Leonhard Euler Research Paper

Abstract—This paper is a report on several of the 18th century’s greatest mathematicians, their investigations, and their monumental contributions in the area of integration. Even though calculus had significantly evolved, especially in the area of integration, a true theory of integration had not been derived. It was through the combined work of many brilliant minds that a true theory began to develop. Amongst these remarkable individuals were Leonhard Euler, Jean Baptiste Joseph Fourier, Augustin Louis Cauchy, and Georg Friedrich Bernhard Riemann to name a few.

Index Terms—Cauchy, Euler, Fourier, Integration, Riemann

I. INTRODUCTION
Throughout the 18th century much was accomplished in the area of calculus. Nevertheless, as new discoveries …show more content…
LEONHARD EULER (1707-1783)
Leonhard Euler, Fig 1, was born in Switzerland son of a Lutheran minister. Euler’s received his first education from his father and at the young age of 14 entered the University of Basel seeking a general education. Three years later, he earned his Master’s degree in philosophy having analyzed the many works and the philosophical viewpoints of Descartes and Newton. However, following his father’s wishes, Euler continued his education seeking a degree in theology with the intention of becoming man of the church. Nevertheless, this did not quite appease Euler and he found himself with the desire to pursue mathematics. After some persuasion by Johan Bernoulli, a friend of his father, Euler was allowed to study mathematics [4]. In 1726, he completed his studies and was soon offered a position as a teacher in St. Petersburg. In 1733, he was appointed the mathematics chair at the Academy [4]. He later married, fathering 13 children of which only 5 …show more content…
His paper Uber die Hypothesen welche der Geometire zu Grunde liegen, became a mathematical classic and his results were integrated into Einstein’s “relativistic theory of gravitation” [1].His ideas regarding “geometry of space” impacted the development of current day theoretical physics and his methods were used in the theory of relativity [3]. Riemann possessed an unparalleled originality in his work, and a plethora of concepts and theorems are named after him. He was crucial in clarifying the idea of the integral by defining what is now known as the “Riemann integral” [1].
Riemann’s contributions to mathematics were impressive and his famous Riemann hypothesis still remains unsolved. Sadly, Riemann perished at the young age of 40. All the same, he was a brilliant individual, who, unquestionably, would have made far greater contributions if not for his early decease.

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