Science & Technology Scholars in Vedic, Post-Vedic and Ancient India

Vedic age marked a new era of development in the field of science and technology. During Vedic times science developed out of religious plane. Vedic people influenced the growth of Indian science. Understanding real-world phenomenon in rational and scientific way started with study of natural phenomenon in the context of rainfall, appearance of the sun, the moon, changes in season and agriculture. This naturally led to theories about physical processes and the forces of nature that are today studied as specific topics within different branches of physical science.

Later advancements in the field of mathematics, astronomy, astrology, medicine, surgery etc. during ancient India were significant by all standards. It can be understood by the contributions made by scholars in different field /subjects.

Sushruta

Rishi Sushruta lived in circa 6^th century BC and belonged to clan of Rishi Vishwamitra. He wrote Sushruta Samhita, which throws light on several achievements of ancient Indians in field of medical science. This treatise has one of the earliest mentions of leprosy, cataract surgery, rhinoplasty etc. Sushruta is sometimes called the father of plastic surgery and general surgery.

Charaka

Charaka was a major contributor to Ayurveda system of Medicine and author of Charaka Samhita.

Panini

During the 5th century BC, the scholar Panini made several discoveries in the field of phonetics, phonology and morphology.

Pingala

Pingala was a BC era mathematician who used binary numbers in the form of short and long syllables, very much similar to Morse code in current times. This indicates his deep understanding of arithmetic. Binary representation has now become the basis of information storage as sequences of 0s and 1s in modern-day computers. Pingala’s work also contains the basic ideas of what we know now as Fibonacci number and a presentation of the Pascal’s triangle.

Aryabhatta-I

Aryabhatta-I, the legendary mathematician was a resident of Patliputra, (5th century AD, Gupta Era). He collected existing concepts and developed the algebraic theories and other mathematical concepts. He wrote a mathematical treatise named Aryabhattiya (circa AD 499) and referred to Algebra as Bijaganitam. He successfully calculated the value of pi and this was much more accurate than the value calculated by the Greeks and is very dose to the present value accepted by mathematicians. In trigonometry, he concluded for a triangle, the result of a perpendicular with the half-side is the area. He also worked on the motions of the solar system and calculated the length of the solar year to 365.8586805 days.

His work Aryabhatiyam sketches his mathematical, planetary, and cosmic theories. This book is divided into four chapters:

• The astronomical constants and the sine table
• Mathematics required for computations,
• Division of time and rules for computing the longitudes of planets using eccentrics and epicycles,
• The armillary sphere, rules relating to problems of trigonometry and the computation of eclipses.

Aryabhata took the earth to spin on its axis; this idea appears to have been his innovation. He also considered the heavenly motions to go through a cycle of 4.32 billion years; here he went with an older tradition, but he introduced a new scheme of subdivisions within this great cycle. According to the historian Hugh Thurston, Not only did Aryabhata believe that the earth rotates, but there are glimmerings in his system (and other similar systems) of a possible underlying theory in which the earth (and the planets) orbits the sun, rather than the sun orbiting the earth. The evidence is that the basic planetary periods are relative to the sun. That Aryabhata was aware of the relativity of motion is clear from this passage in his book “Just as a man in a boat sees the trees on the bank move in the opposite direction, so an observer on the equator sees the stationary stars as moving precisely toward the west.”

In his book named ‘Aryabhattiyam’, Aryabhatta has given lot of references of Suryasidhanta. He had developed instruments like chakra yantra (disk instrument), Gola yantra (type of armillery sphere) and shadow instruments.

Aryabhatta deduced that earth is a rotating sphere: the stars do not move, it is the earth that rotates. Its diameter is 1,050 yojanas. Its circumference is therefore 1050 x 13.6 x π = 44,860 km.

Aryabhatta also deduced that: “The moon eclipses the sun, and the great shadow of the earth eclipses the moon.”

Varahamihira (500 AD)

Varahmihira has done a valuable job of compilation of five astronomical theories, which were in use before Christ, and suryasidhanta is one of them. This compiled book is known as ‘Panchasidhanta’. He had developed some ring and string instruments.

Brahmagupta (598–668 AD)

Brahmagupta (598–668 AD) wrote important treatise on mathematics and astronomy in Brahamasphutasiddhanta in 628 AD. He gave solutions for the general linear equation, two equivalent solutions to the general quadratic equation, explained how to find cube and cube root of an integer, rules for facilitating the computation of squares and square roots and gave rules for dealing with five types of combinations of fractions.

He was able to find (integral) solutions of Pell’s equation. Brahmagupta’s most famous result in geometry is his formula for cyclic quadrilaterals, a theorem on rational triangles and values of (pi).

In chapter seven of his Brahmasphutasiddhanta, entitled Lunar Crescent, Brahmagupta rebuts the idea that the Moon is farther from the Earth than the Sun, an idea maintained in scriptures. He does this by explaining the illumination of the Moon by the Sun.

Bhaskara-I

Bhaskara-I was a 7th-century Indian mathematician, who was apparently the first to write numbers in the Hindu decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata’s work. This commentary, Aryabhatiyabhasya, written in 629 CE, is the oldest known prose work in Sanskrit on mathematics and astronomy. He also wrote two astronomical works in the line of Aryabhata’s school, the Mahabhaskariya and Laghubhaskariya.

Lalla (700 AD)

Lalla was an astronomer and mathematician who followed the tradition of Aryabhata-I and wrote Shishyadhividdhidatantra. He was well known because of twelve instruments which he brought into practice.

Vachaspati Misra (circa. AD 840)

Vachaspati anticipated solid (co-ordinate) geometry eight centuries before Descartes (AD 1644).

Brahmadeva

Brahmadeva (1060–1130) was an Indian mathematician. He was the author of Karanaprakasa, which is a commentary on Aryabhata’s Aryabhatiya. Its contents deal partly with trigonometry and its applications to astronomy.He was well known and intelligent scientist.

Halayudha (10 Century AD)

Halayudha was a 10th-century Indian mathematician who wrote the Mritsanjivani, a commentary on Pingala’s Chandashastra, containing a clear description of Pascal’s triangle, which was expressed as Meru Prastara (Staircase of Meru)

Bhaskara-II (Born 1114)

Bhaskara-II was a 12th century astronomer mathematician. He authored several mathematical treatises. The most important being Siddhanta Siromani. This has four parts :

• Leelavati-Named after his daughter deals with arithmetic and geometry.
• Bijaganita-has contents related to algebra and has a chapter that deals with fundamental operation with positive and negative quantities with zero, solving many types of equations including quadratic equation.
• Grahaganita-deals with astronomy.
• Goladhyaya-deals with astronomy.

He was the first to conceive the concept of differential calculus. He was also well versed in geometry and has given many theories concerning topics like the calculation of altitude, area of triangle and quadrilaterals. He gave formula for calculating area of circle in terms of the chord and vice-versa. The method of graduated calculation was documented in the book entitled the Five Principles (PanchSiddhantika). Bhaskara-II has been called the greatest mathematician of medieval India. He contributed to the fields of mathematics, arithmetic, algebra, trigonometry, calculus, astronomy and engineering. Conceptual design for a perpetual motion machine by Bhaskara II dates to 1150 AD. He described a wheel that he claimed would run forever. He 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.

Madhava

Madhava (c. 1340-1425) developed a procedure to determine the positions of the moon every 36 minutes. He also provided methods to estimate the motions of the planets. He gave power series expansions for trigonometric functions, and for pi correct to eleven decimal places.

Nilakantha Somayaji

Nilakantha (c. 1444-1545) was a very prolific scholar who wrote several works on astronomy. It appears that Nilakantha found the correct formulation for the equation of the center of the planets and his model must be considered a true heliocentric model of the solar system. He also improved upon the power series techniques of Madhava. The methods developed by the Kerala mathematicians were far ahead of the European mathematics of the day