leonhard Euler

Leonhard Euler\'s father was Paul Euler. Paul Euler had studied theology at the University of Basel and had attended Jacob
Bernoulli\'s lectures there. In fact Paul Euler and Johann Bernoulli had both lived in Jacob Bernoulli\'s house while undergraduates
at Basel. Paul Euler became a Protestant minister and married Margaret Brucker, the daughter of another Protestant minister.
Their son Leonhard Euler was born in Basel, but the family moved to Riehen when he was one year old and it was in Riehen,
not far from Basel, that Leonard was brought up. Paul Euler had, as we have mentioned, some mathematical training and he
was able to teach his son elementary mathematics along with other subjects.

Leonhard was sent to school in Basel and during this time he lived with his grandmother on his mother\'s side. This school was a
rather poor one, by all accounts, and Euler learnt no mathematics at all from the school. However his interest in mathematics
had certainly been sparked by his father\'s teaching, and he read mathematics texts on his own and took some private lessons.
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. He
entered the University in 1720, at the age of 14, first to obtain a general education before going on to more advanced studies.
Johann Bernoulli soon discovered Euler\'s great potential for mathematics in private tuition that Euler himself engineered. Euler\'s
own account given in his unpublished autobiographical writings, see [1], is as follows:-

... I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was
very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to
start reading more difficult mathematical books on my own and to study them as diligently as I could; if I
came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon
and he kindly explained to me everything I could not understand ...

In 1723 Euler completed his Master\'s degree in philosophy having compared and contrasted the philosophical ideas of
Descartes and Newton. He began his study of theology in the autumn of 1723, following his father\'s wishes, but, although he
was to be a devout Christian all his life, he could not find the enthusiasm for the study of theology, Greek and Hebrew that he
found in mathematics. Euler obtained his father\'s consent to change to mathematics after Johann Bernoulli had used his
persuasion. The fact that Euler\'s father had been a friend of Johann Bernoulli\'s in their undergraduate days undoubtedly made
the task of persuasion much easier.

Euler completed his studies at the University of Basel in 1726. He had studied many mathematical works during his time in
Basel, and Calinger [23] has reconstructed many of the works that Euler read with the advice of Johann Bernoulli. They include
works by Varignon, Descartes, Newton, Galileo, von Schooten, Jacob Bernoulli, Hermann, Taylor and Wallis. By 1726 Euler
had already a paper in print, a short article on isochronous curves in a resisting medium. In 1727 he published another article on
reciprocal trajectories and submitted an entry for the 1727 Grand Prize of the Paris Academy on the best arrangement of masts
on a ship.

The Prize of 1727 went to Bouguer, an expert on mathematics relating to ships, but Euler\'s essay won him second place which
was a fine achievement for the young graduate. However, Euler now had to find himself an academic appointment and when
Nicolaus(II) Bernoulli died in St Petersburg in July 1726 creating a vacancy there, Euler was offered the post which would
involve him in teaching applications of mathematics and mechanics to physiology. He accepted the post in November 1726 but
stated that he did not want to travel to Russia until the spring of the following year. He had two reasons to delay. He wanted
time to study the topics relating to his new post but also he had a chance of a post at the University of Basel since the professor
of physics there had died. Euler wrote an article on acoustics, which went on to become a classic, in his bid for selection to the
post but he was nor chosen to go forward to the stage where lots were drawn to make the final decision on