The field of calculus is usually attributed to Isaac Newton and Gottfried wilhems lebniz, however, it is worth noting that an Indian mathematician actually introduced calculus before them then what will be your reaction?

Many people believe that India’s status as the golden bird or world guru existed only before the 10th AD, assuming that our knowledge tradition declined thereafter. However, this assumption is incorrect. During a period in India’s history, our gurukuls nurtured brilliant minds such as Aryabhatt, Varahamihir, Mahavir, Bhaskaracharya, and Sushruta. These esteemed scientists have gained worldwide recognition and brought immense pride to India. The golden age of our country began to decline as invasions began in the 10th century, culminating in the burning of the famous Nalanda University library in the 13th century. In the 14th century, when India was facing the brunt of attacks by foreign invaders. At that time “Acharya Madhavji”, a brilliant architect and mathematician, established an ashram in Kerala, where the guru-shishya tradition led to discoveries in mathematics and astronomy that Europe still recognizes and admires.

From the 14th century until the 17th century, India witnessed its second golden age. In 1832, when a British gentleman named Charles Wish shed light on an extraordinary institution during his lecture at the Asiatic Society Of London And Ireland. This remarkable place, known as The Kerala School Of Mathematics and Astronomy, had already gained recognition for its profound teachings and contributions to the field.
Charles, who was employed at The East India Company in India, held a position as an officer. During his time in the Madras region he visited Gurukuls, finding that various types of calculus and many new types of trigonometric series were studied there. When he researched further, he found that there was a school in Kerala in the 14th century where calculus was developed and such trigonometric series has been discovered earlier also. And he also found that the founder of the school was Acharya Madhav. He also found that Acharya Madhva was the person who established the Kerala school of mathematics and astronomy.

 

Who is Madhava of Sangamagrama?

Madhava of Sangamagrama, also known as Acharya Madhava, was a renowned mathematician who dedicated his life to studying the celestial bodies and uncovering their mysteries. Born in the 14th century in the village of Sangamagrama, which was named after Bharat, Madhava’s real name was Irinjada pilli Mana Madhava Namboothiri. His contributions to mathematics were truly remarkable, considering that he lived three centuries before the famous Isaac Newton, who is widely regarded as the founder of modern mathematical theories.

Madhava’s notable accomplishment was his contribution to venu arohanam, also known as “bamboo climbing.” This remarkable work comprised of 74 verses that introduced an innovative approach to accurately determine the moon’s position. Madhava conducted these observations from two rocks located in the eringada pili Sri Krishna temple in Kerala, where he would sit and lie down. These rocks served as his platform for astronomical observations and writing his works. Today, these rocks can still be found at the eringada pili Sri Krishna temple. Madhava gained fame for his expertise in spherical geometry, earning him the title of Kulai.

Madhava’s innovative approach revolutionized the field of astronomy and paved the way for future advancements in celestial navigation. His meticulous observations and calculations allowed him to unravel the secrets of the stars, providing invaluable insights into the workings of the universe.

Madhava’s legacy as a mathematician and astronomer continues to inspire and influence scholars today. His pioneering work in the field of mathematics, especially in the study of celestial bodies, has left an indelible mark on the scientific community. Madhava’s dedication and passion for unraveling the mysteries of the universe has cemented his place as one of the greatest mathematicians in history. Through their exploration of various series and mathematical tools, the scholars at the Kerala School of Mathematics and Astronomy laid the groundwork for many mathematical principles that would eventually make their way to Europe. Their contributions played a significant role in shaping the development of mathematics on a global scale.

 

 

 

The history of Kerala school of mathematics and Astronomy:-

Since the 14th century, this school has continued the legacy of the Guru-Shishya tradition. The initial leadership of the school was assumed by Acharya Madhava, who paved the way for later scholars. After him, Parameshwara took over the responsibilities and was then succeeded by Damodara in the research efforts of the school. Damodarji’s legacy was carried forward by his two disciples, Nilkantha Somiya Ji and Jyesthadeva, who not only maintained the work of the school but also made unprecedented discoveries in the fields of mathematics and astronomy. The tradition of excellence in research and exploration was continued by Shankara Riyara and Achyuta Visaratha, who diligently followed the path laid by their predecessors until the 17th century, ensuring the school’s lasting influence and contribution to knowledge. The Malabar region of Kerala was becoming restless. Portuguese, Dutch and Invaders had started invading from these. So that area was disturbed, due to which the scientific traditions of research got affected. This school managed to thrive until the year 1819, with its final headmaster being the ruler of Kathan Nadu, Shankar warman, who authored the renowned book “Satratna Mala.” Additionally, Jyesthdeva penned a significant work titled “Yukti Bhasha,” which is widely recognized as the earliest publication on calculus. During the period spanning from the 14th to the 17th century, a total of four groundbreaking books were produced. These works include Tantra Sangreh, Yukti Bhasha, Karan Paddhati, and Satratna Mala.

 

Discoveries of Kerala school of mathematics and astronomy :-

 

The Kerala school of mathematics and astronomy made a significant contribution to the field with their discovery of the infinite series. This breakthrough can be found in the 271st shloka of chapter 2 in Tantra Sangraha, where a shloka dedicated to the infinite series is mentioned. In addition to this groundbreaking concept, the Kerala school also made notable advancements in Calculus, Trigonometry, Geometry, and Algebra. It is worth noting that in ancient Indian tradition, whether it was spirituality, literature, or science, everything was written in verse. Furthermore, the Kerala school also developed a unique numbering system known as the bhoot sankhya pranali.

 

 

 

Bhoot Sankhya Pranali:

The numerical values were elegantly transcribed in a poetic structure, which was then transformed into a mathematical formula. This unique process is commonly referred to as the bhoot sankhya pranali.

 

Madhava-Gregory-Leibniz:

The Gregory-Leibniz series, which occurred between 1671 and 1673, is often credited with the discovery of the series for calculating pi. However, it is important to note that Acharya Madhava had actually discovered this series 300 years prior to that. Today, the series is recognized as the Madhava-Gregory-Leibniz series in acknowledgement of Acharya Madhava’s contribution. In addition to this, Acharya Madhava also developed numerous trigonometric infinite series, which are documented in the book ‘Yukti Bhasha’. To determine the exact value of pi, he began studying the pattern of pi and devised a clever trick, which he then transformed into a shloka (a verse). This shloka utilized the bhoot sankhya pranali (a numerical system). By dividing the number obtained from this shloka by 9X10X11, one can obtain the precise value of pi up to 12 decimal places. Acharya Madhava ji accomplished this remarkable feat in the 14th century.

 

Madhava Newton series:

The presence of the infinite series of sine, cosine, and inverse tangent can be observed in this context. These series, which were later referred to as the Newton series, were initially discovered by the Kerala school of mathematics and astronomy. The University of Manchester also supports this belief, further solidifying the connection between the two. As a result, the series was eventually named the Madhava Newton series, acknowledging the contributions of both Madhava and Newton to its development.

The Kerala School of Mathematics and Astronomy stood out as a pioneer, being centuries ahead of any European Universities in terms of mathematical advancements. By delving into Jyesthadevji’s ‘’Yukti Bhasha’’, one can uncover the concept of binomial expansion, showcasing the depth of knowledge possessed by this ancient school. Through their exploration of various series and mathematical tools, the scholars at the Kerala School of Mathematics and Astronomy laid the groundwork for many mathematical principles that would eventually make their way to Europe. Their contributions played a significant role in shaping the development of mathematics on a global scale.

 

 

 

How was the knowledge of Kerala transferred to Europe?

 

The Malabar plateau in Kerala was once a bustling hub of business activity in ancient India. In 1498, Vasco De Gama made his way to this region with the assistance of Indian traders, marking a significant moment in history. It was during this time that the Kerala school of mathematics and astronomy was flourishing, conducting groundbreaking research and making significant contributions to the field. Meanwhile, in Europe, there was a growing interest in discovering new sea routes and exploring uncharted territories. This led to a surge in demand for mathematical and astronomical tools among sea sailors and adventurers, who relied on these instruments for precise navigation across the vast oceans. The knowledge and expertise in celestial navigation, which involved using the stars for guidance, were highly valued during this period. The advancements in astronomy and mathematics being made in Indian schools, particularly in Kerala, caught the attention of European explorers and scholars. They recognized the importance of understanding and learning from the rich traditions and teachings of Indian scholars in order to enhance their own knowledge and capabilities in navigation and exploration. This exchange of knowledge and ideas between India and Europe played a crucial role in shaping the course of history and scientific development during that era.

Another significant motivation during that period was the necessity for Europe to transition from the Julian Calendar to a more accurate system. This prompted a desire to explore various techniques and methods used in other countries to improve the calendar system in Europe. According to an article from the University of Manchester, Pope Gregory XIII initiated the transition from the Julian to the Gregorian calendar by sending Jesuits to different regions. Many of these Jesuits were already present in Kerala, where they were actively promoting Christianity. The Jesuits were instructed to study any existing local astronomical and calendar systems to enhance the accuracy of the calendar. This exchange of knowledge and expertise played a crucial role in the eventual adoption of the Gregorian calendar in Europe.

So these are the reasons why this knowledge of India is reaching Europe through Kerala. All these could be possibilities only but we can’t deny that India was much ahead of Europe in astronomy and mathematics.