A little known school of scholars in southwest India discovered one of the founding principles of modern mathematics hundreds of years before Newton according to new research.
Dr George Gheverghese Joseph from The University of Manchester says the 'Kerala School' identified the 'infinite series'- one of the basic components of calculus - in about 1350.
The discovery is currently - and wrongly - attributed in books to Sir Isaac Newton and Gottfried Leibnitz at the end of the seventeenth centuries.
The team from the Universities of Manchester and Exeter reveal the Kerala School also discovered what amounted to the Pi series and used it to calculate Pi correct to 9, 10 and later 17 decimal places.
And there is strong circumstantial evidence that the Indians passed on their discoveries to mathematically knowledgeable Jesuit missionaries who visited India during the fifteenth century.
That knowledge, they argue, may have eventually been passed on to Newton himself.
Dr Joseph made the revelations while trawling through obscure Indian papers for a yet to be published third edition of his best selling book 'The Crest of the Peacock: the Non-European Roots of Mathematics' by Princeton University Press.
He said: "The beginnings of modern maths is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten.
"The brilliance of Newton's work at the end of the seventeenth century stands undiminished - especially when it came to the algorithms of calculus.
"But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus- infinite series.
"There were many reasons why the contribution of the Kerala school has not been acknowledged - a prime reason is neglect of scientific ideas emanating from the Non-European world - a legacy of European colonialism and beyond.
"But there is also little knowledge of the medieval form of the local language of Kerala, Malayalam, in which some of most seminal texts, such as the Yuktibhasa, from much of the documentation of this remarkable mathematics is written."
He added: "For some unfathomable reasons, the standard of evidence required to claim transmission of knowledge from East to West is greater than the standard of evidence required to knowledge from West to East.
"Certainly it's hard to imagine that the West would abandon a 500-year-old tradition of importing knowledge and books from India and the Islamic world.
"But we've found evidence which goes far beyond that: for example, there was plenty of opportunity to collect the information as European Jesuits were present in the area at that time.
"They were learned with a strong background in maths and were well versed in the local languages.
"And there was strong motivation: Pope Gregory XIII set up a committee to look into modernising the Julian calendar.
"On the committee was the German Jesuit astronomer/mathematician Clavius who repeatedly requested information on how people constructed calendars in other parts of the world. The Kerala School was undoubtedly a leading light in this area.
"Similarly there was a rising need for better navigational methods including keeping accurate time on voyages of exploration and large prizes were offered to mathematicians who specialised in astronomy.
"Again, there were many such requests for information across the world from leading Jesuit researchers in Europe. Kerala mathematicians were hugely skilled in this area."
Researchers in England may have finally settled the centuries-old debate over who gets credit for the creation of calculus.
For years, English scientist Isaac Newton and German philosopher Gottfried Leibniz both claimed credit for inventing the mathematical system sometime around the end of the seventeenth century.
Now, a team from the universities of Manchester and Exeter says it knows where the true credit lies — and it's with someone else completely.
The "Kerala school," a little-known group of scholars and mathematicians in fourteenth century India, identified the "infinite series" — one of the basic components of calculus — around 1350.
Dr. George Gheverghese Joseph, a member of the research team, says the findings should not diminish Newton or Leibniz, but rather exalt the non-European thinkers whose contributions are often ignored.
"The beginnings of modern maths is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten," he said. "The brilliance of Newton's work at the end of the seventeenth century stands undiminished — especially when it came to the algorithms of calculus.
"But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus — infinite series."
He argues that imperialist attitudes are to blame for suppressing the true story behind the discovery of calculus.
"There were many reasons why the contribution of the Kerala school has not been acknowledged," he said. "A prime reason is neglect of scientific ideas emanating from the Non-European world, a legacy of European colonialism and beyond."
However, he concedes there are other factors also in play.
"There is also little knowledge of the medieval form of the local language of Kerala, Malayalam, in which some of most seminal texts, such as the Yuktibhasa, from much of the documentation of this remarkable mathematics is written," he admits.
Joseph made the discovery while conducting research for the as-yet unpublished third edition of his best-selling book The Crest of the Peacock: the Non-European Roots of Mathematics.
1. India invented the Number system. Pingalacharya invented ‘zero.’ in 200 BC.
2. Indians discovered the size, shape, rotation and gravity of earth about 1000 years before Kelvin,Galileo,Newton and Copper Nicus. Aryabhatta I was the first to explain spherical shape,size ,diameter,rotaion and correct speed of Earth in 499 AD.
3. Newton’s law of Gravitational force is an ancient Indian discovery. In Siddhanta Siromani ( Bhuvanakosam 6 ) Bhaskaracharya II described about gravity of earth about 400 years before Sir Isaac Newton.
4. Bhaskaracharya II discovered Differential calculus.
5. Theory of Continued Fraction was discovered by Bhaskaracharya II.
6. The place value system, the decimal system was developed in India in 100 BC.
7. Indians discovered Arithmetic and Geometric progression. Arithmetic progression is explained in Yajurveda.
8. Govindaswamin discovered Newton Gauss Interpolation formula about 1800 years before Newton.
9. Vateswaracharya discovered Newton Gauss Backward Interpolation formula about 1000 years before Newton.
10. Madhavacharya discovered Taylor series of Sine and Cosine function about 250 years before Taylor.
11. Madhavacharya discovered Newton Power series.
12. Madhavacharya discovered Gregory Leibnitz series for the Inverse Tangent about 280 years before Gregory.
13. Madhavacharya discovered Leibnitz power series for pi about 300 years before Leibnitz.
14. Parameswaracharya discovered Lhuiler’s formula about 400 years before Lhuiler.
16. Theorems relating the diameter,volume and circumference of circles discovered by Madhavacharya, Puthumana Somayaji, Aryabhatta, Bhaskaracharya…….
17. The value of pi was first calculated by Aryabhatta I in 499 AD,ie more than 1350 years before Lindemann
18. Boudhayana discovered Pythagorus Theorem in 800BC. ie 300 years before Pythagorus.
19. Algebra, trigonometry and calculus came from India. Quadratic equations were by Sridharacharya in the 11th Century.
20. While the Greeks were using only upto a maximum value 1000, Indians could go upto 18th power of 10 level during Vedic period.
21. Infinity was well known for ancient Indians. BhaskaracharyaII in Beejaganitha (stanza-20) has given clear explanation with examples for infinity
22. Positive and Negative numbers and their calculations were explained first by Brahmagupta in his book Brahmasputa Siddhanta.
23. Sterling formula was discovered by Brahmagupta about 1000 years before Sterling.
24. Demovier’s theorem of positive integral was discovered by Brahmagupta in 628 A.D, i.e around 1000 years before Demovier.
25. Puthumana Somayaji discovered Demovier’s infinite series in 1140 AD,i.e more than 200 years before Demovier.
26. Maharshi Sushruta is the father of surgery. 2600 years ago he and health scientists of his time conducted surgeries like cesareans, cataract, fractures and urinary stones. Usage of anesthesia was well known in ancient India. He was the first person to perform plastic surgery.
27. When many cultures in the world were only nomadic forest dwellers over 5000 years ago, Indians established Harappan culture in Sindhu Valley (Indus Valley Civilization).
28. The world’s first University was established in Takshila in 700BC. More than 10,500 students from all over the world studied more than 60 subjects. The University of Nalanda built in the 4th century BC was one of the greatest achievements of ancient India in the field of education.
29. According to the Forbes magazine, Sanskrit is the most suitable language for computer software.
30. Ayurveda is the earliest school of medicine known to humans.
31. Although western media portray modern images of India as poverty stricken and underdeveloped through political corruption, India was once the richest empire on earth.
32. According to the Gemmological Institute of America, until 1896, India was the only source of diamonds to the world.
33. USA based IEEE has proved what has been a century-old suspicion amongst academics that the pioneer of wireless communication was Professor Jagdeesh Bose and not Marconi.
34. The earliest reservoir and dam for irrigation was built in Saurashtra.
35. Chess was invented in India.
36. The first philosopher who formulated ideas about the atom in a systematic manner was Kanada who lived in the 6th century B.C.
37. All the atomic reactors in the world are in Shiva Linga Shape which is an Indian contribution.
38. Padanjali maharshi discovered Sound waves.
39. Yoga is an ancient Indian gift to the world.
40. Shayanacharya discovered velocity of light.
41. Maharshi Bharadwaja discovered different types of light rays.
42. Maharshi Bharadwaja was the first person to give definition about aeroplane. He explained about different types aeroplanes in his book “Vimana Thantra” about 2000 years before Right Brothers.
43. Maharshi Bharadwaja discovered spectrometer. In his “Yantra Sarvaswa” he explained about more than 100 instruments.
44. The different colours of light, VIBGYOR are mentioned in Rigveda which was written more than 6000 years ago.
45. Maharshi Charaka discovered Psychology and Quantum healing system.
46. Varahamihira discovered the concept of “Budding of plants”.
47. Varahamihira discovered Comets in 505 AD, i.e more than 1100 years before Haley.
48. Gouthama Maharshi discovered the wave nature of sound about 1400 years before Hyghen.
49. Seven continents are mentioned in Padmapurana.
* India invented the Number System. Zero was invented by Aryabhatta.
* The World's first university was established in Takshashila in 700BC. More than 10,500 students from all over the world studied more than 60 subjects. The University of Nalanda built in the 4th century BC was one of the greatest achievements of ancient India in the field of education.
* Sanskrit is the mother of all the European languages. Sanskrit is the most suitable language for computer software - a report in Forbes magazine, July 1987.
* The art of Navigation was bornin the river Sindhu 6000 years ago. The very word Navigation is derived from the Sanskrit word NAVGATIH. The word navy is also derived from Sanskrit 'Nou'.
* Bhaskaracharya calculated the time taken by the earth to orbit the sun hundreds of years before the astronomer Smart. Time taken by earth to orbit the sun: (5th century) 365.258756484 days.
* The value of pi was first calculated by Budhayana, and he explained the concept of what is known as the Pythagorean Theorem. He discovered this in the 6th century long before the European mathematicians.
* Algebra, trigonometry and calculus came from India. Quadratic equations were by Sridharacharya in the 11th century. The largest numbers the Greeks and the Romans used were 106 whereas Hindus used numbers as big as 10**53(10 to the power of 53) with specific names as early as 5000 BCE during the Vedic period. Even today, the largest used number is Tera 10**12(10 to the power of 12).
* IEEE has proved what has been a century old suspicion in the world scientific community that the pioneer of wireless communication was Prof. Jagdish Bose and not Marconi.
* The earliest reservoir and dam for irrigation was built in Saurashtra. According to Saka King Rudradaman I of 150 CE a beautiful lake called Sudarshana was constructed on the hills of Raivataka during Chandragupta Maurya's time.
* Sushruta is the father of surgery. 2600 years ago he and health scientists of his time conducted complicated surgeries like cesareans, cataract, artificial limbs, fractures, urinary stones and even plastic surgery and brain surgery. Usage of anesthesia was well known in ancient India. Over 125 surgical equipment were used. Deep knowledge of anatomy, physiology, etiology, embryology, digestion, metabolism, genetics and immunity is also found in many texts.
* The place value system, the decimal system was developed in India in 100 BC.
