Leonhard Euler Essay, Research Paper

Leonhard Euler

Euler made large bounds in modern analytic geometry and trigonometry. He

made decisive and formative contributions to geometry, calculus and

number theory.

Born: 15 April 1707 in Basel, Switzerland

Died: 18 Sept 1783 in St Petersburg, Russia

Introduction

Euler’s father wanted his son to follow him into the church and sent him

to the University of Basel to prepare for the ministry. However geometry

soon became his favourite subject. Euler obtained his father’s consent

to change to mathematics after Johann Bernoulli had used his persuasion.

Johann Bernoulli became his teacher.

He joined the St. Petersburg Academy of Science in 1727, two years after

it was founded by Catherine I the wife of Peter the Great. Euler served

as a medical lieutenant in the Russian navy from 1727 to 1730. In St

Petersburg he lived with Daniel Bernoulli. He became professor of

physics at the academy in 1730 and professor of mathematics in 1733. He

married and left Johann Bernoulli’s house in 1733. He had 13 children

altogether of which 5 survived their infancy. He claimed that he made

some of his greatest discoveries while holding a baby on his arm with

other children playing round his feet.

The publication of many articles and his book Mechanica (1736-37), which

extensively presented Newtonian dynamics in the form of mathematical

analysis for the first time, started Euler on the way to major

mathematical work.

In 1741, at the invitation of Frederick the Great, Euler joined the

Berlin Academy of Science, where he remained for 25 years. Even while in

Berlin he received part of his salary from Russia and never got on well

with Frederick. During his time in Berlin, he wrote over 200 articles,

three books on mathematical analysis, and a popular scientific

publication Letters to a Princess of Germany (3 vols., 1768-72).

In 1766 Euler returned to Russia. He had been arguing with Frederick the

Great over academic freedom and Frederick was greatly angered at his

departure. Euler lost the sight of his right eye at the age of 31 and

soon after his return to St Petersburg he became almost entirely blind

after a cataract operation. Because of his remarkable memory was able to

continue with his work on optics, algebra, and lunar motion. Amazingly

after 1765 (when Euler was 58) he produced almost half his works despite

being totally blind.

After his death in 1783 the St. Petersburg Academy continued to publish

Euler’s unpublished work for nearly 50 more years.

Euler made large bounds in modern analytic geometry and trigonometry. He

made decisive and formative contributions to geometry, calculus and

number theory. In number theory he did much work in correspondence with

Goldbach. He integrated Leibniz’s differential calculus and Newton’s

method of fluxions into mathematical analysis. In number theory he

stated the prime number theorem and the law of biquadratic reciprocity.

He was the most prolific writer of mathematics of all time. His complete

works contains 886 books and papers.

We owe to him the notations f(x) (1734), e for the base of natural logs

(1727), i for the square root of -1 (1777), for pi, for summation (1755)

etc. He also introduced beta and gamma functions, integrating factors

for differential equations etc.

He studied continuum mechanics, lunar theory with Clairaut, the three

body problem, elasticity, acoustics, the wave theory of light,

hydraulics, music etc. He laid the foundation of analytical mechanics,

especially in his Theory of the Motions of Rigid Bodies (1765).

References

1.Dictionary of Scientific Biography

2.Biography in Encyclopaedia Britannica

3.C B Boyer, The Age of Euler, in A History of Mathematics (1968).

4.A Speiser, Die Basler Mathematiker (Basel, 1939).

5.G du Pasquier, Leonhard Euler et ses amis (Paris, 1927).

6.O Speiss, Leonhard Euler (1929).

7.R Thiele, Leonhard Euler (Leipzig,1982).

8.R Fueter, Leonhard Euler (Basel,1948).

9.J Gray, Leonhard Euler 1707-1783, Janus : archives internationales pour l’histoire de la medecine et pour la geographie medicale 72 (1985), 171-192.

10.Leonhard Euler 1707-1783 : Beitrage zu Leben und Werk (Basel-Boston, 1983).

11.H Bernhard, Euler, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983).