Euler started school when he was 7 years old and was tutored by Johann Bernoulli, Rupee’s rearmost mathematician and family friend, who was hired by his father Bernoulli had a major influence on Lure’s passion for mathematics (Patterson, 1998). By the age of 13, Euler was attending lectures at the local university and in 1723 gained his Master of Philosophy with a dissertation comparing the natural philosophy systems of Newton and Descartes (Patterson, 1998). Euler continued furthering his education by enrolling in more classes and dedicating all of his spare time to studying mathematics (Patterson, 1998).
It wasn’t until 1727 that Lure’s talents began to be recognized (Patterson, 1998). It was here in SST. Petersburg where Euler began working on different theories, including the production of the human voice, sound and music, and the mechanics of vision (Patterson, 1998). He was also working on the telescopic and microscopic perception (Patterson, 1998). The construction of telescopes and microscopes was made possible because of the basis of Lure’s work (Patterson, 1998). Not too long after becoming the
Director of Mathematics at the Imperial Russian Academy of Sciences in 1731 ,Euler married Katharine Sell x (Wisped,2012). The couple had five children who survived childhood out of thirteen x (Wisped, 2012). Euler worked in nearly every area of mathematics including geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, and the lunar theory(Wisped,2012). He introduced the concept of a function, and was the first to write f(x) to denote the function f applied to the argument x (Wisped, 2012).
Later on Calculus became the focus of his studies (Wisped, 2012). He contributed to many great advances (Wisped, 2012). Analysis for his frequent use and development of power series, the expression of functions as sums of infinitely many terms is an advancement that Euler is well known for, such as (Wisped, 2012): From this formula, he proved the power series expansions for e and the inverse tangent function also known as cyclometers functions, which are ergonomic functions with suitably restricted domains (Wisped, 2012).