Leonhard Euler: Swiss man famous for mathematics, and not his chocolate

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1 1 Jose Cabrera Dr. Shanyu Ji Math October 2016 Leonhard Euler: Swiss man famous for mathematics, and not his chocolate Leonhard Euler - one of the most revolutionary figures in 18th century mathematics. His contributions to mathematics vary from a wide range of analytic geometry, algebra, 1 trigonometry, calculus, number/graph theory, and even combinatorics. He has worked on 2 numerous papers that he is said to have produced on average one mathematical paper every week. Leonhard Euler ( ) 1 The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler in 1736 laid the foundations of graph theory and prefigured the idea of topology. 2 Euler was the most prolific mathematical writer of all times - finding time to publish over 800 papers in his lifetime.

2 2 Our famous mathematician was born in Basel, Switzerland in His father, Paul Euler, studied theology at the University of Basel and thus Euler was expected to follow in his father s footsteps at the time. However, Euler s talents lead him to a different path and lifestyle that lead his to become one of the greatest mathematicians of all time. University of Basel in Switzerland Euler s helped his son learn the way of the church and sent him to the University of Basel to prepare him for the ministry. At age 14, Euler entered the University of Basel in Here, Euler met Johann Bernoulli, a great active mathematician in the world during the time (see lecture 29). Bernoulli became a mentor to Euler and was a great effect on his life. Bernoulli 3 trained him and would suggest that he read regularly and come to him only when he was struggling to understand difficult points. Euler s education was not limited only to the study of mathematics and theology. In , Euler completed his Master s degree in Philosophy. Euler s father wanted him to continue pursuing theology (follow his footsteps), but he was passionate about the subject when in 3 He was freely able to go to him on Sundays. 4 Philosophy : The study of the fundamental nature of knowledge, reality, and existence, especially when considered as an academic discipline.

3 3 comparison to mathematics. In 1727, Euler published and submitted an entry for the 1727 Grand Prize of the Paris Academy. At age 20, he earned second place for this essay submission - an incredible feat for a person of his age. Moving forward a couple of years later, we begin to see a phase of Euler s life that would 5 make him notably famous. In 1734, Leonhard solved the Basel Problem. The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite series: Euler used calculus and substitution to obtain a solution. He first attempted to represent the series as the following integral: But arrived at a more modern solution that would give a more accurate accurate approximation: 5 The Basel problem is a problem in mathematical analysis with relevance to number theory, first posted by Pietro Mengoli in 1644.

4 4 The series is approximately equal to Euler announced this discovery in 1735 for the 6 world to know. This problem attacted much attention from mathematicians during that time that it brought him fame at only the age of 28. After completing his first major contribution to mathematics, Euler s next famous contribution to mathematics was amicable numbers. Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. 7 When two numbers meet this condition (see footnote 7) mutually, they are called amicable. Euler found an equation and discovered 59 pairs. After a bit of experiment and error, Euler arrived at the following formula: In 1738, Euler s eyesight began to deteriorate. This meant that his vision (and possibly) his path would be closed from the world of mathematics. In 1771, Euler was completely blind and thus lead him to zero visionary aid from his eyesight. However, Euler paid no attention to his crippling ability as he diligently continued to work on his mathematical studies. In fact, he had an increase in mathematical output (probably from zero visual distractions and his incredible memory to go along with it). 6 The problem proposed in 1644 did not have a solution for almost 100 years! We could see why Euler has fame for solving an unsolved problem. 7 A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.

5 5 On September 18, 1783, Euler tackled the mathematics of Uranus and its orbit. However, on that afternoon, he suffered a massive hemorrhage and passed away. Euler was a master of mathematics, science, and philosophy. His discoveries and contributions to the world impacted almost every field of mathematics and sciences. Euler s 8 Identity which was named the Most Beautiful Mathematical Formula Ever. It s this very strip of mathematical genius that gives him the title of Master of us all. 8 e^(i*pi) + 1 = 0. It s the most beautiful thing as it utilises addition, multiplication, exponentiation, 0, 1, e, i, pi, sin, and cosine.

6 6 Works Cited 1. From Wikipedia Seven Bridges of Konigsberg 2. Dr.Shanyu Ji, (2016). Lecture 30. Euler, Our Master in Everything. 3. Luke Mastin, 18TH CENTURY MATHEMATICS - EULER