Varahamihira, also known as Varaha or Mihira, was a distinguished philosopher, astronomer, and mathematician of sixth-century India, remembered as one of the “Nine Jewels” in the court of King Yashodharman Vikramaditya of Malwa. Residing in Ujjain during the Gupta Empire, he authored foundational works such as the Pancha-Siddhantika, Brihat Samhita, Brihat Jataka, Laghu Jataka, and Yogayatra. In the following discussion, we will be exploring Varahamihira’s historical background, major works, contributions to mathematics and astronomy, his influences, and lasting legacy.
In this article, we shall discuss the Varahamihira; An Indian Mathematician, His Background, Contributions to Mathematics, Major Works, Influences of Varahamihira, & More!
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Who was Varahamihira?
Varahamihira was a prominent scholar of the sixth century CE during the reign of Gupta Empire who made significant contributions to astronomy, mathematics, and astrology.
- He wrote several books on these topics, including the well-known "Pancha Siddhantika," which deals with the five astronomical canons providing a summary of Hellenistic , Roman, Egyptian, and Indian astronomical knowledge.
- He also wrote the extensive treatise "Brihat Samhita," which covers astrology, architecture, planetary motions, cloud formation, eclipses, timekeeping, rainfall, seasons, agriculture, and many other subjects.
- He made his findings in the "Bruhad Samhita" and "Bruhad Jatak," which cover geography, constellations, science, botany, and animal science.
- He studied Greek and praised the Greeks (Yavanas) in his writing for being "highly schooled in the sciences" while being impure in terms of the religious order.
- Some academics believe he is a strong candidate for understanding and popularising the zodiac signs, astrological calculations, and auspicious ritual predictions.
- Ibn Batuta and Al Baruni, two famous Arab explorers, travelled to India specifically to study astrology.
Historical Background of Varahamihira
Varahmihira was born to a Brahmin family in Kapittha, near Ujjain, in present-day Madhya Pradesh. Varahamihira learned astrology from his Sun god-worshiping father, Adityadisha. Varahamihira met the eminent astronomer and mathematician Aryabhata during a trip to Kusumapura. Thus, He decided to pursue a career in astrology and astronomy.
- During the Gupta Empire, Ujjain was the epicentre of learning, with several schools of art, science, and culture flourishing.
- He decided to move to Ujjain, where scholars from all over the world were gathered to study astrology and mathematics.
- Finally, Chandragupta II or Vikramaditya recognised his aptitude for astrology, and appointed him as one of the Nine Gems (Navaratnas) of his court.
- However, this claim was made for the first time in a much later text, and scholars now question its authenticity because neither Varahamihira nor Chandragupta II lived in the same century, nor did Varahamihira live in the same century as many of the other people on the listed in "nine jewels," such as Kalidasa, Harisena, etc.
- In one of his writings, he claims to have received his education at Kapitthaka.
- According to Indian tradition, Varahamihira is believed to be a part of the nine jewels or “Navaratnas” at the court of Malwa king Yashodharman Vikramaditya.
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Major Works of Varahamihira
Varahamihira's literary works significantly impacted the development of Indian literature, astronomy, and astrology, and they are still studied and appreciated by scholars and practitioners today. His writings cover various subjects, including astronomy, mathematics, and astrology. Brihat Samhita, Brihat Jataka, Laghu Jataka, Pancha-siddhantika, Surya Siddhanta, and Yogayatra are some of his major literary works.
Pancha-siddhantika
Pancha-Siddhantika, or "Treatise on the Five Astronomical Canons," is one of the most important works of Varahamihira, an ancient Indian astronomer and mathematician. It is considered one of the most important texts on Indian astronomy and a valuable contribution to the field of ancient Indian science.
- The book covers many topics, including planetary motions, eclipses, solstices and equinoxes, celestial measurements, and other astronomical phenomena.
- It was written around the year 575 CE. It is based on Hellenistic and Vedanga Jyotisha astronomy (having Greek, Egyptian, and Roman elements).
- The book is a summary of five previous works on mathematical astronomy by five different writers, including
- Paitamaha Siddhanta: It is one of the earliest known Hindu astronomical texts and significantly influenced later works in the field, such as the Aryabhatiya and the Surya Siddhanta.
- Romaka Siddhanta: It is the second Siddhanta of Astronomical Siddhantas in Ancient Indian Astronomy and is thought to be based on earlier Greek astronomical knowledge transmitted to India. However, the specific author or authors of the Romaka Siddhanta are unknown.
- Surya Siddhanta: It was thought to have been penned by Latadeva, but it was written by Mayasura, also known as Mamuni Mayan, as stipulated in the text itself.
- Paulisha Siddhanta: It is named after Paulisa of Saintra and was written by Paulisa.
- Vasishtha Siddhanta: It was written by Vishnucandra and was named after one of the Great Bear's stars.
Brihat-samhita
This is a comprehensive work on astronomy, astrology, architecture, gemology, agriculture, mathematics, gemology, fragrances, seasons, cloud formation, rainfall, and other subjects. It is regarded as one of the most important works of ancient Indian literature.
Brihat Jataka
It is a well-known Hindu astrology text that covers the field of horoscopy. It contains in-depth information about the various planetary positions and their effects on human life. Its shorter version is known as Laghu Jataka, which provides an overview of the science of horoscopy.
Surya Siddhanta
Prior to 1000 BC, people in India initiated the use of astronomical instruments, coinciding with the creation of the well-known book for astronomical calculations called the 'Suryasidhanta.' Translated as the 'sun theory,' it involves measurements of star and planet positions. Subsequently, Indian mathematicians developed their instruments and methodologies to comprehend the 'Suryasidhanta' theory. A notable contribution from this period is the introduction of zero in mathematics and the decimal method of calculation. Varahamihira critically analyzed the 'Surya Siddhanta' alongside his other panchsiddhantika treatises, including Paitamaha Siddhantas, Paulisha Siddhantas, Romaka Siddhantas, and Vasishta Siddhantas. Additionally, Aryabhata's writings make references to the Surya Siddhanta.
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Varahamihira’s Contributions to Mathematics
Varahamihira is widely recognised for his contributions to trigonometry (trikonamiti) formulae. He invented new methods for calculating the sine (jya) and cosine (kojya) functions, as well as the cotangent and versine functions. Further, He improved the accuracy of Aryabhata's sine tables.
- He developed the algebraic properties of zero and negative numbers.
- He was also one of the first mathematicians to discover a different form of Pascal's triangle.
- It was used to compute the binomial coefficients.
- His book Brihat-Samhita presented a systematic treatment of algebraic equations, including quadratic equations.
- He was the first to discover the 4x4 magic square.
Trigonometry
Varahamihira refined Aryabhata's work by improving the accuracy of the sine tables, making trigonometric calculations more precise.
Combinatorics
He is credited with creating the earliest known 4×4 magic square, showcasing his expertise in mathematical arrangements.
Optics
Varahamihira made notable contributions to early physics by explaining that reflection occurs due to the backward scattering of particles. He also described refraction as the bending of light when it passes into a new medium, caused by the ability of particles to enter the spaces within that medium, similar to how fluids seep through porous materials.
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Varahamihira’s Other Important Contributions
Varahamihira also made significant contributions to geology, metrology, and ecology.
- He made contributions to meteorology research. He wrote about weather patterns, cloud formation, rainfall (monsoon), and how to predict the weather using astronomical observations.
- In addition, he wrote a lot. His command of the Sanskrit language and poetic rhythm enabled him to express himself uniquely.
- He claimed that termites and plants could detect underground water.
- His works, including the Pancha Siddhantika (Five Principles), the Brihatsamhita (Master Collection), and the Brahjataka (Astrological work), have brought him up to the same level of astrology as Kautilya, Manu, and Panini in terms of political philosophy, law, and grammar.
- Inshort, His comprehensive knowledge and fascinating delivery of even the most boring subjects, like astronomy, helped him become well-known.
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Influences of Varahamihira
The Romaka Siddhanta (The Doctrine of the Romans) and the Paulisa Siddhanta are two Western works that influenced Varahamihira's philosophy.
- The Paulisa Siddhanta is frequently misinterpreted as a single work attributed to Paul of Alexandria (c. 378 CE).
- However, this theory has been rejected by other experts in the field, most notably David Pingree, who stated that; “…the identification of Paulus Alexandrinus with the author of the Paulia Siddhanta is totally false”.
- Many of his works are linked to earlier texts, such as Vedanga Jyotisha.
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Legacy of Varahamihira
Varāhamihira earned renown as the foremost writer on jyotisha even after his demise, with his works surpassing nearly all earlier Indian texts in this field. Many subsequent Indian astrologer-astronomers praise him and consider his works as primary sources. The 11th-century writer Al-Biruni holds him in high regard, describing Varāhamihira as an exceptional astronomer.
Varahamihira was one of the finest minds in ancient India whose work included astronomy, mathematics, astrology, ecology, and literature. His texts like the Pancha-Siddhantika and Brihat Samhita not only comprehensively synthesized the knowledge of India but also incorporated Greek, Roman, and Egyptian traditions, which demonstrated the cosmopolitan nature of idea exchange during the Gupta era. With his development of trigonometry, algebra, astronomical computation, and astrosciences, he established a foundation that inspired Indian as well as foreign scholars for centuries. His enshrinement as one of the "Nine Jewels" reflects his position in the intellectual history of India. Varahamihira's life and achievement reflect scientific, cultural, and knowledge-oriented zeal of the Gupta period—an era justifiably declared the "Golden Age of India."
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