Varahamihira, also known as Varaha or Mihira, is an Indian Mathematician who was born during the early 6th century. He was born in the Avanti region and brought up in Ujjain (Madhya Pradesh, India).
A meeting with the renowned scholar Aryabhata in Kusumapura inspired him to pursue studies in astronomy and astrology. He studied at Kapitthaka. He was one of the “Nine Jewels” of the court of Emperor Yashodharman Vikramaditya of Malwa.
Mathematician Varahamihira is renowned for compiling the Pancha-Siddhantika (Five Treatises), a comprehensive work that brings together astronomical knowledge from Greek, Egyptian, Roman, and Indian traditions.
Varāhamihira’s most well-known work was Brihat Samhita. This book is all about architecture, mathematics, gemology, temples, planetary motions, astrology, cloud formation, eclipses, timekeeping, rainfall, seasons, agriculture, and many other topics.
Some Mathematicians even believed that he had a strong knowledge of predictive calculations and zodiac signs. He used to perform astrological computations and auspicious ceremonies in India in those days. The 11th-century scholar Al-Biruni greatly admired Varahamihira and praised him as an outstanding astronomer.
An Interesting Story behind the name of Varahamihira.
The term Varaha means the boar (which is also the avatar of the Hindu god Vishnu), and the Term Mihira translates to Sun.
As per ancient texts, the King Vikramaditya rewarded Varaha-Mahira with the title ‘Varaha’. King Vikramaditya once asked Varahamihira to predict his son, but he was alarmed by Mihira’s prediction.
After deeply studying the prince’s horoscope, Mihira meditated and foresaw a grave danger to the prince’s life. He predicted that in his 18th year, on a specific day and month, the prince would be killed by a boar, and no human effort could prevent this fate.
It is said that Mihira never made any false predictions. Even though the king took every precaution to protect his son from all odds. But on the predicted day,i.e., on his 18th birthday, the prince was injured and disfigured by the iron hooves of an artificial boar, which was part of the royal emblem fixed to the flagpole, and died.
Vikramaditya honored Mihira with the royal emblem in recognition of his knowledge. From then on, he became known as Varaha Mihira.
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
The five Systems Included in this Treatise are:
Paitamaha Siddhanta – One of the oldest known Hindu astronomical texts, it had a strong influence on later works like Aryabhatiya and Surya Siddhanta.
Romaka Siddhanta – Thought to be inspired by ancient Greek astronomy, though the identity of its author remains unknown.
Surya Siddhanta – Traditionally linked to Latadeva, but the text itself credits its authorship to Mayasura (also known as Mamuni Mayan).
Paulisha Siddhanta – Named after Paulisa of Saintra, this text was authored by Paulisa and reflects Western astronomical thought.
Vasishtha Siddhanta – Attributed to Vishnucandra, this work is named after a star in the Great Bear constellation.
Through Pancha-Siddhantika, Varahamihira preserved and shared the essence of these five important astronomical traditions, making it a treasured text in the history of Indian science.
In this book, he writes about mathematical astronomy and talks about ayanamsa, or the shifting of the equinox is 50.32 seconds. He was the first Mathematician to speak about ayanamsa.
2. Brihat-Samhita
This is the second book written by Varahamihira. This book has 106 chapters, and hence this book is also called “great compilation”. This book is all about divination.
He even writes about other topics like astronomy, clouds, planetary movements, rainfall, eclipses, growth of crops, matrimony, gems, pearls, architecture, manufacture of perfume, domestic relations, and rituals.
It is said that many of his books have been lost. The Arab Travelers Ibn Batuta and Al Baruni, who came to India to learn Vedic Mathematics, have translated their book into different languages.
3 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.
4 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 analysed 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.
Contributions of Varahamihira in 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.
1) Sine tables were created by Aryabhata but were improved by Varahamihira.
2) He developed the algebraic properties of zero and negative numbers.
3) He was also one of the first mathematicians to discover a different form of Pascal's triangle.
4) It was used to compute the binomial coefficients.
5) His book Brihat-Samhita presented a systematic treatment of algebraic equations, including quadratic equations.
6) He was the first to discover the 4x4 magic square.
Interesting facts about Varahamihira
Though he was a Mathematical Astronomer, He had an interest in other fields too.
1) It is said that Varahamihira had constructed the “Meru Stambh”.
2) He proposed that planets and the Moon are lustrous due to sunlight, but not because of their light.
3) He even said that the Earth was spherical.
4) He penned all three main sections of Jyotisha astrology.
5)He was one of the earliest mathematicians to come up with a pattern similar to what we now call Pascal’s Triangle.
6) He was a great astrologer and astronomer. He used to see the positions of stars, the sun, the moon, and planets, and used to predict many things.
7) He explained how zero and negative numbers work in calculations and described the rules for using both positive and negative numbers in algebra.
8) He studied how light behaves when it bounces off surfaces (reflection) and when it passes through materials (refraction), describing these effects as the result of particles either bouncing back or passing through objects.
About Varahamihira Life and Family
Varahamihira lived for 80 years and had many interesting stories associated with his life. His son, Prithuyashas, also became a well-known astrologer.
He wrote two important works—Horasara, a key text in birth chart (natal) astrology, and Shatpanchashika, which focuses on Prasna (a branch of astrology that answers specific questions). While Varahamihira’s own writings were brief and to the point, Horasara was written to explain his teachings in more detail and make them easier to understand.
How did he get the name Varahamihira?
The term Varaha Means the boar (is the avatar of the Hindu god Vishnu) and the Term Mahira Means Talented.
There is a story behind this name
The then king has rewarded Varaha-Mahira with the title ‘Varaha’. King Vikramaditya was alarmed by Mihira’s prediction. King looked around the crowded court and asked in agony, “Can it be true?” No one responded to the king’s question. Breaking the silence, Mihara sadly said, “As per the position of the planets, the prince will die at the age of 18.”
Queen cried and said to the king, “My lord, you should see to it that this prediction proves false.”
It is said that Mihira never made any false predictions. Even though the king took every precaution to protect his son from all odds. But on the predicted day,i.e on his 18th birthday, the prince was been killed by a boar. From that day itself, he was been named as Varaha-Mahira.
