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The Great Minds of India - Aryabhata

Early Life:

Aryabhata was one of the first Indian mathematicians and astronomers belonging to the classical age. He was born in 476 BC in Tarenaga, a town in Bihar, India. It is however definite that he travelled to Kusumapara (modern day Patna) for studies and even resided there for some time. It is mentioned in a few places that Aryabhata was the head of the educational institute in Kusumapara. The University of Nalanda had an observatory in its premises so it is hypothesized that Aryabhata was the principal of the university as well. On the other hand some other commentaries mention that he belonged to Kerala.

Mathematical Work:

Aryabhata wrote many mathematical and astronomical treatises. His chief work was the ‘Ayrabhatiya’ which was a compilation of mathematics and astronomy. The name of this treatise was not given to it by Aryabhata but by later commentators. A disciple by him called the ‘Bhaskara’ names it ‘Ashmakatanra’ meaning ‘treatise from the Ashmaka’. This treatise is also referred to as ‘Ayra-shatas-ashta’ which translates to ‘Aryabhata’s 108’. This is a very literal name because the treatise did in fact consist of 108 verses. It covers several branches of mathematics such as algebra, arithmetic, plane and spherical trigonometry. Also included in it are theories on continued fractions, sum of power series, sine tables and quadratic equations.

Aryabhata worked on the place value system using letters to signify numbers and stating qualities. He also came up with an approximation of pi ( ) and area of a triangle. He introduced the concept of sine in his work called ‘Ardha-jya’ which is translated as ‘half-chord’.

Astronomical Work:

Aryabhata also did a considerable amount of work in astronomy. He knew that the earth is rotating on an axis around the sun and the moon rotated around it. He also discovered the position of nine planets and stated that these also revolved around the sun. He pointed out the eclipses; both lunar and solar. Aryabhata stated the correct number of days in a year that is 365. He was the first person to mention that the earth was not flat but in fact a spherical shape. He also gave the circumference and diameter of the earth and the radius of the orbits of 9 planets.

More about Aryabhata:

Aryabhata was a very intelligent man. The theories that he came up with at that time present a wonder to the scientific world today. His works were used by the Greeks and the Arabs to develop further. A commentary by Bhaskara I, a century later on Aryabhatiya says:

‘Aryabhata is the master who, after reaching the furthest shores and plumbing the inmost depths of the sea of ultimate knowledge of mathematics, kinematics and spherics, handed over the three sciences to the learned world.’

Aryabhata’s Legacy:

Aryabhata was an immense influence to mathematics and astronomy. Many of his works inspired Arabs more particularly. His astronomical calculations helped form the ‘Jalali calendar’. He has been honored in many ways. The first Indian satellite is named after him as ‘Aryabhata’, so is the lunar crater. An Indian research center is called ‘Aryabhata Research Institute of Observational Sciences’.

The Great Minds of India - Brahmagupta

Early Life and Work:

Brahmagupta was an Indian mathematician, born in 598 AD in Bhinmal, a state of Rajhastan, India. He spent most of his life in Bhinmal which was under the rule of King Vyaghramukha. He was the head of the astronomical observatory at Ujjain which was the center of mathematics in India witnessing the work of many extraordinary mathematicians.

Brahmagupta wrote many textbooks for mathematics and astronomy while he was in Ujjain. These include ‘Durkeamynarda’ (672), ‘Khandakhadyaka’ (665), ‘Brahmasphutasiddhanta’ (628) and ‘Cadamakela’ (624). The ‘Brahmasphutasiddhanta’ meaning the ‘Corrected Treatise of Brahma’ is one of his well-known works. It contains a lot of criticism on the work of his rival mathematicians. Brahmagupta had many discrepancies with his fellow mathematicians and most of the chapters of this book talked about the loopholes in their theories.

Contributions to Mathematics:

One of the most significant input of Brahmagupta to mathematics was the introduction of ‘zero’ to the number system which stood for ‘nothing’. His work the ‘Brahmasphutasiddhanta’ contained many mathematical findings written in verse form. It had many rules of arithmetic which is part of the mathematical solutions now. These are ‘A positive number multiplied by a positive number is positive.’, ‘A positive number multiplied by a negative number is negative’, ‘A negative number multiplied by a positive number is negative’ and ‘A negative number multiplied by a negative number is positive’. The book also consisted of many geometrical theories like the ‘Pythagorean Theorem’ for a right angle triangle. Brahmagupta was the one to give the area of a triangle and the important rules of trigonometry such as values of the sin function. He introduced the formula for cyclic quadrilaterals. He also gave the value of ‘Pi’ as square root ten to be accurate and 3 as the practical value. Additionally he introduced the concept of negative numbers.

Contribution to Science and Astronomy:

Brahmagupta argued that the Earth and the universe are round and not flat. He was the first to use mathematics to predict the positions of the planets, the timings of the lunar and solar eclipses. Though all this seems like obvious and simple solutions it was a major improvement in science at that time. He also calculated the length of the solar year which was 365 days, 5 minutes and 19 seconds which is quite accurate based on today’s calculation of 365 days, 5 hours and 19 seconds. He also talked about ‘gravity’ in one of his statements saying: ‘Bodies fall towards the earth as it is in the nature of the earth to attract bodies, just as it is in the nature of water to flow’.

Death:

This great mathematician died between 660 and 670. He was one of the greatest mathematicians in Indian history and his contributions to mathematics and science have made major differences to various mathematical problems by establishing the basic rules which now allow us to find their solutions. He was honored by the title given to him by a fellow scientist ‘Ganita Chakra Chudamani’ which is translated as ‘The gem of the circle of mathematicians’.

The Great Minds of India - Madhava

Mādhava of Sañgamāgrama (c. 1350 – c. 1425) was an important Indian mathematician who also endeavored the field of astronomy. He belonged to Irińńālakkuţa which was a town close to Cochin (in modern day India). Many progressions have been attributed to this great mathematician, for instance he is labeled as being responsible for the founding of Kerala School of Astronomy and Mathematics.

Achievements:

He was the pioneer in formulating infinite series approximations for trigonometric functions. Many people believe that his work helped open a gateway towards ‘Mathematical Analysis’. This well-known astronomer-mathematician contributed in numerous fields which included infinite series, calculus, trigonometry, geometry and algebra. Mādhava was a revolutionary mathematical figure of the Middle Ages, and a few scholars have reason to believe that his work reached through to Europe due to the presence of Jesuit missionaries and traders at an ancient port relevant to his surroundings at that time.

His work:
Many of his writings have been known to be lost, but some of his contributions in astronomy have managed to survive. There have been reports that much of his work was discovered by Keralese mathematicians who were alive till around 100 years after him.

A few of his contributions:

Something of peculiar interest regarding this mathematician includes the fact that he discovered the series equivalent to the Maclaurin expansions (sin x, cos x and arctan x), more than two hundred years ahead of Europe. He determined the explanations of a few ‘transcendental’ equations by a process of repetition. A procedure was unfolded by him to determine the siting of the Moon every 36 minutes, and techniques to evaluate the motions of the planets. His contributions to infinite series and infinitesimal quantities attest his writings’ existence; a lot of his work has been transmitted through other mathematicians after him. To suggest his popularity, there is a formula named Madhava-Leibniz which many students are taught during their college years.

Karana Paddhati is a piece of work which was originally written by Madhava, but was found out through latter mathematicians and brought into the limelight.

In conclusion, this great mathematician might have existed a long time ago; however his work had a great impact on the discoveries and mathematical understandings in Europe after his demise. His Indian background also permits the acknowledgement of the mathematical potential and progress within the region during that era. Each mathematician influenced the upcoming comprehension of Mathematics, in the same way Madhava managed to reach out to Europe with his achievements and contributions.

The Great Minds of India - Mahatma Hansraj

Mahatma Hansraj is an Indian educationist and follower of Arya Samaj. He was born on 19th April 1864 in the village of Bajwara in Hoshiarpur district, Punjab. He was an ardent follower of Swami Dayanand. Swami Dayanand was the founder of Dayanand Anglo-Vedic School system. In 1886 Mahatma Hansraj started the first DAV school at Lahore together with Guru Dutt Vidhyarthi, three years after the death of Swami Dayanand.

His parents are Chunnilal and Hardevi. His father died when he was just 12 and he had to face tough economic conditions in his younger days. He went to a missionary school and completed his Bachelor of Arts degree with excellent marks. He became the founder principal of the DAV school, Lahore.

He was a compatriot of freedom fighter Lala Lajpat Rai. He became the president of the provincial Arya Pradeshik Pratinidhi Sabha in Punjab. This is the DAV section of Arya Samaj. When the Arya Samaj split into two in 1893, one section was led by Mahatma Hansraj and Lala Lajpat Rai and the other section was led by Pandit Lekh Ram and Lala Munshi Ram. Mahatma Hansraj retained the control over the DAV College and served as the principal for 25 years.

Mahatma Hansraj was a great nationalist who was also an untiring relief worker who worked during the earthquakes at Kangra in 1905, Quetta in 1934, Bihar in 1935 and famines of Rajasthan in 1905, Awadh in 1907 and Garhwal in 1918. He supported widow remarriage and advocated the abolition of Sati and early marriages. He was against caste distinctions.

DAV runs over 669 colleges, schools and technical institutions today. Many educational institutions are named after him including Hans Raj College, Delhi. He died on 14th November 1938. He worked for uplifting the poor and downtrodden people of the society and after his retirement he committed his entire life for social service.

The Great Minds of India - Sawai Jai Singh II

It was all very, very romantic. The night sky above the Amber fort, atop the craggy hills overlooking what is now Jaipur city was at its most enchanting. And on a terrace watching the moon and the stars were a princess and a king. The princess had only that day been rescued by the king from a gang of brigands. They were both comely and in love with each other.

But, alas for romance. Though the princess did say it was heavenly, with something of a sigh of rapture, the question she asked was one that no Hollywood or Bombay film script writer would have ever thought of putting into the mouth of any of his heroines. The question was, "How far away are these stars and the moon?"

If the lover in the king was abashed by the question, so also was the astronomer in him. For the king, Sawai Jai Singh II, who had long been interested in astronomy, did not know the answer. When the princess gently chided him for his ignorance, all thoughts of romance fled and he decided that he must find the answer to her question. The princess he had rescued, a Muslim, thus set the Hindu king to a course that made him one of the greatest astronomers and mathematicians of his time.

Astronomers were invited to his court for study and discussions and the king read all the treatises he could find on the subject. Although history has forgotten the name of that beautiful princess, the Jantar Mantar (observatories) which the king built to gain her love and admiration still stand in New Delhi, Jaipur, Varanasi and Ujjain. Unfortunately, the one at Mathura was destroyed by building contractors who wanted the stones.

When Jai Singh was born in 1686, the Moghul Empire was about to disintegrate. He managed to keep good relations with Emperor Aurangzeb from age of 13, when he succeeded to the throne of Amber. He, even upon the Emperor's heart when in 1701 he defeated the Marathas in battle and captured him with the title of "Sawai," meaning that he was a quarter more than a man.

With the death of Aurangzeb in 1707, the Moghul Empire began to crumble. Conspiracy, assassination and dirty politics became a part of the proceedings at the Delhi court. Finally, Muhammad Shah, a young lad of 19, was installed on the throne in Delhi in 1719 and surprisingly survived all attempts to dethrone and assassinate him. His 20-year rule ended when Nadir Shah defeated him in the battle of Panipat, sacked Delhi and took away the famous Peacock Throne.

During those turbulent times, King Jai Singh was consolidating not only his political position but his stature as astronomer and architect. In 1727 he planned and designed a new capital Jaipur (Jai's City), marvelous example of town planning and architecture. He made Pandit Jagannath, a Maratha Brahmin well versed in Persian, Sanskrit and Arabic, his guru. He collected astronomical treatises and tables from Portugal, Arabia and Europe. His collection included the English astronomer, John Flamsteed's Historia Coelestis Britannica, Pere de la Hire's Tabulae Astronomicae, Ulugh Beg's tables, Zij Ulugh Begi, and Ptolemy's Almagest.

He ordered the translation of these treatises into Sanskrit and gave them Sanskrit names. For instance, he called Ptolemy's treatiseSiddhantasurikaustubha, Ulugh Beg's tables Turusurni and la Hire's tables Mithiajeevachayyasurni. He also got a telescope from Europe and even began to build telescopes.

Jai Singh got the telescope late in life. His earlier observations were conducted using astrolabes and other instruments. With these was able to detect errors in the tables of Indian, Arab and European astronomers. Actually, the earlier astronomers were not to blame. The positions of all heavenly bodies had shifted because of a change in direction of the axis of rotation of the earth or "precession."

When Jai Singh brought the errors to the notice of Emperor Muhammad Shah and told him how they affected the timings of Hindu and Muslim religious festivals and rituals, he was asked to correct them and offered money and other help for the task. In 1724, the first Jantar Mantar was built in Delhi and in 1734 Jai Singh published his observations made in Delhi in the form of tables in Persian titled Zij Muhammad Shahi in honor of his patron, the Emperor.

Jantar Mantar is the distorted form of the word which in Sanskrit means "instruments and formulae." For designing these massive instruments Jai Singh consulted Pandit Vidyadhar Bhattacharya, who later also assisted him in designing Jaipur city. In those days, small brass instruments were in use in Europe, but Jai Singh preferred the huge masonry structures of lime and plaster he built similar in design to those in Ulugh Beg's huge observatory in Samarkand. He claimed that these were far more accurate. He made his observatories available to anyone who wanted to study astronomy, hoping to make the science popular.

Among the instruments he designed himself are Samrat Yantra, Ram Yantra, and Jai Prakash. The first is basically a huge right-angled gnomon, a kind of sundial, which measures time to an accuracy of half a minute. It is also used to determine the altitude of the sun and the positions of equinoxes and solstices. The Ram Yantra, a tall pillar inside a graduated cylinder, measures the altitude and azimuth of heavenly bodies to a high degree of accuracy.

The most original of all is the Jai Prakash, a wide concave bowl on which the positions of all heavenly bodies can be mapped round the clock.

Jai Singh made two fundamental contributions to astronomy. One is the measurement of the precession of the equinoxes and the other the obliquity of the ecliptic. His findings are far more accurate than those of his predecessors like Ptolemy and Ulugh Beg.

Surprisingly, Jai Singh confined himself to observation. He never gave thought to whether the earth moves round the sun or vice versa. He accepted Ptolemy's geocentric concept of the universe. Copernicus's heliocentric concept, which claims that the sun is at the center, and all the planets, including the earth, move round it, a widely accepted view then in Europe, made no impression on him. It is possible that he deliberately ignored the Copernicus concept fearing that his support to it would upset the priests.

The Great Minds of India - Annaswamy Ranganath Rao

When the Central Board of Secondary Education (CBSE) made it mandatory for schools across India to have a laboratory for mathematics in 2006, many considered it an innovative move. In the 100-mark Mathematics question paper, the practical lab exam now gets 20 marks in CBSE schools.

This has put one man in Ahmedabad on top of the world. He is 100-year-old mathematics professor, Annaswamy Ranganath Rao, who pioneered the concept of Mathematics labs, which CBSE took up 32 years later. He even set up one at Vikram Sarabhai Community Science Center (VSCSC) in Ahmedabad in 1974. "I taught Mathematics for 33 years; I realized the method of teaching the subject in schools was defective. Mathematics, like philosophy, is an abstract subject. Unlike physics, chemistry or biology, one does not learn Mathematics in a lab and this makes it difficult," says Rao.

Born in Jakkasamudram in Salem district of Tamil Nadu and educated in Wilson College in Mumbai, Rao came to Bahauddin College in Junagadh in 1933 where he spent 27 years. In 1974, eight years after retiring as principal of a Bhavnagar college, he made it his mission to popularize Mathematics and make its learning a playful and enjoyable experience.

"For a Mathematics lab, I had to create physical models that explained various theorems and equations. This meant I had to innovate," says Rao, who has created over 200 models, teaching aids and puzzles that make the otherwise incomprehensible Pythagoras Theorem, Gaussian Curve, quadratic equations, Ramanujan's number and other aspects of geometry, easy to understand.

Models and puzzles, he feels, make a student think. "It is important that the brain is used as an activity room, not just a store-room," says Rao. At home, he is constantly seen creating puzzles and problems using a slate and pen. But he is not satisfied getting just one solution, and keeps working till he finds seven or eight solutions to a single problem. He has compiled all these puzzles in a book, �Brain Sharpeners'.

At 100, he is pursuing his mission with the same zeal. Every day, he takes an auto rickshaw to VSCSC where his students, mostly Mathematics teachers in schools and colleges, eagerly await him. He does not remember how many people have learnt this method of teaching Mathematics but he does keep track of the number of schools and colleges that have introduced the concept of mathematics labs.

"The Mathematics laboratory has been Rao Saheb's most important contribution to mathematics in India. People across India were impressed by this concept; he has been invited to Chennai and Shillong and NCERT headquarters in Delhi to instruct local mathematicians in setting up such laboratories," says Arun Vaidya, a retired professor of mathematics in Ahmedabad who still sees himself as a disciple of Rao.

Rao still traverses the length and breadth of the state to deliver lectures on Mathematics at various conferences and workshops. His perseverance has been recognized by the Indian government's department of science and technology, which has decided to nominate him for UNESCO's prestigious Kalinga Prize for popularizing science. If he bags it, Rao will be in the same league as Bertrand Russell, David Attenborough, Arthur C Clarke and others who have won this prize.

The Great Minds of India - Sir Chhotu Ram

Sir Chhotu Ram was born on 24 Nov 1881 in Ghari Sampla in Rohtak district. His father's name was Chaudhary Sukhi Ram, who died in 1905 leaving behind heavy debt.

School and college life:

Sir Chhotu Ram joined a primary school in Jan 1891, passing out four years later. He studied for his middle school examination in Jhajjar, 12 miles from his village. He left Jhajjar to be enrolled in the Christian Mission School in Delhi, though it was not easy for the family to raise the funds for his education as he belonged to a poor family.

Sir Chhotu Ram's stay at the Christian Mission School was eventful. He organized a strike against the in-charge of the boarding house for which he was given the nickname "General Roberts." In 1901 he returned to his village and passed his intermediate examination inn 1903. Then he enrolled in St. Stephens College from where he graduated in 1905. It was his stay in this college that he was drawn to the Arya Samaj. He studied Sanskrit rather than English. He took his law degree in year 1911 from Agra.

He was particularly concerned with the educational and economical backwardness of Jats. He had a deep desire, which later grew into a passion for uplifting Jat class educationally, economically, socially and politically.

In an article published in the college magazine, he reflected on the ways to improve the life in rural areas, to end the isolation of people and curb the monopoly of the village bania, whom he called 'the incarnation of Shylock in our times.'

Public Life:

In 1905, he worked as the assistant Private Secretary to Raja Rampal Singh of Kalakankar in the United Provinces, but left the job within a month because he resented the Raja's attitude towards him on one particular occasion. He went to Bharatpur but returned to Kalakankar because he could not get suitable job there. After returning he worked as the editor in English newspaper Hindustan and then proceeded to study law in Agra. He took his degree in 1911.

While teaching in St. John's High School and reading his law in Agra, Chhotu Ram studied the local conditions of Agra and Meerut division. This Knowledge strengthened his desire to 'respond to inner call for action in the direction of improving the conditions of the Jats'. In 1911 he became the honorary superintendent of the Jat Boarding House in Agra. In 1912 he set up his legal practice with Chaudhary Lal Chand. Both became involved in recruiting soldiers during the First World War. Owing to their efforts, recruitment figure rose from 6,245 in Jan 1915 to 22,144 in Nov 1918. He was convinced that recruitment to the army was economically beneficial and helped Jats to emphasis their Kshatriyas status.

Sir Chhotu Ram established the Jat Sabha at Rohtak in 1912. He founded educational institutions, including the Jat Arya Vedic Sanskrit School in Rohtak. The school was established on 7 Sept 1913. He encouraged Jat students to join the young Jat Association and study at the Jat School in Rohtak and at St. Stephen's College and provided support to students for the same.

He advises strongly his friends to wear the sacred thread to establish their identity. He saw it as 'a sign of Dwija or twice born, a status conceded to a Jat by the orthodox Hindu only avaricious.

As a leader:

Sir Chhotu Ram worked as the president of the Rohtak District Congress Committee from 1916 to 1920. He resigned on 8 Nov 1920 because the Punjab Provincial Congress Committee identified with the urban and the commercial classes had ignored the rights and claims of the rural population. Other reason behind leaving the Congress was his conviction that a disadvantaged class like Jat could not afford to fight against the Government. He emerged as the sole spokesman of Jat interests. During the war years, and also thereafter, he developed the links between Jat and Arya Samajist leaders, such as Chaudhary Piru Singh, manager of the gurukul in Matindu. Soon he became Piru Singh's legal advisor. His associations with the gurukul also brought him in contact with Swami Shraddhanand. His close ally in Rohtak was Master Nathu Ram, who worked as a 'recruiting orator' and was popular as an Arya Samaj Preacher.

In 1925 Sir Chhotu Ram organized a Mahasabha Jalsa at Pushkar in Rajasthan, momentous event in Jat history. In 1934 he organized a rally of 10,000 Jat peasants in Sikar in Rajasthan to launch an anti-rent campaign. The campaigners clothed the sacred thread, made offerings of ghee and read from the Satyarth Prakash. The rally was a major event and enhanced his stature.

After 1920, Sir Chhotu Ram also tried to create a non-sectarian peasant group consciousness. He was actively associated with the Punjab Zamindar Central Association, established in 1917 to advance the interests of Hindu and Sikh Jat agriculturists. This was the first step towards the formation of a homogeneous rural block based on economics rather than religious interests.

He asserted that the impoverishment of the peasantry was itself the soul cause of indebtedness. He challenged official's assumptions on the 'wasteful habits' of peasants and the 'overspending' on marriage, death and festivals. He insisted that land revenue was the principal cause of indebtedness and ruin. He rejected the advocacy of cooperatives as a method to curb moneylenders, arguing instead that market forces would not release the peasantry from debt.

Writer in the leader:

Sir Chhotu Ram began writing while in college and continued through out his public life. Most influential writings were 'Thug Bazaar ki sair' series of 'Bechara Zamindar' of this series 17 appeared in Jat Gazette. The first series of 'Bechara Zamindar' was written in 1935 and the second in 1936.

His relations with British:

There was an ambivalent relationship between Sir Chhotu Ram and the British, an aspect ignored by historians who have studied his role within the framework of military loyalist and imperial patronage in Punjab. These historians view the Jats as the mainstay if imperial authority in Punjab and regard Chhotu Ram as the spokesman of the rich and middle peasants. The reality, however, is that he was primarily concerned with the plight of the deprived, the downtrodden and the neglected.

Sir Chhotu Ram was equally vocal in assailing the pre-colonial state for its unjustifiable claims over land. He criticized the British for reinforcing pre-colonial principles of 'darkness' by claiming ownership of land. He moved away from the prevalent political rhetoric of Unionist Party (between 1925 and 1933) which was primarily concerned with the greater employment of Zamindars in government services.

He argued that a peasant was called peasant by virtue of his ownership of the land. He also demanded the recognition of women as cultivators. By the 30's, he was disenchanted with the colonial state. His pronouncements disturbed officials in Punjab who went so far as to accuse him of spreading socialism among peasants. While recognizing the role of the colonial state in the life of the peasant Sir Chhotu Ram exposed the Government's discriminatory policy towards agriculturists, and their lack of representation in public services.

Sir Chhotu Ram died in 1945. After his death he was equated with Dayanand Saraswati, their names evoking notions of heroism and serving as reference points for the collective identity of Jats. Muslim Jats too gave him the title of 'Rehbar-I-Azam' (a great protector).

The Great Minds of India - Nagarjuna

Perhaps no man in his time has more tales spun around him than Nagarjuna. He was said to be in communion with gods and goddesses, to have the power to change base metal into gold, to know the secret of making the "elixir of life." He was famous and people looked on him with awe mingled with fear.

Nagarjuna, born at Fort Daihak near Somnath in Gujarat in 931 A.D., was a chemist, rather an alchemist. If he was embarrassed by all the tales told about him, he showed no sign of it. And he only added to the popular belief that he was a messenger of God by writing his treatise, Rasaratnakara, in the form of dialogues between him and the gods.

Rasaratnakara dealt with preparations of rasa (mercury) compounds. It also gave a survey of the status of metallurgy and alchemy in the land. Extraction of metals such as silver, gold, tin and copper from their ores and their purification were also mentioned in the treatise.

To prepare the "elixir of life" and other substances from mercury, Nagarjuna made use of animal and vegetable products, apart from minerals and alkalis. To dissolve diamonds, metals and pearls, he suggested the use of vegetable acids-sour gruel and juices of fruits and plants. A list of apparatus he and earlier alchemists had used was given in the treatise. The process of distillation, liquefaction, sublimation and roasting were also mentioned.

The treatise discussed at length transmutation of metals into gold. Even if no gold could be produced, these techniques could yield metals with gold-like yellowish brilliance. Methods to prepare mercury-like substances from cinnabar and tin-like calamine were also given.

Nagarjuna also wrote Uttaratantra as a supplement to Susrutasamhita, dealing with preparation of medicinal drugs, and an Ayurvedic treatise, Arogyamanjari. His other treatises are Kakshaputatantra, Yogasara and Yogasatak.