Euler

Leonard Euler and his Early
Life
Leonhard Euler (/ˈɔɪlər/ OY-lər;[b] German: [ˈleːɔnhaʁt ˈʔɔʏlɐ] ⓘ, Swiss Standard German: [ˈleɔnhard
ˈɔʏlər]; 15 April 1707 – 18 September 1783) was a Swiss polymath, mathematician, physicist,
astronomer, geographer, logician, and engineer who founded the studies of graph theory and
topology and made pioneering and 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.[6] He is also known for his work in mechanics, fluid dynamics, optics, astronomy, and music
theory.[7] As a result, Euler has been described as a "universal genius" who "was fully equipped with
almost unlimited powers of imagination, intellectual gifts and extraordinary memory".[8]
Euler is regarded as arguably the most prolific contributor in the history of mathematics and science,
and the greatest mathematician of the 18th century.[9][10] Several great mathematicians who
produced their work after Euler's death have recognised his importance in the field as shown by
quotes attributed to many of them: Pierre-Simon Laplace expressed Euler's influence on
mathematics by stating, "Read Euler, read Euler, he is the master of us all."[11][c] 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."[12][d] His 866 publications and his correspondence
are being collected in the Opera Omnia Leonhard Euler which, when completed, will consist of 81
quartos.[14][15][16] 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
−
1
{\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.[17] He gave the current definition
of the constant
{\displaystyle e}, the base of the natural logarithm, now known as Euler's number.[18] Euler made
contributions to applied mathematics and engineering, such as his study of ships which helped
navigation, his three volumes on optics contributed to the design of microscopes and telescopes,
and he studied the bending of beams and the critical load of columns.[10]
Euler is also 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, providing a solution to
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 equals 2, a number now commonly known as the Euler
characteristic. In the field of 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. Euler made
contributions to the study of elastic deformations of solid objects. Euler formulated the partial
differential equations for the motion of inviscid fluid,[10] and further laid the mathematical
foundations of potential theory.[8]
Early life
Leonhard Euler was born on 15 April 1707, in Basel 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.[19] He was the oldest of four children, having two younger sisters, Anna Maria and
Maria Magdalena, and a younger brother, Johann Heinrich.[20][19] Soon after the birth of Leonhard,
the Euler family moved from Basel to the town of Riehen, Switzerland, where his father became
pastor in the local church and Leonhard spent most of his childhood.[19]
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.[19]
In 1720, at thirteen years of age, Euler enrolled at the University of Basel.[7] Attending university at
such a young age was not unusual at the time.[19] 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:[21]
"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."
It was during this time that Euler, backed by Bernoulli, obtained his father's consent to become a
mathematician instead of a pastor
In 1723, Euler received a Master of Philosophy with a dissertation that compared the philosophies of
René Descartes and Isaac Newton. Afterwards, he enrolled in the theological faculty of the
University of Basel.
In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono with
which he unsuccessfully attempted to obtain a position at the University of Basel. In 1727, he
entered the Paris Academy prize competition (offered annually and later biennially by the academy
beginning in 1720)[27] for the first time. The problem posed that year was to find the best way to
place the masts on a ship. Pierre Bouguer, who became known as "the father of naval architecture",
won and Euler took second place.[28] Over the years, Euler entered this competition 15 times,[27]
winning 12 of them.[28]
Bibliography:
1) https://en.wikipedia.org/wiki/Leonhard_Euler

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Leonard Euler and his Early

Euler is credited for popularizing the Greek letter

{\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

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