Today is Jayanthi of Nilkantha Somayaji one of the foremost mathematicians and astronomers of the Kerala school, known for his astronomical treatise Tantrasamgraha and a commentary on Aryabhatta.

One of the most famous schools of mathematics and astronomy in India was the Kerala school of maths and astronomy, founded by Madhava of Sangamagrama during the 14th century, who made pioneering studies in infinite series, calculus, trignometry, geometry and algebra

He was the first to use infinite series approximations for a range of trigonometric functions, which has often been regarded as a significant step to move from the finite step of ancient mathematics towards an inifinite limit.

Most of the mathematical discoveries of the Kerala school, came from an effort to solve astronomy problems. They also provided what is now considered the first example of a power series, two centuries before Europe invented calculus.

Nilkantha was born in a small village near Tirur in Mallapuram district on June 14, 1444. Though he personally claimed he was born on a Kali Day, 1,660,181, a reference to the Kali Yuga, as per his account his father was Jatavedasa and a brother named Sankara.

Again as per his own account Nilakantha Somayaji claimed he was a Bhatta belonging to the Gargya Gotra, and a follower of Asvalayana Sutra. And he belonged to the Kellalur family, his wife’s name was Arya, and he had two sons Rama and Dakshinamurthy.

While he had learnt the Vedanta under Ravi, it was Kottesora Damodara who initiated Neelakantha into astronomy and also basic principles of Maths computations.

Thunchaththu Ezhuthachan, the great Malayalam poet was believed to be his disciple. Nilalkantha got the title Somayaji, as he was assumed to have the performed the Somayajna ritual as per Namboodiri tradition.

He was a true polymath, with mastery over philosophy, grammar, astronomy, math. It’s believed that he could refer to a Mimamsa authority during a debate and also apply a grammatical dictum to same purpose.

Sundaraja a contemporary Tamil astronomer called him sad-darshani-parangata, one who mastered 6 Systems of Indian philosophy. His greatest work to date is Tantrasangraha, completed in 1501, which has around 8 chapters, written in Sanskrit.

In this work he revised Aryabhatta’s model for the center of Mercury and Venus, and it remained the most accurate till Kepler came up with his own laws. His seminal work contains the following chapters

Madhyama-prakaranam- Astronomical computation
Sphuta-prakaranam-Primarily on planets, RSine, sum of series of natural numbers
Chhaya-prakaranam – Sun’s position, and it’s use in computations.
Chandragrahana-prakaranam- On the Lunar Eclipse,

Ravigrahana-prakaranam- On the Solar Eclipse
Vyatipata-prakaranam- Longitudes of Sun and Moon
Drikkarma-prakaranam- Rising and setting of moon and planets
Sringonnati-prakaranam- Lunar cusp.

His other work is Aryabhatiyabhasya, a commentary on Aryabhatta’s work where he developed a computational system for a partially heliocentric model, where the planets orbit the Sun, which in turn moves around the Earth, similiar to Tyco Brahe’s system.

And also Jyotirmimamsa , where he outlines the methodology for astronomical and mathematical work, as also the Vedic influences in the astronomical work.

Some other important works by Nilakantha were
Golasara- Basic astronomical elements and process
Candrachayaganita- Calculation of time based on sun and moon’s shadow
Grahapariksakrama- Verification of astronomical observations.

It is not really possible for me to go into depth of Nilakantha Somayaji’s work, on astronomy and mathematics. This is only a very humble layman’s tribute to one of the great mathematicians we had in medieval times.