CHAPTER 1
Leonhard Eule r (1707-1783)
1.1. Introductio n
1.2. Earl y lif e
1.3. Th e firs t sta y i n St . Petersburg : 1727-1741
1.4. Th e Berli n years : 1741-1766
1.5. Th e secon d St . Petersbur g sta y an d th e las t years : 1766-1783
1.6. Oper a Omni a
1.7. Th e personalit y o f Eule r
Notes an d reference s
1.1. Introductio n
No on e ca n disput e th e statemen t tha t Eule r wa s th e greates t mathematicia n
and natura l philosophe r o f the
18th
centur y an d on e of the greates t o f all time. H e
worked o n al l branches o f mathematics, bot h pur e an d applied , know n i n hi s time.
To the en d o f hi s lif e h e carrie d i n hi s min d th e entir e corpu s o f mathematic s an d
physics o f hi s epoch . H e achieve d universalit y i n th e mos t effortles s manner , an d
many o f th e theme s h e worke d o n ar e stil l activ e today . H e create d ne w branche s
of mathematics, lik e combinatorial topology , grap h theory , an d th e calculus of vari-
ations. H e was the founde r o f modern differentia l an d integra l calculu s a s we know
them today , an d hi s book s introduce d algebr a an d calculu s an d thei r application s
to enormous numbers of students. I t coul d be said without exaggeratio n that h e did
to analysi s wha t Eucli d di d t o geometry , excep t tha t Eule r himsel f create d a hug e
part o f wha t wen t int o hi s books . Wit h hi s lifelon g interes t an d beautifu l contri -
butions, h e started th e proces s of establishing numbe r theor y a s a major disciplin e
in mathematics , a process tha t wa s completed b y Gaus s an d th e publicatio n o f hi s
monumental Disquisitiones Arithmeticae. Eve r since , number theor y ha s attracte d
the attentio n an d interes t o f the greates t mathematicians . A s Laplace said , al l th e
mathematicians o f his tim e wer e his students .
Euler i s easily th e mos t prolifi c mathematicia n o f all time. Th e rang e an d vol -
ume of his output i s simply staggering. H e published ove r 85 0 papers, almos t al l of
substantial length , an d mor e than 2 5 books an d treatises . I n 1907 the Swis s Acad -
emy of Sciences established th e Eule r Commissio n wit h th e charg e of publishin g
the complet e bod y o f wor k consistin g o f al l o f hi s papers , manuscripts , an d corre -
spondence. Thi s project , know n a s Opera Omnia [1], began i n 191 1 and i s still i n
progress. Hi s scientifi c publications , no t countin g hi s correspondence , ru n t o ove r
70 volumes, eac h betwee n approximatel y 30 0 an d 60 0 pages . Thousand s o f page s
of handwritte n manuscript s ar e stil l no t i n print . H e wa s i n constan t communica -
tion wit h al l th e grea t scientist s o f hi s day , an d hi s correspondenc e cover s severa l
thousand pages , takin g u p th e entir e Serie s I V o f Opera Omnia. Th e firs t volum e
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