Anyway, if you’re interested in Indian mathematics, check out this lecture https://www.youtube.com/watch?v=2HmMzhZ8zJg (Sadly I don’t know of any other good online lectures about the subject.)
Most modern day Indians do not take the trouble to learn about India (the notion of which was created by the British). If they did they'd realise that speaking about ancient Hindu culture as something that they can associate with is as silly as the British claiming they invented Democracy just because they were part on the roman empire at some point (as also was Greece who actually could make that claim)
This is a well known fact for many in India.
> In India, the right wing Hindu brigade try very hard to appropriate ancient Indian history as that of the Hindu religion (while also conveniently even denying that it is indeed a religion).
This is where you are wrong. There is no "ancient Indian history". "India" was formed in 1947 and if at all there is any history for India it is the past 70 years. We were called Hindustan before 1947. The word Hindustan was not based on the religion that we know today as "Hinduism". The religion was called Sanathan Dharma. The word Hindu however, as was rightly said in the grandparent comment, a name given by the Persian invaders. What the right wingers do propagate is "Hindutvawadi" or that we are all Hindus -> Hindu-Christians, Hindu-Muslims, Hindu-Sikhs, Hindu-Buddhists, Hindu-Jains, Hindu-Sanatanis etc. Hindu being the geographical name of the Country we reside in and Sanathan Dharma/Islam/Christianity/Jainism/Buddhism etc being the actual religion. Does this make sense?
Mahatma Gandhi said the following: "I call myself a Sanatani Hindu, because I believe in the Vedas, the Upanishads, the Puranas, and all that goes by the name of Hindu scripture, and therefore in avataras and rebirth; I believe in the varnashrama dharma in a sense, in my opinion strictly Vedic but not in its presently popular and distorted crude sense; I believe in the protection of cow. I do not disbelieve in murti puja.". Was Mahatma Gandhi a right winger to call himself a "Sanatani Hindu"? Why call himself a "Sanatani Hindu" if Sanatan and Hindu both mean the same? It is very evident that the word Hindu in pre-independence India mean't geographical boundary and the word Hindu post-independence India means religion.
> Most modern day Indians do not take the trouble to learn about India (the notion of which was created by the British). If they did they'd realise that speaking about ancient Hindu culture as something that they can associate with is as silly as the British claiming they invented Democracy just because they were part on the roman empire at some point (as also was Greece who actually could make that claim)
The problem is that no one claims to be "associating" with ancient Hindu culture because the context of the word "Hindu" changed drastically over the past century. What was once a geographical association pre-Independence has now turned into a religious association. It's extremely sad that it has been distorted in this manner all in the name of Secularism.
Hindu only has religious connotations in English because the West chose to recognize the word as a religion. The actual name of the religion is "Sanathan Dharma". I'm sure it was easier to say Hindu than say "Sanathan Dharma".
Hinduism is ancient, but a living, evolving, and extremely diverse religion. To an outsider, it looks more like a cluster of religions than a unified religion. So it's hard to name appropriately. "Vedic religion" is mostly used for historical traditions more than living ones.
For example, the definition of "Infinity" from the Isha Upanishad (Written in 1st millenium BC. You can find the pronunciation here: https://www.youtube.com/watch?v=0Pn5oo24THM. This was written way before Buddhism or Jainism were founded):
ॐ पूर्णमदः पूर्णमिदम् पूर्णात् पूर्णमुदच्यते | पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते || ॐ शान्तिः शान्तिः शान्तिः ||
It's literal transliteration:
"Om, That is complete, This is complete, From the completeness comes the completeness If completeness is taken away from completeness, Only completeness remains Om, Peace peace peace"
Jainism or Buddhism were later offshoots of Hinduism (almost centuries after Brahmi numerals were invented). They adopted a lot of Hindu scriptures and practices while rejecting the authority of the Vedas at the same time. Their founders were themselves Hindus. For example: Do you know that Yoga is inadvertently associated with Buddhism even though the origins, scriptures and teachings are from Hinduism?
I would have linked various lectures that talk about Hindu mathematicians but unfortunately they are in Hindi. But there is one video by Dr. Dean Brown on Sanskrit, the Upanishads etc which you can find here: https://www.youtube.com/watch?v=yxzXxQrX2Mc
Another video relevant to this discussion: https://www.youtube.com/watch?v=QxgK0dX872k&list=PL6m6y6YFPj...
Edit: I don't mean to take away from your point that Hindu mathematicians contrubuted a significant amount, but I think the word most here is misleading.
> Most Mathematical concepts originated from Hindu Mathematicians
.. is nonsense. For instance, many core tools of mathematics, measuring systems, astronomy, etc. were developed by Sumerians and Akkadians living in Mesopotamia in 4000–1000 BCE. If you’re curious about it, I recommend this recent book, http://amzn.com/069109182X
Other important advances have been made by Chinese, Greeks, Persians, Arabs, Turks, Italians, English, French, Russians, Germans, Hungarians, Americans, ...
It is not "nonsense". Your knowledge of Hindu astronomy is limited. I suggest you to read up on Hindu Astronomy and Measuring systems here: http://www.crystalinks.com/indiastronomy.html
"Ancient India's contributions in the field of astronomy are well known and well documented. The earliest references to astronomy are found in the Rig Veda, which are dated 2000 BC. During next 2500 years, by 500 AD, ancient Indian astronomy has emerged as an important part of Indian studies and its affect is also seen in several treatises of that period. In some instances, astronomical principles were borrowed to explain matters, pertaining to astrology, like casting of a horoscope. Apart from this linkage of astronomy with astrology in ancient India, science of astronomy continued to develop independently, and culminated into original findings, like:
The calculation of occurrences of eclipses Determination of Earth's circumference Theorizing about the theory of gravitation Determining that sun was a star and determination of number of planets under our solar system There are astronomical references of chronological significance in the Vedas. Some Vedic notices mark the beginning of the year and that of the vernal equinox in Orion. This was the case around 4500 BC. Fire altars, with astronomical basis, have been found in the third millennium cities of India.
Yajnavalkya (perhaps 1800 BC) advanced a 95-year cycle to synchronize the motions of the sun and the moon. A text on Vedic astronomy that has been dated to 1350 BC, was written by Lagadha."
Read up on Kalpa and Yuga: https://en.wikipedia.org/wiki/Kalpa_(aeon)#Hinduism and https://en.wikipedia.org/wiki/Yuga
and the "Hindu units of Time": https://en.wikipedia.org/wiki/Hindu_units_of_time
Also read this book on Hindu cosmology and astronomy: https://www.abebooks.com/book-search/title/the-theogony-of-t...
You can find an archive of the entire book for free here: https://archive.org/stream/theogonyofhindoo00bjrn/theogonyof...
Some quotes from the book:
"The antiquity of the Hindoo Astronomy has long been a disputed point among the learned of Europe. Cassini* Bailly,^ Gentil,* and Play/air^ maintain, that there are Hindoo observations extant which must have been made more than 3000 years before Christ, and which evince even then a very high degree of astronomical science."
"Davis, who has also taken up this question, calculates that the celebrated Hindoo astronomer Parasura, judging from the observations made by him, must have lived 1391 years before Christ (Asiatic Researches, vol. ii. p. 288), and consequently had read in the divine book of the heavenly firmament, long before the Chaldees, the Arabs, and the Greeks."
"The religion of the Hindoos, which is called the Brahmin, is the most ancient of the present systems of religion upon the earth, and probably one of the oldest ever known ; in this respect, therefore, it is deserving of a high degree of attention. The doctrine is based upon the books of religion held sacred by the Hindoos, called Vedas, written in the ancient Sanscrit, which bears the same rela- tion to the present dialects of the Sanscrit, the Hindostanee, Bengalee, Tamul, &c, as the Gothic does to the Swedish, and the Latin to the French and Italian, (fhe Hindoos maintain that the Vedas (four books) are contemporary with the creation, and were revealed by Brahma himself) The sacred volume begins with these words : — " (There is only one God, Brahma, omnipotent, eternal, omnipresent, the great soul, of which all other gods are but parts\" Nevertheless the Vedas do not address their hymns to this only God, but to things created by him, as the sun, the moon, the stars, the earth, fire, &c. ; so that this religion, although Monotheistic in its fundamental principle, is tinctured with a kind of Sabceism, which probably constituted the early religion at the time when the ancestors of the Hindoos still dwelt in that country from which they came to India (from 2500 to 3000 years before Christ). The Vedas also contain a Cosmogony, the most ancient that is known."
Also, please don't ignore the fact that most of Hindu knowledge of Mathematics, Astronomy, Science, Philosophy or Religion was transferred by word of mouth for millennia. It was only around 2000-1500 BCE that this knowledge was transferred to scriptures which were written in Devanagari (Sanskrit). Most of these scriptures did not survive, but the knowledge did, because of the stress on rote learning of Mantras (which apart from extolling God and God's virtues also included Scientific/Mathematical concepts). There are many Mantras that have been passed on for generations but the actual scripture is lost.
The problem is that the West had not (and still has not) translated a lot of the Sanskrit scriptures (maybe due to lack of interest) that exist today. The Government of India had setup an ASI (Archaeological Survey of India) to look into translating these scriptures and excavating a lot of ancient cities but due to immense corruption not much progress has happened in this regard. Look up the excavation videos of Submerged City of Dwaraka and why it was abruptly stopped (https://www.youtube.com/watch?v=NVIsjx5X3QM).
Sure. Here is a complete book on Vedāṅga Jyotiṣa (one of the earliest books on Hindu astronomy. It's just 74 pages in total): http://www.worldlibrary.in/articles/Vedanga_Jyotisha
Quoting:
"The Vedāṅga Jyotiṣa, or Jyotiṣavedāṅga (Devanagari वेदाङ्ग ज्योतिष) is one of earliest known Indian texts on astronomy and astrology (Jyotisha). The extant text is dated to the final centuries BCE, but it may be based on a tradition reaching back to about 700-600 BCE. The text is foundational to Jyotisha, one of the six Vedanga disciplines. It was composed by Lagadha.
The Vedanga Jyotisha describes the winter solstice for the period of ca. 1400 BCE. This description has been used to date the Vedanga Jyotisha. According to Michael Witzel, the question is "whether the description as given in the jyotiSa is also the date of the text in which it is transmitted." T. K. S. Sastry[note 1] and R. Kochhar[note 2] suppose that the Vedanga Jyotisha was written in the period that it describes, and therefor propose an early date, between 1370 and 1150 BCE, while David Pingree propose ca. 1180 BCE. The estimation of 1400-1200 BCE has been followed by others, with Subbarayappa adding that the extant form can be possibly from 700-600 BCE."
Ganita, the Sanskrit word for Mathematics, existed since the writing of the Vedas. You can read more about it here: http://veda.wikidot.com/ganita
Even Sulba Sutra (written 8th century BC) explained Pythagorean Theorem before Pythagoras did (6th century BC):
"The diagonal chord of the rectangle makes both the squares that the horizontal and vertical sides make separately."
All the Scientific and Astronomical discoveries of Ancient Hindu scientists has been explained beautifully in this book "Science of the Sacred". The Sulba Sutra part is specifically explained in this page of the book:
https://books.google.co.in/books?id=mZ0ZAgAAQBAJ&pg=PA43&lpg...
https://en.wikipedia.org/wiki/Talk:Indian_mathematics/Archiv...
While there is some level of whitewashing going on, there's a lot of hyperbole of what was discovered during the Vedic period.
Not sure why there's even a need to amplify/attenuate the contributions. There are Indian mathematicians today who are making significant contributions. Probably more productive to focus on mathematical developments in general rather than assigning credit to the past. Assigning credit to a culture is problematic. What about the culture enabled the mathematical development?
Perhaps one day we'll move past assigning credit and towards purely developing ideas in the spirit of the Upanishads written in anonymity.
Where is the hyperbole? All I see is whitewashing of what was discovered during the Vedic period. If you need to understand what whitewashing means: Abrahamic texts/scriptures are classified as History but Hindu scriptures are classified as "Mythology". If this is not systematic whitewashing explain to me what is.
How can you compare an unscientific paper written in the close of 20th century with Vedic scriptures (Vedas and the Upanishads) written 2000 years ago?
EDIT: Again, just to confirm we are on the same page: I'm talking about whitewashing of discoveries during the Vedic period. Not papers written in the 20th century by unknowns.
"Although Vedic mathematicians are known primarily for their computational genius in arithmetic and algebra, the basis and inspiration for the whole of Indian mathematics is geometry. Evidence of geometrical drawing instruments from as early as 2,500 B.C.E has been found in the Indus Valley. The beginnings of algebra can be traced to the constructional geometry of the Vedic priests, which are preserved in the Shulba Sutras. Exact measurements, orientations, and different geometrical shapes for the altars and arenas used for the religious functions (yajnas), which occupy an important part of the Vedic religious culture, are described in the Shulba Sutras. Many of these calculations employ the geometrical formula known as the Pythagorean Theorem.
This Theorem (c. 540 B.C.E.) equating the square of the hypotenuse of a right angle triangle with the sum of the squares of the other two sides, was utilized in the earliest Shulba Sutras (the Baudhayana) prior to the eighth century B.C.E. Thus, widespread use of this famous mathematical theorem in India, several centuries before its being popularized by Pythagoras, has been documented.
The exact wording of the theorem as presented in the Shulba Sutras is: "The diagonal chord of the rectangle makes both the squares that the horizontal and vertical sides make separately". The proof of this fundamentally important theorem is well known from Euclid's time until the present for its excessively tedious and cumbersome nature; yet the Vedas present five different extremely simple proofs for this theorem. One historian, Needham, has stated: "Future research on the history of science and technology in Asia will in fact reveal that the achievements of these peoples contribute far more in all pre-Renaissance periods to the development of world science than has yet been realized.""