Nilakantha Somayaji lived from 1444 to 1544, spanning both the 15th and 16th centuries.

Nilakantha Somayaji is credited with deriving the Taylor series expansion for the sine and cosine functions, a fundamental concept in calculus.

Nilakantha Somayaji's most renowned work is the Tantrasangraha, an extensive treatise covering various mathematical and astronomical topics.

Nilakantha Somayaji introduced the concept of infinity in his mathematical work, a significant advancement in mathematical thought.

Nilakantha Somayaji primarily employed geometric methods to solve mathematical problems, demonstrating his expertise in geometry.

Nilakantha Somayaji successfully predicted a solar eclipse, showcasing his proficiency in astronomical calculations.

Nilakantha Somayaji derived various trigonometric identities, contributing to the advancement of trigonometry as a mathematical field.

Nilakantha Somayaji employed the method of exhaustion to approximate the value of pi, demonstrating his ingenuity in mathematical problem-solving.

Nilakantha Somayaji derived the product rule in calculus, a fundamental result used in differentiation.

Nilakantha Somayaji introduced the concept of the precession of the equinoxes in his astronomical work, demonstrating his understanding of celestial mechanics.

Nilakantha Somayaji emphasized problem-solving exercises in his teaching, encouraging students to apply mathematical concepts to real-world scenarios.

Nilakantha Somayaji utilized the concept of arithmetic progression to solve problems related to motion, demonstrating his understanding of mathematical sequences.

Nilakantha Somayaji derived the cubic formula, a significant achievement in the field of algebra.

Nilakantha Somayaji employed the factorial method to solve problems involving permutations and combinations, demonstrating his expertise in combinatorial mathematics.

Nilakantha Somayaji emphasized critical analysis of mathematical concepts, encouraging students to deeply understand the underlying principles rather than simply memorizing formulas.