2015, Vol. 1, Issue 3, Part A

author(s)
V Ramesh Babu

abstract
Leonhard Euler (1707–1783) was a pioneering Swiss mathematician whose prolific work laid foundational stones across numerous branches of mathematics and physics. His contributions span analysis, number theory, calculus of variations, mechanics, and applied mathematics, profoundly shaping modern mathematical thought. Euler introduced the concept of a function and formalized the use of exponential and logarithmic functions, including their extension to complex numbers. He developed power series expansions for fundamental functions such as the exponential and inverse tangent, and solved classical problems like the Basel problem. Euler also pioneered analytic number theory by linking analysis and number theory, proving the infinitude of primes, and advancing the distribution of prime numbers. His introduction of notations such as ݑ’e, ݜˏ€, ݑ–i, and summation symbols standardized mathematical language. Despite losing his eyesight late in life, Euler authored hundreds of memoirs that influenced 18th- and 19th-century mathematics and continue to inspire contemporary research. His works include seminal textbooks and treatises that systematized calculus, mechanics, and differential equations, making him one of the most influential figures in the history of mathematics.