Leonhard Euler

Leonhard Euler (/ˈɔɪlər/ OY-lər; 15 April 1707 – 18 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. Euler has been called a "universal genius" who "was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory". He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia.

Euler is credited for popularizing the Greek letter ${\displaystyle \pi }$ (lowercase pi) to denote the ratio of a circle's circumference to its diameter, as well as first using the notation ${\displaystyle f(x)}$ for the value of a function, the letter ${\displaystyle i}$ to express the imaginary unit ${\displaystyle {\sqrt {-1}}}$, the Greek letter ${\displaystyle \Sigma }$ (capital sigma) to express summations, the Greek letter ${\displaystyle \Delta }$ (capital delta) for finite differences, and lowercase letters to represent the sides of a triangle while representing the angles as capital letters. He gave the current definition of the constant ${\displaystyle e}$, the base of the natural logarithm, now known as Euler's number. Euler made contributions to applied mathematics and engineering, such as his study of ships, which helped navigation; his three volumes on optics, which contributed to the design of microscopes and telescopes; and his studies of beam bending and column critical loads.

Euler is credited with being the first to develop graph theory (partly as a solution for the problem of the Seven Bridges of Königsberg, which is also considered the first practical application of topology). He also became famous for, among many other accomplishments, solving several unsolved problems in number theory and analysis, including the famous Basel problem. Euler has also been credited for discovering that the sum of the numbers of vertices and faces minus the number of edges of a polyhedron that has no holes equals 2, a number now commonly known as the Euler characteristic. In physics, Euler reformulated Isaac Newton's laws of motion into new laws in his two-volume work Mechanica to better explain the motion of rigid bodies. He contributed to the study of elastic deformations of solid objects. Euler formulated the partial differential equations for the motion of inviscid fluid, and laid the mathematical foundations of potential theory.

Euler is regarded as arguably the most prolific contributor in the history of mathematics and science, and the greatest mathematician of the 18th century. His 866 publications and his correspondence are being collected in the Opera Omnia Leonhard Euler. Several great mathematicians who worked after Euler's death have recognised his importance in the field: Pierre-Simon Laplace said, "Read Euler, read Euler, he is the master of us all"; Carl Friedrich Gauss wrote: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it."

Leonhard Euler was born in Basel on 15 April 1707 to Paul III Euler, a pastor of the Reformed Church, and Marguerite (née Brucker), whose ancestors include a number of well-known scholars in the classics. He was the oldest of four children, with two younger sisters, Anna Maria and Maria Magdalena, and a younger brother, Johann Heinrich. Soon after Leonhard's birth, the Eulers moved from Basel to Riehen, Switzerland, where his father became pastor in the local church and Leonhard spent most of his childhood.

From a young age, Euler received schooling in mathematics from his father, who had taken courses from Jacob Bernoulli some years earlier at the University of Basel. Around the age of eight, Euler was sent to live at his maternal grandmother's house and enrolled in the Latin school in Basel. In addition, he received private tutoring from Johannes Burckhardt, a young theologian with a keen interest in mathematics.

In 1720, at age 13, Euler enrolled at the University of Basel. Attending university at such a young age was not unusual at the time. The course on elementary mathematics was given by Johann Bernoulli, the younger brother of the deceased Jacob Bernoulli, who had taught Euler's father. Johann Bernoulli and Euler soon got to know each other better. Euler described Bernoulli in his autobiography:

the famous professor Johann Bernoulli [...] made it a special pleasure for himself to help me along in the mathematical sciences. Private lessons, however, he refused because of his busy schedule. However, he gave me a far more salutary advice, which consisted in myself getting a hold of some of the more difficult mathematical books and working through them with great diligence, and should I encounter some objections or difficulties, he offered me free access to him every Saturday afternoon, and he was gracious enough to comment on the collected difficulties, which was done with such a desired advantage that, when he resolved one of my objections, ten others at once disappeared, which certainly is the best method of making happy progress in the mathematical sciences.