people wanted to appropriate the invention of modern numerals. They said that oh ancient Greeks they have
24:30 - 25:00 discovered or Egyptians or Jews or the Arabs. And they actually have not been able to provide any substantial evidence that those civilizations used this 10 numerals. And they also ignore certain facts that the people in ancient Greece had two different systems of numerals. One was based on the Roman system and the other one was alphabetical which is the one used by Hebrews that is the Jews.
25:00 - 25:30 Both of them did not have zero as well as any place value system. So it was not possible to talk about very large or very small numbers and the system was not much useful for advanced scientific work. However certain absurd theories were floated regarding origin of modern numerals in the western world. One is that from Egypt and North Africa it was propounded that these numerals were invented by a person who was a glass maker come geometer from a place Maghreb which is
25:30 - 26:00 a region in northern Africa that is Algeria, Libya, Mauritiana, Morocco, Tunisia. According to this theory he created shapes of 9 numerals by inserting angles from each numbers the number of angles being equal to the value of the numeral. So if you see this one like 1 you write like this and put an angle here and this 2 you write like this like a Z and put 2 angles here. This 3 you put in the form of
26:00 - 26:30 straight lines joined by certain angles here. Then this 4, 4 is represented as crossing of a 2 lines which is like a red cross and you can put 4 angles here and so on so 5, 6, 7, 8, 9. So this in itself looks so absurd but anyway this is one of the theories. Another theory was propounded by a French author called Wiseart. He published a paper in the journal Nature
26:30 - 27:00 Les Chiffres Arabes et Lure origin that means the origin of Arabian numerals and he was apparently influenced by a writer in Genoa whose name was Catholico Militare and according to this the numerals were formed by number of lines being equal to the value of the numeral. So this is the way it is represented 1 1 line. So 2 you put 2 lines and this red thing which I have put it is my own thing so that means 2 you join by a hypothetical line here and 3
27:00 - 27:30 you put 3 lines and then you join by certain hypothetical lines. So similarly 4, 5 and so on. Again it looks very absurd. And similar theories were propounded by certain writers in Italy, Germany and France. I am just naming them here for example one Italian writer Mario Bettini. So he wrote certain thing called Aperia Universae Philosophiae Mathematica in 1642 and another person is
27:30 - 28:00 German, George Philipp Hausdorfer. He wrote something in Deloitte Mathematicae et Physicae 1651 and it is again, I have put certain references here. There is a Frenchman and so on. So this is number of dots hypothesis. That means you put 1 dot, 2 dot, 3 dot and so on. Another one is by some Arabian astrologer named
28:00 - 28:30 Abel Regal and then there is some theory propounded in Spain, France and Germany, some another theories, so on. The problem of so I have sourced these from certain references. There is a paper by Florian Casori and also there is a book by George Ifrah, The Universal History of Numbers the second volume. This describes all these things. So the problem with these hypothesis is that
28:30 - 29:00 it appears that the shapes of numerals were designed based on a single person's thought process. Appearance of numerals have spontaneous generation and follow some perfectly logical and rational geometrical reasoning and it is not based on any historical evidences in the form of plagues, palm leaves, manuscripts, tablets, inscriptions, etc. There is no continuity of usage in any part of the world of these types of symbols. They completely ignore that numerous shapes and the
29:00 - 29:30 forms used in different civilizations and regions of the world. It also ignores continuous evolution of various shapes around the world. The naming of these numerals as Arabic itself is a historical blunder. It appears to have been named so that because Arabs carried from India and went to Europe. So if you look at the historical history, so during 7th century onwards Arabians they started
29:30 - 30:00 invading other places. So like they came from Iraq, Iran and then Afghanistan and to Indian subcontinent and then definitely they would have travelled to and fro. So they would have gone back and then said at the same time many of them they went to Europe. They invaded Spain, Portugal and other places. So definitely the scientific knowledge also was carried from India to Europe. So they since Arabs carried it so they
30:00 - 30:30 started calling it Arabic numerals. However, I will show you the evidences of the writings of Arabian scholars who say that it is of Indian origin and the most scientific argument against these to be of Arabian, Egyptian or Greek origin is that the Greeks had made great innovations in astronomy, physics, mechanics, medicine, mathematics and philosophy. If they had invented this system of numerals they would have been able to make tremendous progress using decimal and place value system and
30:30 - 31:00 the fact that they used only Roman and Jews system clearly establishes that these hypotheses are absurd and they should be discarded. So now I will present certain evidences from the European and Arabian literature which establishes that the modern numeral system is from India. So I start from certain quotations from starting from some Europeans. So I think everybody knows the name of Laplace is the most famous French scientist because
31:00 - 31:30 of his monumental contributions to physics, astronomy, mathematics and so many areas. So he says that the ingenious method of expressing every possible number using a set of 10 symbols where each symbol has a place value and an absolute value, it emerged in India. See this important point see if you look at say Roman numerals so you have 1,
31:30 - 32:00 then you have 2, then you have 3, then you have 4. Now 4 is written differently, it is not 4 bars here it is something called V and then you put a one I before and if you put that I afterwards it becomes 6 and if you don't put anything then it is 5. So what is that? So there is no absolute or place value meaning there but here if you look at like this number which is written as 1814 so here 4 has an absolute value 4 and the place value is also 4 here.
32:00 - 32:30 If you look at 1 here, 1 is having the absolute value 1 but the place value is 10. So this originality, this came from the Indian counting system. So the ingenious, so this is said by Laplace in 1814 the ingenious method of expressing every possible number using a set of 10 symbols where each symbol has a place value as well as an absolute value, it emerged
32:30 - 33:00 in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated the calculation and placed arithmetic foremost among useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of antiquity that is Archimedes and Apollonius.
33:00 - 33:30 Then I have written actually many quotations from various European scientists. One of them is Montucla. So in 1798 he wrote a big book, it is called Histories, Des Mathematics and here he says that ingenious number system which serves as the basic for modern arithmetic was used by Arabs long before it reached Europe. It would be a mistake however to believe that this invention is Arabic. There is a great deal of evidence, much of it provided by the Arabs themselves that
33:30 - 34:00 this arithmetic originated in India. And then you have John Wallis. John Wallis is one of the most famous original British mathematicians and in 1695 he wrote a big volume called Opera Mathematica and he refers to the nine numerals as Indian numerals. In fact, John Wallis is one of the founders of Royal Society and Newton actually read his mathematics before developing his own. Then Italian mathematician Cattanovo who lived from 1510
34:00 - 34:30 to 1774 and he wrote a book in 1546 and he says the nine figures of India. Then you have German scholar Jodok Willitsch who lived from 1501 to 1552 and he wrote a book in 1540 where he says that is the Indian figures. One of the oldest known arithmetic tracts in English that is called the craft of number.
34:30 - 35:00 See this is written in a different see the craft of numbers but it is written as the craft of numbering. So this is written differently but that is the ancient English 1350. It says furthermore the most so you cannot read this thing because it is written in the original English style that in this craft been used 10 figures as here been written for example 0 9 8 7 is written differently 6 5 4 3 2 1 in
35:00 - 35:30 which we use 10 figures of Inde so he clearly says that these are from India. Then another Danish scholar it is called Patrish of Dacia he worked in Paris and Italy he was one of the faculty members in the University of Bologna. University of Bologna is one of the most ancient universities in the modern Europe which started in 12th century so he wrote a commentary on a work entitled Algarmisa by Sacrobosco that not every number can be represented in the
35:30 - 36:00 Indian figures which is actually a wrong statement but he talks about anyway Indian figures. Then there is a Byzantine monk from Greece his name is Maximus Claudus and he composed a work called Logistic Indic that is Indian arithmetic and the Indian way of counting so the book was written in Greece and here he says the great calculation according to the Indians he says that there are only 9 figures 1 2 3 4 5 6 7
36:00 - 36:30 8 9 and he so this I have written in the modern form and he further writes that a sign known as Ziphra can be added to this which according to Indians it means nothing the 9 figures themselves are Indians and the Ziphra is written as 0 and then you have Alexander de Villa which is a French grammarian the most important is Fibonacci Leonardo Pisano he is one of the most significant European mathematician from 12th century so
36:30 - 37:00 you have this Fibonacci numbers I think anybody who has studied little bit mathematics you know about the Fibonacci series of numbers where you have each number written as the sum of the preceding two numbers a n is equal to a n minus 1 plus a n minus 2 and it was developed as some sort of rabbit breeding model the genetic model for the breeding of the rabbits and so on and also we now call whatever is Brahmagupta Fibonacci identity so in 1202 he wrote a book Liber Abhati that is a book
37:00 - 37:30 of calculation and in this he clearly demonstrated the usage of Indian numerals to be superior to Roman numerals and he can be actually regarded as the first European mathematician to propound the usage of Indian numerals in the western world and he writes my father was a public scribe of Vizagia where he worked for the customs department he asked me to learn calculations using 9 Indian figures and he further writes this is why that with this 9
37:30 - 38:00 numerals and with this sign 0 one can write all the numbers there are many more evidences so maybe I don't have to read each of them this is Robert of Chester Raymond of Toledo Adelaide of Bath and so on so there are so many in fact if you go back I have written the earliest European reference as Vigila in 976 and he wrote a manuscript called Codex Vigilans and here he says the Indian race have a most subtle talent when it comes to arithmetic
38:00 - 38:30 and other mathematical arts and this is clear in the 9 figures with which they are able to designate each and every degree of every other numbers and the figures look like 9, 8, 7, 6, 5, 4, 3, 2, 1 so then let us go back to the Arabian quotations starting from the first one I have written in 1547 to 1621 so there is an Iranian scholar and around 1600 he wrote the title of his book is
38:30 - 39:00 Khulasat Al-Hisab that is the quotations of calculation and here he writes it was actually Indians who invented the 9 characters then there is another Arabian mathematician in Spain Kalasadi and he wrote a commentary on a book by Ibn Al-Banna who himself was a Moroccan and here he says the origin of this 9 figures is traditionally attributed to an Indian of course I mean this original author himself
39:00 - 39:30 wrote that it is of Indian origin so there are some more references I think maybe I can just skip it so we have lot of references here actually probably the most important is by Al-Biruni I think
39:30 - 40:00 everybody has heard the name of Al-Biruni who was actually a traveler when this Islamic invasion was happening so he was traveling with some of them and he lived actually in India for almost 30 years his timeline is 973 to 1048 and he wrote a number of books between 1010 to 1030 and one of them is called Kitab Al-Argam that
40:00 - 40:30 is called the book of figures and here he has a chapter something is written in Arabic so I will not read it so what he says arithmetic and counting using Sindh and Indian figures then again Kitab Fi Thakik something it says one of the most important works about India to be written at that time and he mentions the diversity of graphical forms of the figures used in India now
40:30 - 41:00 this is another thing I am simply giving certain quotations by the European and Arabic authors and so on but what about Indian evidence itself after this I will present that but this is mentioned by Al-Biruni himself he mentions the diversity of the graphical forms of the figures which were used in India and insists that the figures used by Arabs originated in India and he makes the remark like us the Indians use these numerical signs in
41:00 - 41:30 their arithmetic I have written a tract which shows in as much detail as possible how much more advanced the Indians are than we are in this field so let us go back to evidence from a pre-Islamic Syria so there is a Syrian bishop named who studied philosophy, mathematics and astronomy at the monastery of Kansari which is at the banks of Euphrates the place was exposed so that is
41:30 - 42:00 the modern day Iraq in Iraq you have this what we used to call Dajla Parat rivers so they are probably at the confluence of that so he was exposed to a wealth of knowledge because the travellers like Greek travellers, Mesopotamian travellers or Indian travellers going so that means he was exposed to many things and he wrote a manuscript which says the Hindus who are not even Syrians have made subtle discoveries in the field of astronomy which
42:00 - 42:30 are even more ingenious than those of Greeks and the Babylonians as for their skillful methods of calculation and their computing which belies description they use only nine figures if those who think they are the sole pioneers of science simply because they speak Greek had known of these innovations they would have realised that there are others who speak different languages who are also knowledgeable this evidence by Sebok it proves
42:30 - 43:00 that the Indian counting system was known and esteemed outside India by the middle of the 7th century so let us look at the continuity thing which is very important I have shown you ratios and the geometrical constructions in the Harappan civilization and continuity in the Indo -Gangetic civilization ok so when the measures are being used so that means some method of
43:00 - 43:30 calculation must be there because as I showed you like 108 into 1.76 something so that is coming to modern day 1.9 meter and there are some units of that one so how can they multiply if they don't know the number system isn't it so although here I am showing the current evidence which is produced by reading down the manuscripts and all which are present which are present because the manuscripts or the palm leaves or
43:30 - 44:00 the tablets and so on 100 years back ok but if then it is much older could
44:00 - 44:30 have been even much older see now I am giving the this is no so kind of thing and developed no it is
44:30 - 45:00 developed years before that because that is a collection of who wrote that manuscript he himself invented everything so if you look at all these things maybe I can go to now Indian evidences that graphical forms which was mentioned by Al Biruni so this is another thing if you look at all parts of the
45:00 - 45:30 Indian subcontinent like starting from Kashmir to Tamil Nadu to Gujarat to Assam in every place you have local tradition so I think people are here from different regions and you can appreciate that let me start from the beginning so that is first one is called Nagri figures so this geographical area is the present
45:30 - 46:00 day Uttar Pradesh, Madhya Pradesh Rajasthan, Himachal Pradesh Haryana etc. Delhi and here you can see the different forms of writing writing down the numbers 1 2 I have written several because and here you can see some variation also like this in some place 4 is written like this similarly the 5 if you see it is written quite differently for example when I was studying in school in about 45-50 years
46:00 - 46:30 back we used to write 5 like this so I will show Kannada also yeah I will show that so 6, 7, 8, 9, 9 you can see so many versions are there 0 so I think those who have studied in vernacular languages some of you can identify and depending upon the region like let us go to next one anybody from Maharashtra
46:30 - 47:00 here yeah so can you identify this if you have studied in Marathi so like for example 5 or say 7 or 8 or 6 actually we write like Nagari figure yeah so actually what I am showing it is not complete list it is some sample from every region I have collected certain sample and
47:00 - 47:30 that is what I am showing here but I think certainly you can identify many things here so this is Marathi figure which is in the Konkhal, Goa, Daman, Maharashtra and so on then something called Punjabi figures so from the region of Punjab I don't know whether any person is there from north so Punjab also has several not one we will just show some more this is one I have
47:30 - 48:00 named it differently because I have taken from a text this is called Sindhi figures then you have Gurumukhi which is again Punjabi only the last one if you see anybody can relate to this last line the last line can anybody relate to this ok Hyderabad
48:00 - 48:30 in Pakistan Gujarat, Bhupesh ji is not there something called Kayathi figures it is written here Bihar, Gujarat etc but I have seen this thing actually by people who keep leisure actually in the shops I used to see in our village the shopkeeper will keep a book
48:30 - 49:00 of account and there he will write in Kayathi figures so it is usually by those people so these are the figures then the people here from Bengal yeah so you can identify some of these then north Bihar that is Madli figures I don't
49:00 - 49:30 know whether anybody is there from Madli region then I have put Odia figures here Odia anybody is from Odisha yeah this I have drawn I have taken from some sources but I have drawn it here this by hand I have drawn yeah yeah it is there in some manuscript you know
49:30 - 50:00 people in Marwad area and also in UP area they use Mudia language actually Kayathi and Mudia they are used by this people business people Marwadi people yeah Mudia also as well as this Kayathi both and I have seen that yeah I have also seen that and actually they have this you know long bahi lal lang kahi unh aise uthaya lal lang ki rakhte hai register o number 1 ke account yeh hota hai number 2 yeh hota
50:00 - 50:30 hai you have pointed correctly so I have this is a sample actually even the text from where I have taken they have listed many more so but I have not listed because this is to be drawn and then scanned etc so I have done only this one then there are certain figures which are used in the which is a variant of Dogri basically this is called Takari figures again these are used that Kashmir and Punjab that
50:30 - 51:00 is called Sharda figures so Sharda figures I have put so many of them like 1, 2, 3 so many of them are there ok and 0 is written as dot dot dot then Nepali by Nepali simply we mean that this is also Indian subcontinent only so I mean they are all not distinct actually so these are Gurkhali figures then this is
51:00 - 51:30 Tibetan figures so there is another theory which was propounded that since in Tibet also so whether it came from the Chinese but Chinese themselves did not have this because the Chinese figures are quite different so that means that hypothesis is false so Tibetans were influenced by Indians I mean basically Tibetan region and all because there was lot of travel at that
51:30 - 52:00 time now only it is separate this one anybody from Tamil Nadu you are there so in the ancient Tamil 0 was missing which also shows some historicity of this one that probably is of even older origin ok so Malayalam and Tamil they do not have 0 symbol there but again you can see that
52:00 - 52:30 Malayalam and Tamil they have different scripts here so which shows the different kingdoms were there one was chair kingdom and another was trowel kingdom then Telugu figures now you can see 0 is there and I think Kannada figures are here so certain things which I have not presented here but they are available in
52:30 - 53:00 the manuscripts they are the Singhalese so that means something which is present in Sri Lanka Burmese the present day Myanmar so they are all part of the extended Indian subcontinent actually then Thai, Khmer, Balinese, Javanese figures so those who have done little bit of contemporary history you know that the Indian civilization extended up to Southeast Asia actually isn't it now this
53:00 - 53:30 is about the presentation of the symbolism so by modern time I mean from maybe like 200 BC or 300 BC onwards so that is modern time for me because we are starting from the Harappan or
53:30 - 54:00 Mohenjo-Daro civilization that is Indus Saraswati civilization so that means they are the older times and anything which is say which we study that means the history which we study in schools present day which starts from Buddha and Bimbisara and Ajat Chaturthi so from that time I will consider modern times so now from that time onwards Sanskrit became one of the most important languages so I think those people
54:00 - 54:30 who are working in the ancient manuscripts and all we know that now about a million manuscripts are available which have been discovered in various parts of the country and I think more than 80% of them are in Sanskrit isn't it and of course there are manuscripts which are available in other regional languages also so now the latter part of the research or you can say the Indological research
54:30 - 55:00 has shifted to the knowledge of Sanskrit and then interpreting from there that what does it contain so now coming to mathematics again we are doing the same thing here so let us look at that in the Sanskrit shlokas how the numbers are represented so for each number they have used different synonyms so let me just present these things here and with a few examples actually so for example the number one it is having the name eka
55:00 - 55:30 okay so it is having synonyms as pitamah, adi, tanu, tanu means body chiti, arth, abja, indu, soma and so on that means the things which are one they can be used as the synonyms of the number one and in Sanskrit shlokas when the numbers are represented they have used this so I will show
55:30 - 56:00 some examples let us firstly read this then let us read two the number two the common name in Sanskrit we say gvi okay so you have ashwin that is the horseman so two horsemen are there ashwin it is also ashwini kumar that is also two then yama that is the primordial couple then you have yamal, yugal so again this is twins or couple etc you have two eyes so
56:00 - 56:30 netra bahu, two arms then you have gulpau that is the ankles then you have paksha so paksha again it has two meanings wings for the birds it is the wings so two wings or it is the shukla paksha and krishna paksha that is the fortnight two fortnights in a month so paksha is used for gvi or two three that is three so the in Sanskrit we say three so
56:30 - 57:00 we have three guna that is the three primordial property that is sat guna, rajo guna and tamo guna then we have three loka that is the you have patal loka, akash loka and prathy loka trikal again bhavishikal, bhutikal, vartamankal agni that is fire har netra that is the eyes of lord shiva so we say he has three eyes, isn't it chatur
57:00 - 57:30 is the four chatur disha so you have this uttardakshan purvapashyam chatur sindhu chatur yuga that is satyug, retayug, dwaparyug, kalyug chatur irya, haribahu four arms of vishnu four faces of brahma that is brahmashya then pancha that is for
57:30 - 58:00 five, pancha bana the proverbial pancha bana of that kamdev's arrows, pancha indriya so we say that pancha tattva we have chitijalpavagagan samira five faces of rudra rudrasya, pancha bhuta pancha mahayagya shat shatras, shatang shanmukh that is the five faces of kartikeya sapta, so we have sapta
58:00 - 58:30 proverbial ashwas sapta nag sapta nag that is the seven mountains then we have sapta rishis sapta swara, sapta sagar sapta dweep it is another thing if you look at the sapta dweep and try to think scientifically if you say sapta dweep that is the seven continents that means the existence of antarkatika was known ok, so I think one has to appreciate
58:30 - 59:00 that part it is not a latter day invention then ashta ashta gaja, ashta nag ashta nag ashta murti nava, nava anka, nava graha nava chitra and so on zero is shunya, bindu kha, gagan, akash, ambar vyom and so on now this is not an exhaustive list because Indian scholars they have used diverse items for synonyms of numerical symbols these symbols are
59:00 - 59:30 all taken from nature human morphology animals, plants everyday life, legions, traditions religions, attributes of the divinities of vedic brahmin, hindu, jain buddhist, pantheons and diverse social conventions again it shows that the usage of mathematics in the advanced form is very much prevalent during that time otherwise
59:30 - 60:00 these things would not have, so I am just giving some example here so this is from surya siddhanta ok, so shloka it will be difficult for me to read it here because it is written in English version of it so if you translate it it says the upsides of the moon in a yuga and that sequential terminology that is there it starts from fire that is agni, vacuum that is the shunya ashwin that is the horseman,
60:00 - 60:30 then the vasu, then serpent that is the sarpa then you have arnava that is the ocean and its waning mode again vasu, fire, primordial couple, horseman, fire now for Indian astronomers these represent the numbers 4,88,203 and 2,32,238 so if you consider the translation of let us see how the place value system is used here, let me put
60:30 - 61:00 them in the order, the first term is agni that is 3 shunya 0 then ashwin is 2, vasu is 8, sarpas are 8 and arnava that is ocean is 4 so you put it like this in the same order 3, 0, 2, 8, 8, 4 and you convert it to the place value system that is 3 plus 0 into 10 plus 2 into 10 square plus 8 into 10 cube plus 8 into 10 to the power
61:00 - 61:30 4 plus 4 into 10 to the power 5 and it becomes 4,88,200 let us see the second one vasu is 8 then agni is 3 yama is 2, ashwin is 2, shikhi is 3 dasara is 2 another important point which you should notice here that in the slem shloka for example 2 is coming 3 times here but they have used 3 different synonyms they have not written yama yama yama 3 times or they have
61:30 - 62:00 not written agni agni 2 times, they have used different synonyms that shows an advanced stage of understanding and the usage of this if you convert it into the using the place value system it becomes 8 plus 3 into 10 plus 2 into 10 square and so on, this number translates to 2,32,238 so this shows that there is a perfect understanding of 0 as well as the place
62:00 - 62:30 value system which uses the decimal as a base that is 10 as a base system it is a type of symbolic representation subject to many variations yet the numerical symbols were always perfectly comprehensible to the Indian astronomers even if the value of certain words could vary according to the author, the region or the time when they were written, the context always confirmed the intended numerical value so I will
62:30 - 63:00 just give certain more citations from south east asia etc so this is a inscription from java so present day java it is in indonesia and there is a shaka date, it is in the state of changal and it is written as that is the inscription found there, so let us look at the translation of this so shruti means veda so there
63:00 - 63:30 are that is 5 and then the that is the 6 senses, so you translate it using the place value system so it becomes 4 into 4 plus 5 into 10 plus 6 into 10 square that is 654 so if you convert it to the christian era you add 78 it becomes 732 christian era so this is an inscription in 732 A .D it is from java then you look at another inscription from champa anybody can tell
63:30 - 64:00 what is champa cambodia so it is in the state of some mison and the shaka date is written as anand amrit something, so let us look at the translation of this thing, so 6 so i have written it in reverse here 9 plus 0 into 10 plus 6 into 100, it becomes 609 plus
64:00 - 64:30 78 so this is even older than that, that is 687 A.D then there is something from cambodia so probably champa is i think vietnam so the next one is khagvi sharar so you look at this one 0 plus 2 into 10 plus 5 into 100 that is 520 plus 78 that is the 598 A.D so this proves that the
64:30 - 65:00 use of sanskrit word symbols it had spread to all over south east asia in the 6th century itself again i want to show certain continued tradition also the continued tradition means that as i said that from ancient to modern so there is no break of mathematics actually, so you look at the, i have listed here the text here, so trishatika it is by sridharacharya date is unknown, i have
65:00 - 65:30 written here but most probably it is in the 6th or 7th century then karnadi patyati it is 8th century text by puttum, it is from andhra, then there is a siddhanta viveka it is by kamalakar, it is 7th century then siddhanta darpana by neelkanth, it is 15th century then dragantika, that is by parmeshwar,
65:30 - 66:00 it is 1431 C.E then vakya panchadhyay it is 14th century then siddhanta shiromani, this is of course by subhaskaracharya, 1150 then rajmraganka, that is by bhoja in 1042 siddhanta that is by sripati 1039 so you can see
66:00 - 66:30 from all the years, different years we have seen that these are all available another thing which i want to show that it is not that they are using these numbers only for some recreational purpose that they have only certain very small numbers or some useful numbers only they are used for various purposes and it will be clear if you see the
66:30 - 67:00 first few examples that i will show you here so you look at this example this is from bhaskara 1 ok, so they want to say a chaturyuga is made up of these many years ok, that is something like 43 lakh 20 thousand years, ok so how he is writing this one, so it is written in the shloka form like viyad ambar akash shunya again you see this 0 is
67:00 - 67:30 used 4 times but this 4 times 0 he is using 4 different names here, so viyad ambar akash shunya and then of course yama and rama and then veda, so if you look at this one the translation becomes 0 0 0 0 2 3 4, so using the decimal place value system it will become 43 lakh 20 thousand number there is
67:30 - 68:00 another one example from bhaskara which is actually in the commentary on R. A. Bhatti here so again there is a big number here, you look at this this is a 10 digit number so that means in astronomical calculations they have used very large numbers also this is a 10 digit number but
68:00 - 68:30 another important point which I think one may miss here, this is this one you see he is writing 0 3 7 3 and I told you the synonyms for 0 1 2 9 but there is a synonym used for 12 also with sankhya paddhati so
68:30 - 69:00 the purpose of presenting all this is actually just to show that various regions of India in various traditions in various languages everywhere mathematics
69:00 - 69:30 was used so you are giving an example from Surdas that is a Surdas I think this one which you have told it means that we cannot say that Surdas was studied in a university or somewhere can you repeat again it is a foreign word it means that what has been done by foreigners in India in 1859 every meal the meaning of
69:30 - 70:00 the word bird every meal means death means 30 days and there is no return there is no return and he is talking to Uddhav I think Gopiyan they are talking to Uddhav and he is telling the reason why
70:00 - 70:30 I said that Uddhav is a beast in 1020 27 stars 4 planets 9 planets 4 planets and you are a beast that is what Uddhav is saying so you can see this is
70:30 - 71:00 very interesting actually we have read it in school but now I don't remember so you can see the jugglery of numbers along with the corresponding half of them that is beast and then they are saying it is wish so that kind of thing cannot be given unless you have a very developed mathematical understanding so I think the point is very well
71:00 - 71:30 made now this example is again very important one which I am showing here you see Kha is for 0 Agni is for 3 then Adri is for 7 Rama is for 3 Arka see this is 0 1 to 9 we are saying but they have used a synonym for 12 here that is a 2 digit number we have this Dwadash Aditya so for 12 that is the sun they have used 12 here and then Rasa but
71:30 - 72:00 then again somebody may feel that they will make a mistake in the calculation but if you see this here 0 plus 3 into 10 plus 7 into 10 square plus 3 into 10 cube plus 12 into 10 to the power 4 but it is understood that it is a 2 digit number so 10 to the power 5 is not there and the next one you can see 6 into 10 to the power 6 so they have taken care of this ok which translates to this particular 10 digit number so it is
72:00 - 72:30 surprising to see that in a place value system word symbols denoting values higher than or equal to 10 they are also used to express a number which contains 2 orders of units and the value this 1 9 8 6 1 2 3 7 3 0 and it is clearly indicated in figures according to the place value system in the next line of the Sanskrit text which accompanied by the words it says in figures it reads and
72:30 - 73:00 they have written the corresponding this one in order to prevent any ambiguity and there is another example where Bhaskaracharya has given Sanskrit as well as the corresponding numeral notation this is a very big number you can see this is I think this is a 19 digit number this is a 19 digit number which is there in the Bhaskara's description ok
73:00 - 73:30 so there are examples from Varaha Mihir and so on there is a jain work that is called Lokavibhag that is the parts of the universe and here they have used like minus 1 is represented by Ruponaka ok so that means the concept of negative integers was
73:30 - 74:00 there there is a number which is represented like 1 4 2 3 6 7 1 3 that is a 8 digit number so that is another one is called dating of the Lokavibhaga so this dating has also been done through a shloka here the shloka is given here and if you translate it, it turns out to be 387 so if you
74:00 - 74:30 add 78 so that is coming to 452 Christian era Namaskar Sir I have only one question here see as we can understand that we were great, we did you know this and that many thing and said it is from India and
74:30 - 75:00 all those things what was the enabling factor there at that moment our idea has to be what is today and what are we going to do tomorrow what we are today and what we are going to do so what was the enabling factor there which got missed out during the period now what we have to create here so that we can again be great I believe that one of the idea of the IKS is that we will not only glorify that we were great
75:00 - 75:30 question is how we can become great now in today and tomorrow I would like to know this thank you so I think first thing that I would like to say that there is a great misconception that something has gone wrong or something see it only happened, I will just tell you see when the colonial period came then the wealth of the country was sent outside so country became very
75:30 - 76:00 poor that is the only thing that we can say it is not that knowledge became poor or anything else became poor or scientific development became poor, no the ship building industry was there that time also in fact if you look at the Maratha ship building industry and so on it was there and even when the Britishers have come even in the Bengal also the ship building industry was there so things were there, it is only that the wealth of the country was transferred to England and therefore the country became poor, that
76:00 - 76:30 means the common man became extremely poor, when India became independent they hardly had anything I mean there was no money, I mean the GDP that time if you look at there was nothing and so you did not have the food grains they destroyed the industries and so on so if you look at the scientific thing it became subdued because of the gross poverty and the gross you can say deprivation of the population so something I think if you read the things probably things will become very clear the development of the science
76:30 - 77:00 continued in fact what we call renaissance period and so on but it was actually a continued tradition only what we say that when the British universities started like in Calcutta, Bombay and all these places and then again no it is not because of that it was already there because now we are going through the literature which is available now that means what mathematical developments are there and other things they were being done that time also so
77:00 - 77:30 it is only some sort of misconception that we will become great one day and so on, there is nothing to become great actually the knowledge is there and actually because this is a limited time I cannot present so if you look at last hundred years itself how much mathematical contributions Indians have made so I could not present all those things because this requires may be another three hours time see because we start from the ancient one
77:30 - 78:00 and we cannot go to the new things which are there so this is for example Ramanujam's mathematics so you will say that where from Ramanujam is studied see Ramanujam did not have very good formal education because he was passionate about mathematics itself and in mathematics then he continued doing of course he got an opportunity of going to Europe so that his work became popularized but it does not mean that the G.
78:00 - 78:30 H. Hardy or Littlewood helped him to prove anything he in fact proved everything they only helped to popularize it so that the results came in open later on entire of his manuscripts they have been proved by one two American mathematician that Bruce E. Burnt and George Andrews and they have published some twelve volumes he has proved around 5000 results 5000 results and out of those 5000 only may be 10 results were not correctly proved all other 4990 results are correct so
78:30 - 79:00 he made monumental contributions and this is so he is considered one of the greatest mathematicians now you will say what after that so Ramanujam is one but then there is a full tradition so for example in a mathematics we have fully school of algebraic geometry those people who work in algebraic number theory and so on they have published great number of results the evolutionary algorithm I think it was proved in 2014 or 15 which is now
79:00 - 79:30 considered to be the number one result in the world because of the highest it has more than a lakh citations actually and professor Kalyan Mahadev he was alumnus of IIT Kharagpur now he was working in IIT Kanpur now he has gone abroad so he has proved that thing artificial intelligence blockchain all these ideas are coming from the west why not from India not necessary that all are from west
79:30 - 80:00 but sir as I mentioned just now evolutionary algorithm is an Indian thing the Karmakar's algorithm why are we sitting here we are here in IKS because we want to feel happy that we have a great genes we have a great past and we have to go again great so that how many more and more noble prizes and other thing are coming from India I believe it is one of the idea of our investment over here so how we can do those things like medical
80:00 - 80:30 transcription and you know artificial intelligence ok the current sampling theory which is used the sampling methodology which is used worldwide most of it is developed in India and it was done
80:30 - 81:00 in 1930s and 40s by statisticians which were led by P.C. Malanobis who established Indian statistical institute and I can show some quotations maybe we always look for certain approval from western world I think that may be the reason otherwise we have done that so most
81:00 - 81:30 important contributions are related to the large scale sample surveys we introduced the concept of pilot surveys and advocated the usefulness of the sampling methods so this include the topics such as consumer expenditure, tea drinking habits public opinion crop Harald Hotling he was an American statistician he wrote no technique of random sample has so far as I can been developed in the United States or elsewhere which can compare in accuracy which is described by P.C. Malanobis
81:30 - 82:00 R.A. Fisher is considered the founder of statistical methods and he says that Indian statistical institute has taken the lead in the original development of the technique of sample surveys the most potent fact finding process available to the administration and so on so I will not get too much into this thing let us look at other things also when country
82:00 - 82:30 become poor then knowledge, science academic that take the back seat because survival itself becomes a thing now we have spent almost how much 25 years already economy has come up to a certain level we have now schools, colleges,
82:30 - 83:00 universities all over there was a survey done in but rejuvenate intellect was existing throughout if it was our fundamental that we had a very shaped society we had governance norms we had growth parameters so once we are into a shallow phase of economy we were not rulers so that time we were not the rulers after colonization things are happening like if
83:00 - 83:30 you start from 1947 onwards so what has happened education has been given lot of importance and that is why things are happening so what I am saying is that we should not people are having some sort of feeling that why they are doing you look at what you are doing isn't it? as far as patenting or IPR regime is concerned whosoever makes the first take on them
83:30 - 84:00 they get the rights so how are we going to defend it? zero is protected haldi got protected team got protected pasmati got protected because it's a transient variety of pasmati that has been so how do we go about further into publication and preservation of this legacy? I mean would it pass into the folklore and get automatically protected?
84:00 - 84:30 because copyright I think is going to be difficult original scripts and the original authors they are not there so a copyright and 100 years after they die to their survivors that is out of question so now what are we going to do? patenting also is not possible because the original people who had formulated that patent you have to defend it actually there are policies even like things made up of haldi which were being patented in USA but then it was
84:30 - 85:00 defended by Indian scientists and now the patent has not been granted to them but to the Indian thing so actually you have to fight it's not a word which is ideal word you have to come up and say things, if you don't say then see for example I am a statistics person, I publish research papers isn't it? and we publish in all the journals which are supposed to be good journals like you have some list of journals where you can publish so suppose I say no I am
85:00 - 85:30 great I won't publish there, I will publish my own thing then nobody will recognize me see you have to fight at the equal level see like you say that now world cup football is being played Indian team is not there because it doesn't qualify in the top 32 countries whatever isn't it? but you cannot say that no we are great players, we have great players but we don't play there so how will you show? so you cannot I mean so why not
85:30 - 86:00 why not India starts it's own procedures isn't it? is it not possible for India? universally acceptable no no that is what you have to come up with that thing see for example you look at see I will just give very very simple example you look at the game of cricket ok the cricket was domination of England and Australia and till 70s like when we were children so England
86:00 - 86:30 and Australia they were the top always whatever policies are there it will held the meeting will be held in MCC in England in the what is that Lodge and so on so there was some sort of subjugation like Indians they are useless I mean they are all ok they also play but one player may be good but all are the country itself was considered to be weaker but what happened after 1983 we have defeated them there and now where is India in the world of cricket I mean whatever India says that
86:30 - 87:00 has to be followed so because you have created a system where you are making the rules isn't it so unless you become great let us take another example now till 1950s 60s 70s what was the status of China unnoticed means it was considered backward poor and all that kind of 1977 onwards they went on a liberalization drive and then they have developed but what they have done perception about
87:00 - 87:30 the battery is changed earlier foreign
87:30 - 88:00 foreign foreign foreign foreign foreign foreign
88:00 - 88:30 foreign foreign foreign foreign foreign foreign foreign yeah I mean there are lot of points but I will end with one comment please study study books study literature and see things at various places do not make your thoughts based on Q whatsapp forwards or facebook messages ok
88:30 - 89:00 read originals and books which are available in India and read what others are doing, read what we are doing. Since when I took up this ICASE and so on, I have been reading a lot. See if you read like, I mean, I think that professor, he asked the question about why we are not doing things. I think we are doing, but you see, unless you read about what we are doing, then you cannot say what we are doing. I can say that another hundred things, but
89:00 - 89:30 you have to do what you need to read ourselves. Otherwise, it's only like what I am saying, then you have to understand. That's why. Thank you.