We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific discovery could have been made . – Albert Einstein

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged 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 calculation and placed arithmetic foremost amongst useful inventions. The importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of antiquity, Archimedes and Apollonius.– Laplace

Every person aware of modern science if also well aware that mathematics is the soul of modern science. Computers, Medical equipments, missiles, reactors, automobiles, electronic equipments, economics, finance, banks every where we need mathematics.

Romans used to represent every number using its own unique symbol or a unscientific combination of symbols. This was where west started its mathematics only to be discarded later due to its impractical nature to do bigger calculations.

I,V,X were used to represent numbers till 49 and when they run out of symbols then L was used to represent 50, similarly C for hundred, D for 500, M for thousand.. etc and etc

Any person who has worked using this roman number system knows very well that doing even a simple multiplication is a monumental task in this system. Higher mathematics like calculus, algebra, trigonometry are simply impossible here. I dont think a person has ever seen a simple linear equation in roman system!!!!

If the world had depended on western roman roots for modern science we would have been still in stone ages of science where the greatest achievement would have been counting the number of visible stars in the night sky !!!!!

Ancient Indians took a different approach and this was more than 3000-4000 years before romans invented roman numbers!!! While ancient Indians were working advanced mathematics (which finds its first reference in the ancient Vedas and is called as Vedic mathematics, this is part of the Atharva Veda which is all about engineering) the western world was still in stone age!!

The roots of modern mathematics is based on the concept of place value system, which we take for granted, but accoding to me is the most ingenious invention in mathematics. This is what Indians invented to have a complete scientific system of working with numbers. (In my series Alien Twist to God I have argued that this mathematics which has its roots in the vedas and the sanskrit language in which vedas are written in, both are of an alien origin, which is why sanskrit is the only human language capable of becoming a computer programming language)

In the place value system a limited set of symbols is taken and used to represent any and every possible number upto infinity down to minus infinity!!!

The number of symbols we select indicates the base of the system. We normally use base 10 which has 9 symbols aka 1,2,3,4,5,6,7,8,9

Once we have the set of symbols the value of a symbol depends on the position of the symbol in the number. First position has a unit value, second position has a base value, third position has a (base)X(base) value, then (base)X(base)X(base) value and so on,..

So in base 10, first position has a value of 1 times the value of symbol, second position has a value of 10 times the value of symbol, third position has a value of 100 times the value of the symbol.. and so on.

So when we say 42 it represents a number whose value is 4 times 10 + 2 times 1 !!
We who are used to this system find it so simple!! The simplicity of this invention is what makes it so great bcos remember this is the root of whole modern mathematics and if this itself is complicated then we would be back to square one as romans!!!

Once the place value system was invented Indian mathematicians had another difficulty. Suppose there was a place in the number which had no value at all!!!!

Consider the case of 100 here 1 should be used in third place which is base X base .. but then the two places down have no value!!!! This is why Indians invented ZERO!!!! In sanskrit Zero is called Shoonya, which means nothing.. presence of zero at a place means that place has no value in the number and should be ignored!!!

This in itself explains the great power of zero and its role in place value systems which makes it a key element of modern mathematics. Thats why once somebody said, I think it was Bernard Shaw, The greatest contribution of Indians to the world is Nothing :)

Ancient Indians bcos of their strong mathematical basis becames champions in astronomy and related calculations. More than a thousand years before Giordano was burnt alive in the west by the church for claiming Sun is the center of the solar system, More than a thousand years before Galileo had to apologize for proposing the motion of the earth, Aryabhata in India had written great works on helio centric systems, and more than 3000-4000 years before aryabhata vedas had all this in their roots..

Then in modern times Buddhist missionaries from India spread this knowledge of mathematics and easy counting to the eastern world of China, Thailand, Japan etc.

Arab merchants who came to India to trade spices to the west, saw this simple way of doing counting more easier than roman system and adopted the same and also spread it to the west, this is the reason them modern base 10 system symbols are called “Hindu Arabic Numerals” meaning borrowed from the land of hindus and spread to the rest of the west by Arabs. After learning this system of mathematics, arab mathematician wrote the book “Al Jabr” which gave way to modern algebra.

Still there are gaps in this whole system. Arab merchants learnt only the basic counting required to do business and spread it to the western world. And from there west developed its own mathematics based on these Indian roots where Newton’s Calculus etc came into picture.

Unfortunately, west again had started looking at maths with a roman mindset for higher level of generalization and students today are taught partial differential equations which require pages together to solve. Indian approach of Vedic mathematics is purely mental mathematics and generally doesnt require pen and paper to solve problems. The approach is also completely different in Indian mathematics, there are more specific formulae than generic, while this means more to learn, but once a child is used to it, problems will be more easy to solve. For instance in multiplication using vedic mathematics, the formula to multiply a two numbers which end with 5 is different from an approach to solve two numbers which have even numbers in their units place!! MANY WESTERN SCHOOLS TODAY TEACH VEDIC MATHEMATICS IN THE NAME OF MENTAL MATHEMATICS WITHOUT GIVING THE ANCIENT INDIANS AND THE VEDAS THE DUE CREDIT THEY DESERVE, which I feel is a total hypocrisy on the teachers part.

However, every thing including modern calculus, pythagoras theorems etc were already developed and documented in ancient Indians mathematics with its roots in vedic mathematics and the Indian approach to calculus etc is quite different from that of western approach. Bhaskaracharya wrote Leelavati (a book named after his daughter) more than 1000 years before newton and has detailed explanations for problems of differential calculus and the theory of calculus itself !!!

The historian Florian Cajori, one of the most celebrated historians of mathematics in the early 20th century, said “Diophantus, the father of Greek algebra, got the first algebraic knowledge from India”.

Even Pythagoras was familiar with the ancient Indian text of Upanishads. It is also said that he had visited India from where he picked up the “hypotenuse” theorem and spread it in the west, which today is given his name inspite of the fact that he never gave a proof of this theorem!!! Pythagorean theorem finds its first reference in the sulva sutras of Vedic mathematics which is more than 4000 years before pythagoras! And if pythagoras was familiar with Upanishads, there is no doubt that he would have also studied the related Vedas and Sulva Sutras..

Herodotus (father of Greek history) wrote that the Indians were the greatest nation of the age. Megasthenes – who travelled extensively through India in the 4th C. B.C also left extensive accounts that paint India in highly favorable light (for that period).

Panini who lived around 500 BC has mentioned in his works about boolean logic and the use of the operator null. Panini was an expert in language theory and has written extensively on describing Meta Syntax used to describe context free grammars which is used while defining modern computer programming languages. Hence the modern Backus Naur form BNF is also referred to as Panini Backus Form !

The ancient Chinese mathematics also has its roots in the Indian mathematics which was spread to China by Indians along side spreading Buddhism. There is an article in my site on the ancient Chinese proof of Pythagoras theorem

In an essence ancient India is both the spiritual and scientific mentor of modern world. Note that even the christian teachings by Jesus have its roots in Buddhism (Buddha lived in ancient India 400 years before Christ and any person who has studied the preachings of both Buddha and Christ will find obvious resemblance in both). It is also said that Jesus studied one of the ancient Indian univeristies Takshashila I think where he learnt the buddhist teachings. I had read some works which had done extensive research on this subject indicating Christ name in the list of students at one of the buddhist monestaries in Ladakh region of India.

Kerala in India is the root of modern martial arts. The Keralean Kalaripayat is the world’s oldest form of martial arts and is practiced in Kerala state of India. It was transmitted to China by a sage named Boddhidharma in the 5th century. The Chinese called him Po-ti-tama. He taught this art in a temple. This temple is today known as the Shaolin temple. Thus Judo, Karate, Kung Fu and other similar marshal arts which are today identified with the far-east actually originated from India !

It is known history that when Ottoman turks captured constantinople there by blocking the land based route to India from Europe, this disturbed the entire Europe which depended on India extensively for trade for all items ranging from spices to diamonds to garments to what not. Till 1896 India was the only source of diamonds to the entire world! Unable to trade with India due to locking of the land route by turks, european nations started a race to discover a sea route to India and great sailors like columbus, vasco da gama, amerigo vespucci all set out from spain, portuguese etc to discover a sea route to India and this is how Columbus ended up discovering modern american continent (named after Amerigo who landed up in main land of the continent). In other words the modern super power america was introduced to the rest of the world, courtesty India!!! Columbus thought he had landed in the east coast of India when he discovered America and thats why the native americans are called Red Indians !!!!

Severus Sebokt of Syria in 662 BC said I shall not speak here of the science of the Hindus, who are not even Syrians, and not of their subtle discoveries in astronomy that are more inventive than those of the Greeks and of the Babylonians; not of their eloquent ways of counting nor of their art of calculation, which cannot be described in words – I only want to mention those calculations that are done with nine numerals. If those who believe, because they speak Greek, that they have arrived at the limits of science, would read the Indian texts, they would be convinced, even if a little late in the day, that there are others who know something of value

The Constructions and these tables imply a great knowledge of geometry, arithmetic and even of the theoretical part of astronomy. But what, without doubt is to be accounted, the greatest refinement in this system, is the hypothesis employed in calculating the equation of the centre for the Sun, Moon and the planets that of a circular orbit having a double eccentricity or having its centre in the middle between the earth and the point about which the angular motion is uniform. If to this we add the great extent of the geometrical knowledge required to combine this and the other principles of their astronomy together and to deduce from them the just conclusion;the possession of a calculus equivalent to trigonometry and lastly their approximation to the quadrature of the circle, we shall be astonished at the magnitude of that body of science which must have enlightened the inhabitants of India in some remote age and which whatever it may have communicated to the Western nations appears to have receied another from them.– John Playfair

http://en.wikipedia.org/wiki/Indian_mathematics