INDIAN MATHEMATICAL BRAINS

Chinese records indicate knowledge of a dozen books of Indian origin. Brahmagupta's Sidhanta as well as Charaka's and Susrata's Samhitas were translated into Arabic in the 9th or 10th centuries A.D.In ancient Indian mathematics was known by the general name of Ganita, which included arithmetic, geometry, algebra, astronomy and astrology.
It was Aryabhatta, who gave a new direction to trigonometry. The decimal system too was an innovation of India. By the third century B.C. mathematics, astronomy and medicine began to develop separately. In the field of mathematics ancient Indians made three distinct contributions, the notation system, the decimal system and the use of zero. The earliest epigraphic evidence of the use of decimal system belongs to the fifth century A.D. Before these numerals appeared in the West they had been used in India for centuries. They are found in the inscriptions of Ashoka in the third century B.C.Indians were the first to use the decimal system. The famous mathematician Aryabhata (A.D. 476-500) was acquainted with it. The Chinese learnt this system from the Buddhist missionaries, and the western world borrowed it from the Arab as when they came in contact with India. Zero was discovered by Indians in about the second century B.C. From the very beginning Indian mathematicians considered zero as a separate numeral, and it was used in this sense in arithmetic. In Arabia the earliest use of zero appears in A.D. 873. The Arabs learnt and adopted it from India and spread it in Europe. So far as Algebra is concerned both Indians and Greeks contributed to it, but in Western Europe its knowledge was borrowed not from Greece but from the Arabs who had acquired it from India. In the second century B.C. Apastemba contributed to practical geometry for the construction of altars on which the kings could offer sacrifices. It describes acute angle, obtuse angle, right angle etc. Aryabhata formulated the rule for finding the area of a triangle, which led to the origin of trigonometry. The most famous work of his time is the Suryasiddanta the like of which was not found in Contemporary ancient east.
During the Gupta period mathematics was developed to such an extent and more advanced than any other nation of antiquity. Quite early India devised a rudimentary algebra which led to more calculations than were possible for the Greeks and led to the study of number for its own sake. The earliest inscription regarding the data by a system of nine digits and a zero is dated as 595 A.D. evidently the system was known to mathematicians some centuries before it was employed in inscriptions. Indian mathematicians such as Brahmagupta (7th century), Mahavira (9th century) and Bhaskara (12th century) made several discoveries which were known to Europe only after Renaissance. The understood the importance of positive and negative quantities, evolved sound system of extracting squares and cube roots and could solve quadratic and certain types of indeterminate equations. Aryabhata gave approximate value of pie. It was more accurate than that of the Greeks. Also some strides were made in trigonometry, empirical geometry and calculus. Chiefly in astronomy the mathematical implications of zero and infinity were fully realized unlike anywhere in the world. Among the various branches of mathematics, Hindus gave astronomy the highest place of honour.

Vedic Mathematics in India

Indian scriptures - the perennial source of knowledge and wisdom have many subjects hidden in them. The ancient seers saw mathematics in nature and have expressed profound mathematical concepts in the form of hymns and verses starting from the fundamental place values to advanced astronomical concepts. Ancient Maths was not just related to one specific historical time or area, but it's found in all schools of thought and faiths. It's said that the ruler of Baghdad invited a scholar from Ujjain, where he taught science and maths. They also translated Indian books into Arabic. This system then traveled to Europe in the 11th century. A scholar named Al-Biruni traveled to India to learn the Indian sciences. Living for thirty years he wrote a number of books, one of them was called 'Hisab-al-Hindi'.

In the Jain books such as, 'Ganitasarasangraha of Mahaviracharya'- 850 A.D, talks about a quantity that grows until it reaches six, then it decreases in reverse order. The Indian mathematicians had a passion for numbers of huge value. The Jain scholars have mentioned numbers 10190, 10250 and 10421 in the book Lalitavistara. One lakh, which is 10^5, is also mentioned in the book before 308 A.D. Jinabhadra Gani of sixth century A.D in Brihatshetrasamasa, expresses place value system for 224,400,000,000.

With development of maths and science, Astronomy had a far- reaching impact on research. Knowledge of the Universe and its behavior is well noted. Indians did not just stop at inventing zero and the decimal system, but went into depth and quantity as well. Numerals and writings went hand in hand in the ancient world. Numerals were not just needed for certain segments of work but were also used in poetry, grammar and philosophy. Playing with numerals was a fun game in those days. The concept of the basic and important numeral zero stems from philosophical thinking. Zero literally means void or empty- a mystical figure. Zero is like a kingmaker a person who has got no independent value of it's own but attains greatness in combination with ordinary persons. As when zero is suffixed to numerals l to 9. Such people have place-value. Zero is neither positive nor negative; it's neutral. In this way ordinary numerals have great gravity. The examples and quotations below are an ample testimony of wide-spread acceptance of Vedic Maths.

pythagorus theorem was discovered by INDIANS but not by pythagoras:

Yes, ancient Indians mathematicians discovered Pythagoras theorem! This might come as a surprise to many, but it's true that Pythagoras theorem was known much before Pythagoras and it was Indians who actually discovered it at least 1000 years before Pythagoras was born! It seems that Pythagoras stole this theorem from India and was given credit for it. It's one of the many examples of cases when Greek mathematicians/scientists took credit of various Indian discoveries/inventions and the original Indian contributers were forget.

pythagoras theorem was discovered by INDIANS BAUDHAYANA:

So which Indian mathematician discovered Pythagoras theorem originally? We now know that it was Baudhāyana who discovered the Pythagoras theorem.

Baudhāyana listed Pythagoras theorem in his book called Baudhāyana Śulbasûtra (800 BCE). Incidentally, Baudhāyana Śulbasûtra is also one of the oldest books on advanced Mathematics. The actual shloka (verse) in Baudhāyana Śulbasûtra that describes Pythagoras theorem is given below -

dīrghasyākṣaṇayā rajjuH pārśvamānī, tiryaDaM mānī, cha yatpṛthagbhUte kurutastadubhayāṅ karoti.

Interestingly, Baudhāyana used a rope as an example in the above shloka which can be translated as - A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together. As you see, it becomes clear that this is perhaps the most intuitive way of understanding and visualizing Pythagoras theorem (and geometry in general) and Baudhāyana seems to have simplified the process of learning by encapsulating the mathematical result in a simple shloka in a layman's language (sanskrit was the language of choice back then).

Some people might say that this is not really an actual mathematical proof of Pythagoras theorem though and it is possible that Pythagoras provided that missing proof. But if we look in the same Śulbasûtra, we find that the proof of Pythagoras theorem has been provided by both Baudhāyana and Āpastamba in the Sulba Sutras! To elaborate, the shloka is to be translated as -

The diagonal of a rectangle produces by itself both (the areas) produced separately by its two sides.

The implications of the above statement are profound because it is directly translated into Pythagorean theorem (and graphically represented in the picutre on the left) and it becomes evident that proved Pythagoras theorem using area calculation and not geometry (as shown in the picture on left). Since most of the later proofs (presented by Euclid and others) are geometrical in nature, the Sulba Sutra's numerical proof was unfortunately ignored. As I mentioned before though, Baudhāyana was not the only Indian mathematician to have provided pythagorean triplets and proof. Āpastamba also provided the proof for Pythagoras theorem, which again is numerical in nature but again unfortunately this vital contribution has been ignored and Pythagoras was wrongly credited by Cicero and early Greek mathematicians for this theorem. For the sake of completeness, I should also mention that Baudhāyana also presented a geometrical proof using isosceles triangles so, to be more accurate, we attribute the geometrical proof to Baudhāyana and numerical (using number theory and area computation) proof to Āpastamba.

pythagaros theorem discovered by INDIAN BHASKARA:

ancient Indian mathematician called Bhaskara later provided a unique geometrical proof as well (picuture illustrating Bhaskara's proof on right) which is known for the fact that it's truly generalized and works for all sorts of triangles and is not incongruent (not just isosceles as in some older proofs).

One thing that is really interesting is that Pythagoras was not credited for this theorem till atleast three centuries after! It was much later when Cicero and other greek philosophers/mathematicians/historians decided to tell the world that it was Pythagoras that came up with this theorem! How utterly ridiculous! In fact, later on many historians have tried to prove the relation between Pythagoras theorem and Pythagoras but have failed miserably. In fact, the only relation that historians have been able to trace it to is with Euclid, who again came many centuries after Pythagoras! This fact itself means that they just wanted to use some of their own to name this theorem after and discredit the much ancient Indian mathematicians without whose contribution it could've been impossible to create the very basis of algebra and geometry!

Many historians have also presented evidence for the fact that Pythagoras actually travelled to Egypt and then India and learned many important mathematical theories (including Pythagoras theorem) that western world didn't know of back then! So, it's very much possible that Pythagoras learned this theorem during his visit to India but hid his source of knowledge he went back to greece! This would also partially explain why greeks were so reserved in crediting Pythagoras with this theorem!

Looking at the implications of such fundamental laws like Pythagorean theorem that have been so grossly wrongly credited to greek mathematicians who have nothing to do with them, I wonder how many more other important ancient Indian discoveries and inventions have been wrongly credited so far!