Great Indian Hindu Sages who revolutionised the field of Science
भारतीय वैज्ञानिक
Great Indian Hindu Sages who revolutionised the field of Science
Aryabhatta (476 CE) – Master Astronomer and Mathematician
Aryabhatta (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the Aryabhattya (499 CE, when he was 23 years old) and the Arya-siddhanta.
Time and place of birth
Aryabhatta mentions in the Aryabhatiya that it was composed 3,600 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476.
Aryabhatta provides no information about his place of birth. The only information comes from Bhaskara I, who describes Aryabhatta as asmakiya, "one belonging to the Asmaka country." During the Buddha's time, a branch of the Asmaka people settled in the region between the Narmada and Godavari rivers in central India; Aryabhatta is believed to have been born there.
Education
It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as well as Bhaskara I (CE 629), identify Kusumapura as Pa?aliputra, modern Patna. A verse mentions that Aryabhatta was the head of an institution (kulapa) at Kusumapura, and, because the university of Nalanda was in Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhatta might have been the head of the Nalanda university as well. Aryabhatta is also reputed to have set up an observatory at the Sun temple in Taregana, Bihar
Works
Aryabhatta is the author of several treatises on mathematics and astronomy, some of which are lost. His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry. It also contains continued fractions, quadratic equations, sums-of-power series, and a table of sines.
Highlights
Place value system and zero
Approximation of ?
Trigonometry
Indeterminate equations
Algebra
Astronomy
Motions of the solar system
Eclipses
Sidereal periods
Heliocentrism
Legacy
Bhaskaracharya || (1114-1183 BCE) – Genius in Algebra
Bhaskaracharya (Bhāskara the teacher) was an Indian mathematician and astronomer of 12th century AD.
He is refered as Bhāskara II to avoid confusion with Bhāskara I (of 7th century AD).
He was born near Vijjadavida (Bijapur in modern Karnataka) and lived between 1114-1185 AD.
He represented the peaks of mathematical knowledge in the 12th century and was the head of the astronomical observatory at Ujjain, the leading mathematical centre of ancient India.
Bhaskara II’s family belonged to Deshastha Brahmin community, which served as court scholars at Kings forts.
He learned Mathematics from his father Maheswara, an astrologer.
He imparted his knowledge of mathematics to his son Lokasamudra, whose son had started a school to study the works of his grandfather in 1207 AD.
His main work Siddhānta Shiromani, (Sanskrit for “Crown of treatises,“) is divided into four parts called Lilāvati(beautiful woman, named after his daughter Lilavati), Bijaganita, Grahaganita (mathematics of planets) and Golādhyāya (study of sphere/earth).
These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karna Kautoohala.
Bhāskara’s work on calculus predates Newton and Leibniz by over half a millennium.
He is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhāskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential calculus.
Lilavati (meaning a beautiful woman) is based on Arithmetic. It is believed that Bhaskara named this book after his daughter Lilavati. Many of the problems in this book are addressed to his daughter. For example “Oh Lilavati, intelligent girl, if you understand addition & subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10 & 100, as well as [the remainder of] those when subtracted from 10000.” The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical & geometric progressions. Many of the methods in the book on computing numbers such as multiplications, squares & progressions were based on common objects like kings & elephants, which a common man could understand.
Bijaganita is on Algebra & contains 12 chapters.
“A positive number has two square-roots (a negative root & a positive root)“. This was published in this text for the very first time. It contains concepts of positive & negative numbers, zero, the ‘unknown‘ (includes determining unknown quantities), surds, simple equations & quadratic equations.
Bhaskara was the first to introduce the concept of Infinity : If any finite number is divided by zero, the result is infinity.
Also the fact that if any finite number is added to infinity then the sum is infinity. He developed a proof of the Pythogorean theorem by calculating the same area in two different ways & then cancelling out two terms to get a2 + b2 = c2.
He is also known for his calculation of the time required (365.2588 days) by the Earth to orbit the Sun which differs from the modern day calculation of 365.2563 days, by just 3.5 minutes!
The law of Gravitation had been proved by Bhaskara 500 years before it was rediscovered by Newton.
Bhaskaracharya’s contributions
Mathematics
Some of Bhaskara’s contributions to mathematics include the following:
A proof of the Pythagorean theorem by calculating the same area in two different ways and then canceling out terms to get a2 + b2 = c2.
In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations are explained.
Solutions of indeterminate quadratic equations (of the type ax2 + b = y2).
Integer solutions of linear and quadratic indeterminate equations (Kuttaka). The rules he gives are (in effect) the same as those given by the Renaissance European mathematicians of the 17th century
A cyclic Chakravala method for solving indeterminate equations of the form ax2 + bx + c = y. The solution to this equation was traditionally attributed to William Brouncker in 1657, though his method was more difficult than the chakravala method.
The first general method for finding the solutions of the problem x2 − ny2 = 1 (so-called “Pell’s equation“) was given by Bhaskara II.
Solutions of Diophantine equations of the second order, such as 61x2 + 1 = y2. This very equation was posed as a problem in 1657 by the French mathematician Pierre de Fermat, but its solution was unknown in Europe until the time of Euler in the 18th century.
Solved quadratic equations with more than one unknown, and found negative and irrational solutions.
Preliminary concept of mathematical analysis.
Preliminary concept of infinitesimal calculus, along with notable contributions towards integral calculus.
Conceived differential calculus, after discovering the derivative and differential coefficient.
Stated Rolle’s theorem, a special case of one of the most important theorems in analysis, the mean value theorem. Traces of the general mean value theorem are also found in his works.
Calculated the derivatives of trigonometric functions and formulae. (See Calculus section below.)
In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results. (See Trigonometry section below.)
Arithmetic
Bhaskara’s arithmetic text Leelavati covers the topics of definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon, methods to solve indeterminate equations, and combinations.
Lilavati is divided into 13 chapters and covers many branches of mathematics, arithmetic, algebra, geometry, and a little trigonometry and mensuration. More specifically the contents include:
Definitions.
Properties of zero (including division, and rules of operations with zero).
Further extensive numerical work, including use of negative numbers and surds.
Estimation of π.
Arithmetical terms, methods of multiplication, and squaring.
Inverse rule of three, and rules of 3, 5, 7, 9, and 11.
Problems involving interest and interest computation.
Indeterminate equations (Kuttaka), integer solutions (first and second order). His contributions to this topic are particularly important, since the rules he gives are (in effect) the same as those given by the renaissance European mathematicians of the 17th century, yet his work was of the 12th century. Bhaskara’s method of solving was an improvement of the methods found in the work of Aryabhata and subsequent mathematicians.
His work is outstanding for its systemisation, improved methods and the new topics that he has introduced. Furthermore the Lilavati contained excellent recreative problems and it is thought that Bhaskara’s intention may have be.
Algebra
His Bijaganita (“Algebra”) was a work in twelve chapters. It was the first text to recognize that a positive number has two square roots (a positive and negative square root).
His work Bijaganita is effectively a treatise on algebra and contains the following topics:
Positive and negative numbers.
Zero.
The ‘unknown’ (includes determining unknown quantities).
Determining unknown quantities.
Surds (includes evaluating surds).
Kuttaka (for solving indeterminate equations and Diophantine equations).
Simple equations (indeterminate of second, third and fourth degree).
Simple equations with more than one unknown.
Indeterminate quadratic equations (of the type ax2 + b = y2).
Solutions of indeterminate equations of the second, third and fourth degree.
Quadratic equations.
Quadratic equations with more than one unknown.
Operations with products of several unknowns.
Bhaskara derived a cyclic, chakravala method for solving indeterminate quadratic equations of the form ax2 + bx + c = y.
Bhaskara’s method for finding the solutions of the problem Nx2 + 1 = y2 (the so-called “Pell’s equation“) is of considerable importance.
Trigonometry
The Siddhanta Shiromani (written in 1150) demonstrates Bhaskara’s knowledge of trigonometry, including the sine table and relationships between different trigonometric functions. He also discovered spherical trigonometry, along with other interesting trigonometrical results. In particular Bhaskara seemed more interested in trigonometry for its own sake than his predecessors who saw it only as a tool for calculation. Among the many interesting results given by Bhaskara, discoveries first found in his works include the now well known results for sin(a + b) and sin(a – b)
Calculus
His work, the Siddhanta Shiromani, is an astronomical treatise and contains many theories not found in earlier works. Preliminary concepts of infinitesimal calculus and mathematical analysis, along with a number of results in trigonometry, differential calculus and integral calculus that are found in the work are of particular interest.
Evidence suggests Bhaskara was acquainted with some ideas of differential calculus. It seems, however, that he did not understand the utility of his researches, and thus historians of mathematics generally neglect this achievement. Bhaskara also goes deeper into the ‘differential calculus‘ and suggests the differential coefficient vanishes at an extremum value of the function, indicating knowledge of the concept of ‘infinitesimals‘.
There is evidence of an early form of Rolle’s theorem in his work
If f (a) = f (b) = 0, then f ‘ (x) = 0 for some x with a<x<b then
He gave the result that if x =(approx) y then sin(y) – sin(x) =(approx) (y-x) cos(y), thereby finding the derivative of sine, although he never developed the notion of derivatives.
Bhaskara uses this result to work out the position angle of the ecliptic, a quantity required for accurately predicting the time of an eclipse.
In computing the instantaneous motion of a planet, the time interval between successive positions of the planets was no greater than a truti, or a 1⁄33750 of a second, and his measure of velocity was expressed in this infinitesimal unit of time.
He was aware that when a variable attains the maximum value, its differential vanishes.
He also showed that when a planet is at its farthest from the earth, or at its closest, the equation of the centre (measure of how far a planet is from the position in which it is predicted to be, by assuming it is to move uniformly) vanishes. He therefore concluded that for some intermediate position the differential of the equation of the centre is equal to zero.
In this result, there are traces of the general mean value theorem, one of the most important theorems in analysis, which today is usually derived from Rolle’s theorem. The mean value theorem was later found by Parameshvara in the 15th century in the Lilavati Bhasya, a commentary on Bhaskara’s Lilavati.
Madhava (1340–1425) and the Kerala School mathematicians (including Parameshvara) from the 14th century to the 16th century expanded on Bhaskara’s work and further advanced the development of calculus in India.
Astronomy
Using an astronomical model developed by Brahmagupta in the 7th century, Bhaskara accurately defined many astronomical quantities, including, for example, the length of the sidereal year, the time that is required for the Earth to orbit the Sun, as 365.2588 days which is same as in Suryasiddhanta. The modern accepted measurement is 365.2563 days, a difference of just 3.5 minutes !
His mathematical astronomy text Siddhanta Shiromani is written in two parts: the first part on mathematical astronomy and the second part on the sphere.
The twelve chapters of the first part cover topics such as:
Mean longitudes of the planets.
True longitudes of the planets.
The three problems of diurnal rotation.
Syzygies.
Lunar eclipses.
Solar eclipses.
Latitudes of the planets.
Sunrise equation
The Moon’s crescent.
Conjunctions of the planets with each other.
Conjunctions of the planets with the fixed stars.
The paths of the Sun and Moon.
The second part contains thirteen chapters on the sphere. It covers topics such as:
Praise of study of the sphere.
Nature of the sphere.
Cosmography and geography.
Planetary mean motion.
Eccentric epicyclic model of the planets.
The armillary sphere.
Spherical trigonometry.
Ellipse calculations.
First visibilities of the planets.
Calculating the lunar crescent.
Astronomical instruments.
The seasons.
Problems of astronomical calculations.
Engineering
The earliest reference to a perpetual motion machine date back to 1150, when Bhāskara II described a wheel that he claimed would run forever.
Bhāskara II used a measuring device known as Yasti-yantra. This device could vary from a simple stick to V-shaped staffs designed specifically for determining angles with the help of a calibrated scale.
Acharya Kanada (600 BCE) – Founder of Atomic Theory
Maharshi Kanada discovered Atomic theory 2,600 years ago, not Dalton of England.
Introduction to Sage Kanada
When the entire people credit the Western World for modern physics and its development, it is India’s own scientist “Sage Kanada”, otherwise known as “Acharya Kanada”, who should be highly revered and credited. He discovered the atomic structure, atomic theory, and even sub-atomic particles some 2600 years before. Kanada in Sanskrit denotes the smallest particle. He is revered as the “Father of Atomic Theory”. He has rendered Kanada Sutras, which are the Aphorisms of Kanada, which is considered as one of the greatest works in the field of physics. He is not only revered in Hinduism but also in Jainism and Buddhism, where his concepts are highly praised.
Life of Acharya Kanada:
He was believed to have born in the year 600 BC or 800 BC in Gujarat, India. His father was a philosopher Ulka. His birth name was Kashyap. As a child, he always accompanied his father and observed many things. But despite of all those things around him, his interest was always on the smallest things. He was able to look beyond the general concepts which were underlying in the universe.
When he was able to conceptualize the idea of the smallest particle, he noted down his ideas and was able to explain it to people. Many people also with great reverence call him Acharya Kanada.
Legend of Acharya Kanada:
When Acharya Kanada was young, he always admired the grain of rice. It was the tradition of the early Hindu family, to scatter grains of rice along the streets, for the people to follow it as a ritual. The young boy was looking at the ant, which was eating the rice. He was fascinated by the idea that a small piece of rice could become food for a small creature like an ant, but it needs a lot of grains, collected together to make a complete meal for a person, which could satiate his hunger.
The idea of looking deep and beyond was highly fascinating, and he started to look deep into the rice particle, which suggested to him the concept of “Anu”, the smallest particle.
Acharya Kanada’s contribution:
The theory of “Anu”, the atom was postulated even before Dalton’s theory. But, may people do not consider it, as it is not highly empirical. He was able to bring a theory on the creation and existence of the universe. He was able to parallelly bring mystical realities of “Atma”, along with “atom”, which is bound by energy. Every “Atma” wants moksha, which is the ulterior goal of every soul born in this world.
He described the universe with six categories, which are Dravya, which is defined as a substance. Guna, which is defined as the quality. Karman, which is defined as a motion. Samanya, which is defined as Generic Species. Visesa, which is defined as a unique Trait, and Samavaya is defined as inherence
Conclusion:
Thus, great philosophers and Saints like Sage Kanada were parallelly able to travel on both philosophy and spirituality. He has made several people think about science and was a great inspiration for several other philosophers and thinkers.
Nagarjuna (100 BCE) – Wizard of Chemical Science
He was an extraordinary wizard of science born in the nondescript village of Baluka in Madhya Pradesh . His dedicated research for twelve years produced maiden discoveries and inventions in the faculties of chemistry and metallurgy. Textual masterpieces like ” Ras Ratnakar ,” “Rashrudaya” and “Rasendramangal” are his renowned contributions to the science of chemistry. Where the medieval alchemists of England failed, Nagarjuna had discovered the alchemy of transmuting base metals into gold. As the author of medical books like “Arogyamanjari” and “Yogasar,” he also made significant contributions to the field of curative medicine. Because of his profound scholarliness and versatile knowledge, he was appointed as Chancellor of the famous University of Nalanda . Nagarjuna’s milestone discoveries impress and astonish the scientists of today.
Major Contributions of Nagarjuna in Alchemy (Chemistry), Metallurgy, and Ayurveda
1. His books deal with the preparation of mercury (rasa) compounds.
2. He described extraction of metals such as gold, silver, copper, tin from their ores and their purification.
3. Described design of chemical lab including instruments to be used in the lab, shape and size of instruments and their uses.
4. Described preparation of medicinal drugs.
5. Described preparation of the elixir of life – of creating medicines for increasing lifespan.
6. Described corrosion and loss on heating.
7. Wrote on metals and their stability.
8. Described preparation of yellow metal which shines like gold, but not gold.
Nagarjuna had a standard laboratory of his own where he conducted experiments. There are evidences of his experimental laboratory in Nagalwadi village of Maharashtra. Nagalwadi is located in Saoner Taluka in the district of Nagpur. Probably Nagarjuna migrated from Gujarat to Maharashtra and settled here. Considered the most prominent scholar in Indian Alchemy, Nagarjuna is featured in the National Science Centre (Delhi) in the ‘Our Science & Technological Heritage of India’ gallery. His typical alchemical laboratory called the Rasashala is recreated in this gallery.
Besides the various experiments, Nagarjuna also experimented in various dimensions in the field of metallurgy and alchemy. He contributed a lot towards developing curative medicines for various ailments.
Acharya Charaka (600 BCE) – Father of Medicine
The legend of Maharishi Charaka: The father of Ayurveda
Ayurveda is a Sanskrit word in which ‘Ayur’ means life and ‘Veda’ means science. Ayurveda is the science of life. This wellness system that originated in India around 5000 years ago, focuses on mindful nutrition, stress reduction, and cultivation of a balanced lifestyle. It is the oldest form of medical practice known to man. This ancient Indian medical science is celebrated by people across the world for its efficiency in curing ailments without any side effects. But not many people know about Acharya Charak a.k.a Maharishi Charaka, the father of Ayurveda.
The father of Ayurveda:
Born in 300 BC, Acharya Charaka is crowned as the father of Ayurveda due to his contribution to Ayurveda. He became a principal contributor to the science of Ayurveda who developed the art of Ayurvedic culture. His work ‘Charaka Samhita’ is considered as the Encyclopedia of Ayurveda. While the other parts of the world were struggling with the science of anatomy, Acharya Charaka was already an expert in human anatomy, embryology, pharmacology, blood circulation and diseases like diabetes, tuberculosis, heart disease, etc
According to Charaka’s translations, health and disease are not predetermined. Our lifestyle and environment play a major role in our health and wellness. His works preached that one can live a healthy and peaceful life if he lives in harmony with nature. The Ayurvedic system provides preventive measures and solutions to all kinds of illnesses and ailments. It tells us a way to restructure our life to align with the course of nature. This guarantees complete wellness.
How did Maharishi Charaka receive the gift of Ayurveda?
The legend goes that the Lord Brahma created Ayurveda. He then transmitted this knowledge to his son, Daksha Prajapati. Daksha passed it down to the twin Vedic gods Ashwini Kumaras who then became the physicians of the gods and the Devas of Ayurveda. The twin gods presented Ayurveda to Indra, the king of gods. Indra had three physicians as his disciples, namely Acharya Bharadwaj, Acharya Kashyapa, and Aacharya Divodas Dhanvantari.
From Acharya Bharadwaj’s teaching, his student Agnivesha developed the fundamental Ayurvedic text of internal medicine. Aginivesha wrote all his study in the form of an ancient script, known as ‘Agnivesa Samhita’. Agnivesha’s disciple, Acharya Charak then revised this body of work and compiled it into an easily understandable Ayurvedic guide called ‘Charaka Samhita’ and passed down the knowledge of Ayurveda from gods to sages.
Charaka Samhita:
According to Charaka Samhita, anything and everything in the universe is composed of vata, pitta, and kapha. They are considered as the force of nature in Ayurveda that helps us understand the universe better. In essence, they are derived from the five basic elements: Space, air, water, fire, and earth. It contains over 8,400 metrical verses and is divided into eight divisions (ashtanga sthanas) viz., sutra, nidana, vimana, sharia, indriya, chikitsa, kalpa and siddha sthanas. Each division is further divided into numerous chapters, it describes existing knowledge about medical aspects and the logic and philosophy behind the medical systems.
Ayurveda is one of the greatest gifts India has gifted mankind and Maharishi Charaka played a significant role in this. Ayurveda is not just a medicinal system. It is a life guide that steers us along the path of happy and healthy living.
Acharya Sushruta (600 BCE) – Father of Plastic Surgery
Sushruta, or Suśruta (Sanskrit: सुश्रुत, IAST: Suśruta, lit. 'well heard') was an ancient Indian physician and surgeon known today as the “Father of Surgery” and “Father of Plastic Surgery” or "father of brain surgery" for inventing and developing surgical procedures. His work on the subject, the Sushruta Samhita (Sushruta's Compendium) is considered the oldest text in the world on plastic surgery and is highly regarded as one of the Great Trilogy of Ayurvedic Medicine, the Brihat-Trayi; the other two being the Charaka Samhita, which preceded it, and the Astanga Hridaya, which followed it.
The Sushruta Samhita is one of the most important surviving ancient treatises on medicine and is considered a foundational text of Ayurveda. The treatise addresses all aspects of general medicine, but the impressive chapters on surgery have led to the false impression that this is its main topic. The translator G. D. Singhal dubbed Suśruta "the father of surgery" on account of these detailed accounts of surgery, and many scholars have repeated this cachet, usually as part of an provenance claim about the history of science.
The Compendium of Suśruta locates its author in Varanasi, India
Date
The early scholar Rudolf Hoernle proposed that some concepts from the Suśruta-saṃhitā could be found in the Śatapatha-Brāhmaṇa, which he dates to the 600 BCE, and this dating is still often repeated. However, during the last century, scholarship on the history of Indian medical literature has advanced substantially, and firm evidence has accumulated that the Suśruta-saṃhitā is a work of several historical layers. Its composition may have begun in the last centuries BCE and it was completed in its present form by another author who redacted its first five chapters and added the long, final chapter, the "Uttaratantra." It is likely that the Suśruta-saṃhitā was known to the scholar Dṛḍhabala [Wikidata] (fl. 300–500 CE), which gives the latest date for the version of the work that has come down to us today. It has also become clear through historical research that there are several ancient authors called "Suśruta" who might be conflated.
Sushruta Samhita
The Suśruta-saṃhitā, in its extant form, in 184 chapters contains descriptions of 1,120 illnesses, 700 medicinal plants, 64 preparations from mineral sources and 57 preparations based on animal sources.
The text discusses surgical techniques of making incisions, probing, extraction of foreign bodies, alkali and thermal cauterization, tooth extraction, excisions, and trocars for draining abscess, draining hydrocele and ascitic fluid, removal of the prostate gland, urethral stricture dilatation, vesicolithotomy, hernia surgery, caesarian section, management of haemorrhoids, fistulae, laparotomy and management of intestinal obstruction, perforated intestines and accidental perforation of the abdomen with protrusion of omentum and the principles of fracture management, viz., traction, manipulation, apposition and stabilization including some measures of rehabilitation and fitting of prosthetic. It enumerates six types of dislocations, twelve varieties of fractures, and classification of the bones and their reaction to the injuries, and gives a classification of eye diseases including cataract surgery.
Citations
According to Bhishagratna, an influential translator who published in 1907, the Mahabharata, an ancient Indian epic text, represents a Suśrut as one of the sons of the ancient sage Vishvamitra. Bhisagratna also asserted that Sushruta was the name of the clan to which Vishvamitra belonged. In the century since Bhishagratna, our knowledge of Suśruta and the Suśrutasaṃhitā has been transformed by newer discoveries and scholarship, most of which has been surveyed in volume IA of Meulenbeld's History of Indian Medical Literature (5 vols, 1999-2002).
The name Suśruta appears in later literature in the treatise on medicinal garlic that is included in the Bower Manuscripts (sixth century CE), where Suśruta is listed as one of the ten sages residing in the Himalayas.
Followers
Sushruta attracted a number of disciples who were known as Saushrutas and were required to study for six years before they even began hands-on training in surgery. Before starting their training, they had to take a solemn oath to devote themselves to healing and to do no harm to others;which can be compared to Hippocratic Oath. After the students had been accepted by Sushruta, he would instruct them in surgical procedures by having them practice cutting on vegetables or dead animals to perfect the length and depth of an incision. Once students had proven themselves capable with vegetation, animal corpses, or with soft or rotting wood – and had carefully observed actual procedures on patients – they were then allowed to perform their own surgeries. These students were trained by their master in every aspect of the medical arts, including anatomy.
Sushruta on Medicine & Physicians
Sushruta wrote the Sushruta Samhita as an instruction manual for physicians to treat their patients holistically. Disease, he claimed (following the precepts of Charaka), was caused by imbalance in the body, and it was the physician's duty to help others maintain balance or to restore it if it had been lost. To this end, anyone who was engaged in the practice of medicine had to be balanced themselves. Sushruta describes the ideal medical practitioner, focusing on a nurse, in this way:
That person alone is fit to nurse, or to attend the bedside of a patient, who is cool-headed and pleasant in his demeanor, does not speak ill of anyone, is strong and attentive to the requirements of the sick, and strictly and indefatigably follows the instructions of the physician. (I.34)
Legacy
Like other Sanskrit texts, the Sushruta Samahita also traveled from India to other parts of the world. During the early 8th century, the text was translated into Arabic as ‘Kitab Shah Shun al-Hindi’, by an Indian medical practitioner named Mankah on orders of Yahya Barmakid, a powerful minister of Caliph Harun-al-Rashid of Baghdad.There are also historical references to this in the court of king Yasovarman I (889 CE-900 CE) of Cambodia as well as in the monasteries of Tibet. The first European translation of Sushruta Samhita was published by Hessler in Latin in the early 19th century. The first complete English translation was done by Kaviraj Kunja Lal Bhishagratna in three volumes in 1907 in Calcutta.
The highlight of Sushruta’s surgical magnificence was the surgery of nasal reconstruction or rhinoplasty (repairing the disfigured nose with a flap of skin from the forehead) that he used to reconstruct noses that were amputated as a punishment for crime. The technique is practised almost unchanged to this day, the pedicled forehead flap being named the Indian flap. This knowledge of plastic surgery existed in India up to the late 18th century as can be seen from reports in the Gentleman’s Magazine, London, October 1794.
In "The source book of plastic surgery", Frank McDowell aptly described Sushruta as “through all of Sushruta's flowery language, incantations and irrelevancies, there shines the unmistakable picture of a great surgeon . Undaunted by his failures, unimpressed by his successes, he sought the truth unceasingly and passed it on to those who followed. He attacked disease and deformity definitively, with reasoned and logical methods. When the path did not exist, he made one.”
Varahmihira (499-587 BCE) – Eminent Astrologer and Astronomera
Varāhamihira (c. 505 – c. 587), also called Varāha or Mihira, was an ancient Indian astrologer, astronomer, and polymath who lived in Ujjain (Madhya Pradesh, India). He was born at Kayatha, in the Avanti region, roughly corresponding to modern-day Malwa (part of Madhya Pradesh, India), to Adityadasa. According to one of his own works, he was educated at Kapitthaka. The Indian tradition believes him to be one of the "Nine Jewels" (Navaratnas) of the court of ruler Yashodharman Vikramaditya of Malwa. However, this claim appears for the first time in a much later text and scholars consider this claim to be doubtful because neither Varahamihira and Vikramaditya lived in the same century nor did Varahamihira live in the same century as some of the other names in the "nine jewels" list such as the much older Kalidasa.
Varāhamihira's most notable works were the Brihat Samhita, an encyclopedic work on architecture, temples, planetary motions, eclipses, timekeeping, astrology, seasons, cloud formation, rainfall, agriculture, mathematics, gemology, perfumes and many other topics. According to Varahamihira, in some verses he was merely summarizing earlier existing literature on astronomy, Shilpa Sastra and temple architecture, yet his presentation of different theories and models of design are among the earliest texts that have survived. The chapters of the Brihat Samhita and verses of Varahamihira were quoted by the Persian traveler and scholar Al Biruni.
Varāhamihira is also credited with writing several authoritative texts on astronomy and astrology. He learned the Greek language, and praised the Greeks (Yavanas) in his text for being "well trained in the sciences", though impure in ritual order. Some scholars consider him to be the strong candidate as the one who understood and introduced the zodiac signs, predictive calculations for auspicious ceremonies and astrological computations.
Works
Pancha-Siddhantika
Varāhamihira's main work is the book Pañcasiddhāntikā (“Treatise on the Five Astronomical Canons”) dated c. 575 CE, which gives us information about older Indian texts which are now lost. The work is a treatise on mathematical astronomy and it summarises five earlier astronomical treatises by five authors, namely the Surya Siddhanta, Romaka Siddhanta, Paulisa Siddhanta, Vasishtha Siddhanta and Paitamaha Siddhanta. It is a compendium of Vedanga Jyotisha as well as Hellenistic astronomy (withGreek, Egyptian and Roman elements). Varahamihira was the first one to mention that the Ayanāṃśa, or the shifting of the equinox, is 50.32 arc seconds per year.
They [the Indians] have 5 Siddhāntas:
Sūrya-Siddhānta, the siddhānta of the Sun, thought to be composed by Lāṭadeva, but actually composed by Mayasura also known as Mamuni Mayan as stated in the text itself.
Vasishtha-siddhānta, so called from one of the stars of the Great Bear, composed by Vishnucandra,
Paulisa-siddhānta, so called from Paulisa, the Greek, from the city of Saintra, which is supposed to be Alexandria, composed by Paulisa.
Romaka-siddhānta, so called from the Rūm, ie. the subjects of the Roman Empire, composed by Śrīsheṇa.
Paitahama-siddhānta.
Brihat-Samhita
Another important contribution of Varahamihira is the encyclopedic Brihat-Samhita. Although the book is mostly about divination, it also includes a wide range of subjects other than divination. It covers wide-ranging subjects of human interest, including astronomy, planetary movements, eclipses, rainfall, clouds, architecture, growth of crops, manufacture of perfume, matrimony and domestic relations. The volume expounds on gemstone evaluation criterion found in the Garuda Purana, and elaborates on the sacred Nine Pearls from the same text. It contains 106 chapters and is known as the "great compilation".
On Astrology
Hora Shastra or Brihadjathaka is a most acclaimed astrological work by Mihira. It is mostly in code language. More than a dozen commentaries have been written for this work. The Kerala School of Astrology is mainly based on the Brihadjathaka.
His son Prithuyasas also contributed to Hindu astrology; his book Hora Sara is a famous book on horoscopy. Khana (also named Lilavati elsewhere), the medieval Bengali poet astrologer, is believed to be the daughter-in-law of Varahamihira.
Contributions
Trigonometry
Varahamihira improved the accuracy of the sine tables of Aryabhata.
Combinatorics
He also records the first known 4×4 magic square[citation needed].
Optics
Among Varahamihira's contribution to physics is his statement that reflection is caused by the back-scattering of particles and refraction (the change of direction of a light ray as it moves from one medium into another) by the ability of the particles to penetrate inner spaces of the material, much like fluids that move through porous objects.
Acharya Patanjali (200 BCE) – Father of Yoga
Patanjali was a great spiritual leader of ancient times who refined the spirit of the spiritual path into the word of wisdom called Yoga Sutras. He defined the steps every soul must go through in its journey back to the infinite spirit. As per one legend, he fell from heaven into the hands of a woman (Anjali) in the form of a little snake, thus named Patanjali.
Life history
The life history of Patanjali is almost unknown. It is full of legends and contradictions. There is no clear evidence available about the birth of the Maharshi Patanjali. The dates projected for Patanjali’s birth and life differ by a millennium. Most scholars date the second and third centuries BCE, while others insist that he lived in the 4th to 7th centuries BCE. Due to modifications and additions made by later writers to his works that create confusion, Maharishi Patanjali lived in Nepal, Kashmir, Sri Lanka, and several places in India.
There is an explanation about Patanjali in Matsya, Vayu, and Skanda Purana that Maharishi Patanjali’s life period proves to be around that of Vyas and Panini. Rishis were tremendously proficient with Yoga power and used to live for thousands of years. They had the capability of living or dying according to their wish. This is the reason for the presence of rishis in modern times. In the Puranas, the life of rishis is believed to be for many ages, and Shri Patanjali is one of these powerful Rishis.
Most researchers date Patanjali based on the written version of the Yoga Sutras that has come down to us. But Patanjali himself likely lived in a much earlier age.
There are also stories about his spiritual powers and incredible birth. The truth is that nobody knows much about his life, not even when he lived. But it does not matter. However, we know him by his works.
Incarnation of AdiShesha
It is believed that Maharishi Patanjali was the incarnation of Adishesha, Vishnu’s serpent, who is the first ego expansion of Lord Vishnu. Ancient texts often refer to Patanjali as an incarnation of the thousand-headed serpent king named Ananta Shesha. He is sometimes depicted as half human and half serpent.
Yoga Sutra of Patanjali
It is said that Patanjali has often been called the founder of the Yoga Sutra. The origin of Yoga had been handed down in an oral tradition over thousands of years from ancient times. Patanjali’s Yoga is one of the famous darshans of Hindu Philosophy. Patanjali synthesized and organized knowledge about Yoga from much older traditions. The yoga sutra is one of the foundational texts of classical Yoga Philosophy.
Maharishi Patanjali is considered the compiler of the Yoga Sutras and the author of a commentary on Panini’s Ashtadhyayi, referred to as Mahabhasya. The Yoga sutras have 196 Sanskrit sutras organized in 4 chapters. The yoga sutras were collected sometime between 500 BCE and 200 BCE. All the four chapters of Patanjali’s Yoga Sutra are named according to their subjects; Samadhi Pada, Sadhana Pada, Vibhuti Pada, and Kaivalya Pada.
1. Samadhi Pada: The first chapter of Patanjali’s Yoga Sutras provides a definition and the purpose of Yoga. Various approaches that can be used to achieve the objectives of Yoga are included.
2. Sadhana Pada: The second chapter includes the practical approach to attaining the goals of Yoga. It also stated about eight limbs of Yoga called Astanga yoga.
3. Vibhuti Pada: It is about the results, power, and manifestation acquired by Yoga.
4. Kaivalaya Pada: The last chapter of the Patanjali Yoga sutra includes the path of devotion, the path of Karma, and the path of knowledge.
The yoga sutras of Patanjali are also sometimes called Raja Yoga or the Royal Yoga.
Ashtanga Yoga
The eight limbs of Yoga, Ashtanga yoga, as defined in the 2nd chapter, are as follows.
Yamas: they are guidelines for how to interact with the outside world at a social level.
Niyamas: it represents guidelines for self-discipline.
Asana: Asana refers to the seated posture, which should be steady and comfortable so the yogi can sit and meditate for long periods.
Pranayama: Pranayama means control over our energy or life force.
Pratyahara: through it, one gains the ability to withdraw the sense from their objects, thus achieving perfect control over the senses.
Dharana: It involves focusing the Mind on a single object.
Dhyana: It includes the state of mediation.
Samadhi: It simply means the state of oneness with God. By meditating deeply on any aspect of God, one loses self-awareness and becomes completely absorbed in that.
As per Patanjali, the meaning of Yoga is the restraint of the modifications of the mind-stuff. He has also written books on Ayurveda. It is believed that he must have had very little connection as far as social life is concerned; that is why there is no information available about any incidence of his life. But the world will always remain pleased with him for writing very useful books and giving the world the great tradition of Yoga.
Patanjali’s teaching is a deep and inspiring scripture. Yet also practical, accessible, and applicable to any spiritual seeker. The Yoga sutra shows the peripheral way to lasting happiness and freedom. It’s not just another intellectual exploration but a handbook for the proper exercise of Yoga.
Acharya Bharadwaja (800 BCE) – Pioneer of Aviation Technology
Acharya Bharadwaj had a hermitage in the holy city of Prayag and was an ordent apostle of Ayurveda and mechanical sciences. He authored the ” Yantra Sarvasva ” which includes astonishing and outstanding discoveries in aviation science, space science and flying machines. He has described three categories of flying machines: 1.) One that flies on earth from one place to another. 2.) One that travels from one planet to another. 3.) And One that travels from one universe to another. His designs and descriptions have impressed and amazed aviation engineers of today. His brilliance in aviation technology is further reflected through techniques described by him:
1.) Profound Secret: The technique to make a flying machine invisible through the application of sunlight and wind force.
2.) Living Secret: The technique to make an invisible space machine visible through the application of electrical force.
3.) Secret of Eavesdropping: The technique to listen to a conversation in another plane.
4.) Visual Secrets: The technique to see what’s happening inside another plane.
Through his innovative and brilliant discoveries, Acharya Bharadwaj has been recognized as the pioneer of aviation technology.
Acharya Kapila (3000 BCE) – Father of Cosmology
Celebrated as the founder of Sankhya philosophy, Acharya Kapil is believed to have been born in 3000 BCE to the illustrious sage Kardam and Devhuti. He gifted the world with the Sankhya School of Thought. His pioneering work threw light on the nature and principles of the ultimate Soul (Purusha), primal matter (Prakruti) and creation. His concept of transformation of energy and profound commentaries on atma, non-atma and the subtle elements of the cosmos places him in an elite class of master achievers – incomparable to the discoveries of other cosmologists. On his assertion that Prakruti, with the inspiration of Purusha, is the mother of cosmic creation and all energies, he contributed a new chapter in the science of cosmology. Because of his extrasensory observations and revelations on the secrets of creation, he is recognized and saluted as the Father of Cosmology.
Panini
Born: about 520 BC, Shalatula (near Attock), now Pakistan
Died: about 460 BC
Summary
Panini was a Sanskrit grammarian who gave a comprehensive and scientific theory of phonetics, phonology, and morphology.
Biography
Panini was born in Shalatula, a town near to Attock on the Indus river in present day Pakistan. The dates given for Panini are pure guesses. Experts give dates in the 4th , 5th , 6th and 7th century BC and there is also no agreement among historians about the extent of the work which he undertook. What is in little doubt is that, given the period in which he worked, he is one of the most innovative people in the whole development of knowledge. We will say a little more below about how historians have gone about trying to pinpoint the date when Panini lived.
Panini was a Sanskrit grammarian who gave a comprehensive and scientific theory of phonetics, phonology, and morphology. Sanskrit was the classical literary language of the Indian Hindus and Panini is considered the founder of the language and literature. It is interesting to note that the word "Sanskrit" means "complete" or "perfect" and it was thought of as the divine language, or language of the gods.
A treatise called Astadhyayi (or Astaka ) is Panini's major work. It consists of eight chapters, each subdivided into quarter chapters. In this work Panini distinguishes between the language of sacred texts and the usual language of communication. Panini gives formal production rules and definitions to describe Sanskrit grammar. Starting with about 1700 basic elements like nouns, verbs, vowels, consonants he put them into classes. The construction of sentences, compound nouns etc. is explained as ordered rules operating on underlying structures in a manner similar to modern theory. In many ways Panini's constructions are similar to the way that a mathematical function is defined today. Joseph writes in [2]:- [Sanskrit's] potential for scientific use was greatly enhanced as a result of the thorough systemisation of its grammar by Panini. ... On the basis of just under 4000 sutras [rules expressed as aphorisms], he built virtually the whole structure of the Sanskrit language, whose general 'shape' hardly changed for the next two thousand years. ... An indirect consequence of Panini's efforts to increase the linguistic facility of Sanskrit soon became apparent in the character of scientific and mathematical literature. This may be brought out by comparing the grammar of Sanskrit with the geometry of Euclid - a particularly apposite comparison since, whereas mathematics grew out of philosophy in ancient Greece, it was ... partly an outcome of linguistic developments in India.
Joseph goes on to make a convincing argument for the algebraic nature of Indian mathematics arising as a consequence of the structure of the Sanskrit language. In particular he suggests that algebraic reasoning, the Indian way of representing numbers by words, and ultimately the development of modern number systems in India, are linked through the structure of language.
Panini should be thought of as the forerunner of the modern formal language theory used to specify computer languages. The Backus Normal Form was discovered independently by John Backus in 1959, but Panini's notation is equivalent in its power to that of Backus and has many similar properties. It is remarkable to think that concepts which are fundamental to today's theoretical computer science should have their origin with an Indian genius around 2500 years ago.
At the beginning of this article we mentioned that certain concepts had been attributed to Panini by certain historians which others dispute. One such theory was put forward by B Indraji in 1876. He claimed that the Brahmi numerals developed out of using letters or syllables as numerals. Then he put the finishing touches to the theory by suggesting that Panini in the eighth century BC (earlier than most historians place Panini) was the first to come up with the idea of using letters of the alphabet to represent numbers.
There are a number of pieces of evidence to support Indraji's theory that the Brahmi numerals developed from letters or syllables. However it is not totally convincing since, to quote one example, the symbols for 1, 2 and 3 clearly do not come from letters but from one, two and three lines respectively. Even if one accepts the link between the numerals and the letters, making Panini the originator of this idea would seem to have no more behind it than knowing that Panini was one of the most innovative geniuses that world has known so it is not unreasonable to believe that he might have made this step too.
There are other works which are closely associated with the Astadhyayi which some historians attribute to Panini, others attribute to authors before Panini, others attribute to authors after Panini. This is an area where there are many theories but few, if any, hard facts.
We also promised to return to a discussion of Panini's dates. There has been no lack of work on this topic so the fact that there are theories which span several hundreds of years is not the result of lack of effort, rather an indication of the difficulty of the topic. The usual way to date such texts would be to examine which authors are referred to and which authors refer to the work. One can use this technique and see whom Panini mentions.
There are ten scholars mentioned by Panini and we must assume from the context that these ten have all contributed to the study of Sanskrit grammar. This in itself, of course, indicates that Panini was not a solitary genius but, like Newton, had "stood on the shoulders of giants". Panini must have lived later than these ten but this is absolutely no help in providing dates since we have absolutely no knowledge of when any of these ten lived.
What other internal evidence is there to use? Well of course Panini uses many phrases to illustrate his grammar any these have been examined meticulously to see if anything is contained there to indicate a date. To give an example of what we mean: if we were to pick up a text which contained as an example "I take the train to work every day" we would know that it had to have been written after railways became common. Let us illustrate with two actual examples from the Astadhyayi which have been the subject of much study. The first is an attempt to see whether there is evidence of Greek influence. Would it be possible to find evidence which would mean that the text had to have been written after the conquests of Alexander the Great? There is a little evidence of Greek influence, but there was Greek influence on this north east part of the Indian subcontinent before the time of Alexander. Nothing conclusive has been identified.
Another angle is to examine a reference Panini makes to nuns. Some argue that these must be Buddhist nuns and therefore the work must have been written after Buddha. A nice argument but there is a counter argument which says that there were Jaina nuns before the time of Buddha and Panini's reference could equally well be to them. Again the evidence is inconclusive.
There are references by others to Panini. However it would appear that the Panini to whom most refer is a poet and although some argue that these are the same person, most historians agree that the linguist and the poet are two different people. Again this is inconclusive evidence.
Let us end with an evaluation of Panini's contribution by Cardona in [1]:-
Panini's grammar has been evaluated from various points of view. After all these different evaluations, I think that the grammar merits asserting ... that it is one of the greatest monuments of human intelligence.
Baudhayana
Who is Baudhayana?
Baudhayana (800 BC - 740 BC) is said to be the original Mathematician behind the Pythagoras theorem. Pythagoras theorem was indeed known much before Pythagoras, and it was Indians who discovered it at least 1000 years before Pythagoras was born! The credit for authoring the earliest Sulba Sutras goes to him.
It is widely believed that he was also a priest and an architect of very high standards. It is possible that Baudhayana’s interest in Mathematical calculations stemmed more from his work in religious matters than a keenness for mathematics as a subject itself. Undoubtedly he wrote the Sulbasutra to provide rules for religious rites, and it would appear almost certain that Baudhayana himself would be a Vedic priest.
The Sulbasutras is like a guide to the Vedas which formulate rules for constructing altars. In other words, they provide techniques to solve mathematical problems effortlessly.
If a ritual was to be successful, then the altar had to conform to very precise measurements. Therefore mathematical calculations needed to be precise with no room for error.
People made sacrifices to their gods for the fulfilment of their wishes. As these rituals were meant to please the Gods, it was imperative that everything had to be done with precision. It would not be incorrect to say that Baudhayana’s work on Mathematics was to ensure there would be no miscalculations in the religious rituals.
Works of Baudhayana
Baudhayana is credited with significant contributions towards the advancements in mathematics. The most prominent among them are as follows:
1. Circling a square.
Baudhayana was able to construct a circle almost equal in area to a square and vice versa. These procedures are described in his sutras (I-58 and I-59).
Possibly in his quest to construct circular altars, he constructed two circles circumscribing the two squares shown below.
Now, just as the areas of the squares, he realised that the inner circle should be exactly half of the bigger circle in area. He knew that the area of the circle is proportional to the square of its radius and the above construction proves the same. By the same logic, just as the perimeters of the two squares, the perimeter of the outer circle should also be √2 times the perimeter of the inner circle. This proves the known fact that the perimeter of the circle is proportional to its radius. This led to an important observation by Baudhayana. That the areas and perimeters of many regular polygons, including the squares above, could be related to each other just as the case of circles.
2. Value of π
Baudhayana is considered among one of the first to discover the value of ‘pi’. There is a mention of this in his Sulbha sutras. According to his premise, the approximate value of pi is to 3.1416. in 499AD.
Several values of π occur in Baudhayana's Sulbasutra, since, when giving different constructions, Baudhayana used different approximations for constructing circular shapes.
Some of these values are very close to what is considered to be the value of pi today, which would not have impacted the construction of the altars. Aryabhatta, another great Indian mathematician, worked out the accurate value of π
3. The method of finding the square root of 2.
Baudhayana gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2. The measure is to be increased by a third and by a fourth decreased by the 34th. That is it’s diagonal approximately. That is 1.414216, which is correct to five decimals.
Baudhāyana (elaborated in Āpastamba Sulbasūtra i.6) gives the length of the diagonal of a square in terms of its sides, which is equivalent to a formula for the square root of 2:
samasya dvikaraṇī. pramāṇaṃ tṛtīyena vardhayettac caturthenātmacatustriṃśonena saviśeṣaḥ
Sama – Square; Dvikarani – Diagonal (dividing the square into two), or Root of Two
Pramanam – Unit measure; tṛtīyena vardhayet – increased by a third
Tat caturtena (vardhayet) – that itself increased by a fourth, Atma – itself;
Caturtrimsah savisesah – is in excess by 34th part
Baudhayana is also credited with studies on the following:
It can be concluded without a doubt that there is a lot of emphasis on rectangles and squares in Baudhayana’s works. This could be due to specific Yajna Bhumika’s, the altar on which rituals were conducted, for fire-related offerings.
Some of his treatises include theorems on the following.
In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90 degrees)
The diagonals of a rectangle are equal and bisect each other.
The midpoints of a rectangle joined forms a rhombus whose area is half the rectangle.
The area of a square formed by joining the middle points of a square is half of the original one.
Brahmagupta: mathematician and astronomer
Biography
Brahmagupta (598–668 CE)
The great 7th Century Indian mathematician and astronomer Brahmagupta wrote some important works on both mathematics and astronomy. He was from the state of Rajasthan of northwest India (he is often referred to as Bhillamalacarya, the teacher from Bhillamala), and later became the head of the astronomical observatory at Ujjain in central India. Most of his works are composed in elliptic verse, a common practice in Indian mathematics at the time, and consequently have something of a poetic ring to them.
It seems likely that Brahmagupta’s works, especially his most famous text, the “Brahmasphutasiddhanta”, were brought by the 8th Century Abbasid caliph Al-Mansur to his newly founded centre of learning at Baghdad on the banks of the Tigris, providing an important link between Indian mathematics and astronomy and the nascent upsurge in science and mathematics in the Islamic world.
In his work on arithmetic, Brahmagupta explained how to find the cube and cube-root of an integer and gave rules facilitating the computation of squares and square roots. He also gave rules for dealing with five types of combinations of fractions. He gave the sum of the squares of the first n natural numbers as n(n + 1)(2n + 1)⁄ 6 and the sum of the cubes of the first n natural numbers as (n(n + 1)⁄2)².