Nilakantha Somayaji lived in the 15th century.

Nilakantha Somayaji's most famous work is Tantrasamgraha, a comprehensive treatise on various branches of mathematics.

Nilakantha Somayaji discovered the concept of calculus, which is a branch of mathematics that deals with rates of change.

Nilakantha Somayaji used the Nilakantha series to approximate the value of π.

The formula for the Nilakantha series is $$\pi = 3 + \frac{4}{2 \cdot 3 \cdot 4} - \frac{4}{4 \cdot 5 \cdot 6} + \frac{4}{6 \cdot 7 \cdot 8} - \cdots$$.

The value of π approximated by the Nilakantha series up to 10 terms is 3.141592653589793.

Nilakantha Somayaji studied all of the trigonometric functions, including sine, cosine, and tangent.

Nilakantha Somayaji discovered the sum-to-product identity, which states that $$\sin A + \sin B = 2 \sin \frac{A + B}{2} \cos \frac{A - B}{2}$$.

Nilakantha Somayaji studied all of the algebraic concepts, including quadratic, cubic, and quartic equations.

Nilakantha Somayaji used the method of completing the square to solve quadratic equations.

Nilakantha Somayaji did not develop a method to solve cubic equations.

Nilakantha Somayaji did not develop a method to solve quartic equations.

Nilakantha Somayaji's work had a significant impact on the development of mathematics in India.

Nilakantha Somayaji's mathematical discoveries were largely forgotten until the 20th century.

D. D. Kosambi rediscovered Nilakantha Somayaji's work in the 20th century.