__MATHEMATICS, ASTRONOMY AND MEDICINES IN ANCIENT INDIA__

__Contents__

· Introduction

· Early settlements

· Mathematics, Astronomy and Medicines

__Mathematics__

· Zero

· Decimal System

· Algebra

· Geometry

· Trigonometry

· Pi (π)

__Astronomy__

· Rotation of earth

· Sidereal Astronomy

· Eclipses

· Other astronomical inventions

__Medicines__

· Sushruta Samhita

· Charaka Samhita

__Introduction__

It is true that the major modern inventions in the field of science and technology are reflections of Vedic knowledge. They speak of the facts that were already mentioned in the *Vedas *over thousands years back. The modern replicas of scientific theories are in similitude with ‘revealed’ explanations of the Vedic scriptures.

Any Vedic slokah reveals more than one meaning. For instance, an encrypted slokah in the 10^{th} text of the *Rig Veda *apparently speaks in praise of Lord Indra. However, the slokah – when translated in a technical manner – unfolds the value of pi up to an impressive 28 digits. The accuracy of this calculation is quite fantastic which would even fail any modern-day computer. With great effort, today’s scientists have made the calculation of pi possible on computer, and that too only till 16 digits!

Important inventions in the field of science and technology in ancient India are described as follows –

__Early Settlements__

Ancient civilizations had uniquely combined their social and religious values with the knowledge of science and technology. Earlier civilizations blended science and technology in their daily utilities, and that too without causing any harm to the ecological system. Applied science already bloomed as mainstream engineering during Indus Valley Civilization (The Bronze Age culture à 2600-1750 BC). The archeological survey remains have shown the following mainstream developments during Indus Valley Civilization –

· Scientific irrigation

· Modern metallurgy

· Fired bricks and pottery making

· Measurements of areas and volumes

Later the Aryans invaded the Indus Valley Civilization (Indo-Aryan migration 1500-1200 BC). It is believed that the decendents of the Aryans later wrote the classic Vedic manuscripts.

__Mathematics, Astronomy and Medicines__

The rising years of Anno Domini – especially between 500-1200 AD – brought out significant achievements in the field of mathematics, astronomy and medicines. Ancient mathematics or Ganita included arithmetic, algebra, astrology, geometry and astronomy. As per Chinese records, many books written during the 9^{th} and 10^{th} centuries, such as *Brahmagupta’s Sidhanta*, *Charaka Samhita, *and* Susrata Samhita* were translated into Arabic, and later from Arabic to many other languages including German.

__Mathematics__

Major inventions in mathematics took place during the Gupta period. The most primitive inscriptions of nine digits and a zero were found dated as early as 595 AD. Apparently, this numerical system was in use quite before its date of inscription.

__Zero__ – Some historians believe that Zero was in usage amongst the ancient Indian intellectuals since 2^{nd}century AD. Zero was considered as a separate number during those times. However, many scholars and historians also opine that it was Aryabhata (476–550 AD) who first introduced the concept of ‘Zero’ in his mathematical theories. Unfortunately, he did not document his invention in good order. Later, based on his book *Aryabhatia* and its commentaries, the first official usage of the zero was made in 873 AD.

__Decimal System__ – The epigraphic records of the decimal system is of the 5^{th} century AD. The numerals were used in India long before they were introduced in the western countries. The earliest inscriptions of numerals were found of the 3^{rd} century AD, belonging to the times of Ashoka the Great.

Archeological records prove that the Indians were the first to invent and start the usage of decimal system. It is believed that Bhaskara I (600-680 A.D.), an eminent mathematician and commentator of *Aryabhatia* (629 AD), mentioned in his Sanskrit prose the usage of sine and decimal system (with a circle as zero). From India, the decimal system had spread to Buddhist, Chinese and Arabs; and from Arabs to the western world.

__Algebra__ – Both Indians and Greeks are believed to have contributed to the development of Algebra. However, Algebra was passed on to Western Europe from the Arabs who borrowed it from India. The plethora of subjects covered in Aryabhata’s book *Aryabhatia *also includes interesting solutions in algebra. Bhaskara II (1114 – 1185 AD) – the commentator of Aryabhata’s works – has also further explained the theory of Bijaganita (Algebra) in his book *Siddhanta Shiromani*.

__Geometry__ – In the 2^{nd} century BC a renowned scholar Apastamba offered significant help in the field of practical geometry in the construction of altars for grand sacrifices at king’s court. Through his altar graph Apastamba solved important problems on acute angle, obtuse angle, right angle and many more.

__Trigonometry__ – Aryabhata led to the invention of trigonometry when he first devised the theorem for finding the area of a triangle. He became the foremost proponent of trigonometry and was the first to calculate the sine formulae for the angle greater than (<) 90°. He used a table of sine difference which was subjected to extensive research amongst his successors and commentators. He also played with sine, cosine, and inverse formulas to mould the base of trigonometry for specific needs. The logic of versine = 1 – cosine was also introduced by him.

__Pi (π)__ – To quote Aryabhata what he has written in one his books about the calculation of Pi, “Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given.” Thus, he helped many succeeding scholars in solving tough indeterminate equations by determining the value of Pi (π) as 3.1416.

__Astronomy__

Initially, during the Vedanta period primitive astronomy started taking place for finding suitable dates and times for conducting periodical sacrifices. Astronomy was initially jumbled with Jyotisha (astrology), but eventually gained its individuality as the study of stars and sun. The Greek influence in the growth of Indian astronomy was evident as Greek astronomical terminology was translated in Sanskrit. Erudite scholars like Aryabhata (*Aryabhata-siddhanta* in 6^{th} century) and Varahamihira (*Romaka Sidhanta* in 7^{th} century) first explored astronomy in India via their arithmetical and computational abilities. However, western astronomy introduced the concept of Zodiac, a seven-day week, 60 minutes an hour etc. in India.

__Rotation of earth__ – Aryabhata first put forward his theory of epicycles, describing how rotation of earth takes place around its axis contrary to the stars which are fixed in the space.

__Sidereal Astronomy__ – Aryabhata’s sidereal rotation period of the earth stood at 23 hours, 56 minutes 4.1 seconds. (Presently, it stands as 23 hours, 56 minutes 4.091 seconds.)

Aryabhata’s sidereal year was calculated as 365 days 6 hours 12 minutes 30 seconds. (Presently, it is 365 days 6 hours 9 minutes 10 seconds).

__Eclipses__ – Aryabhata explained solar and lunar eclipses as the consequences the intersection of either orbital planes or earth-sun or earth-moon at lunar nodes. His theories on reflections and elliptically shaped planetary orbits provided new dimensions in the field of astronomy eradicating the age old superstitions related to pseudo-planetary demons (such as Rahu and Ketu).

__Other astronomical inventions__ – Brahmagupta (598 – 668 AD), in his book *Brahmasphuta siddhanta* in 628 AD, made interesting astronomical advances especially in number systems and algorithms for square roots. He also found solutions with the applications of quadratic equations. Bhaskara II (1114 – 1185 AD) in his book*Siddhanta Shiromani* in 1150 AD wrote extensively on Grahaganita i.e. Mathematics of the planets 365-Day Year, and Goladhyaya i.e. Astronomy and Spheres.

__Ayurveda (Medicine)__

Ayurveda was originally written in the *Atharva* *Veda*, one of the four *Vedas*. Around seven hundred Vedic hymns in *Atharva Veda *refer to Ayurvedic topics. Since, the medicines prescribed in the hymns are supplied with spells and magical charms, their method could not quite grow along the scientific lines. Though, historical records show that since 800 BC, medicine became a major subject of research at Varanasi and Taxila study centers. The former specialized in surgical procedures. The physicians or Vaidyas were venerable members of the society and were given higher status in the social hierarchy.

Two ancient scholars who made their names in the field of the Ayurvedic healing system were Sushruta and Charaka. Sushruta wrote *Sushruta Samhita* which, till today, acts as a reference for Ayurvedic scholars researching on various surgical and diet methods for patients. There are around 121 surgical applications mentioned in *Sushruta Samhita, *including the very critical stone surgery. As per the facts, *Sushruta Samhita*was later compiled in the 4^{th} century AD by its followers.

*Charaka Samhita* authored by the 2^{nd} century Ayurvedic practitioner Charaka is considered as an encyclopedia of Indian medicines. The text mentions different types of illness including leprosy, tuberculosis, hysteria and fever. It also describes the efficient usage of various plants and herbs in various treatments. Along with ancient medicines, *Charaka Samhita *is also used for the study of chemistry. Based on *Charaka Samhita*, major developments in Indian medicines took place in the subsequent years. The Vedic hymns in the text attribute several diseases to spirits and demons. The hymns also correctly prescribe the remedies for the symptoms of pulmonary tuberculosis, and for problems linking dropsy to heart diseases.

*Charaka Samhita *and *Sushruta Samhita *eventually got translated in other Asian languages including Manchurian and Tibetan. In the 8^{th} century AD both the *Samhitas* greatly influenced Arabs who passed on the knowledge to the Europeans. *Charaka Samhita* was translated in the Arabic language in the year 1550 AD.

Functions of lungs, spinal cord and existence of other internal organs, including nervous system, were also discovered by the ancient Indians. Though the roots of surgery can be traced to Vedic period, it was since the time of Sushruta, different surgical methods started getting prominence in medicines. For child birth, various surgeries were performed for extracting the fetus out of the womb and this included c-section and caesarian. Other sophisticated surgeries were nose, ear, lip plastic surgeries; fistula treatment; and stone removal from bladder. It is believed that the ancient doctors had very little knowledge on the true functions of the brain and its psychological functions.

Despite these achievements, ignorance of physiology and anatomy greatly hampered the growth of medicine in ancient India. Also, touching the dead bodies was considered a taboo by many during those times – a serious situation which hampered medical growth.