of this serie s i s completely devote d jus t t o a catalogu e an d brie f summarie s o f let -
ters writte n b y hi m an d t o him . Opera Omnia, o f which I shal l giv e mor e detail s
later, include s his books on differential an d integra l calculus , calculus of variations,
his grea t treatise s o n algebr a an d o n analysis , hi s unfinishe d treatis e o n numbe r
theory, an d hi s justly famou s Letters to a German Princess on Different Subjects
in Natural Philosophy , whic h i s on e o f th e mos t popula r book s o n scienc e eve r
written, translate d int o eigh t language s an d reprinte d countles s time s [2] . Whe n
publication i s completed, Opera Omnia wil l be a giganti c landmar k i n th e histor y
of science . It s page s wil l contai n a substantia l par t o f al l mathematica l researc h
that wa s carrie d ou t i n th e middl e o f the 18th century . Th e 18th centur y ca n thu s
be trul y sai d t o b e th e ag e o f Euler. Furthermore , larg e part s o f th e mathematic s
of th e 19th centur y flowed ou t o f hi s work . Wha t i s eve n mor e remarkabl e i s tha t
some of his themes hav e generate d ne w interes t an d attentio n eve n today . I n spit e
of th e fac t tha t h e wa s almos t totall y blin d i n th e las t fifteen year s o f hi s life , h e
wrote ove r 40 0 memoirs durin g tha t time , abou t hal f o f his entire output , man y of
which require d colossa l calculation s tha t h e carrie d ou t entirel y i n hi s head . Th e
memoirs h e submitte d t o th e St . Petersbur g Academ y wer e stil l bein g publishe d
decades afte r hi s death; indeed , on e of them wa s not publishe d til l 1862, almost 8 0
years afte r hi s death .
Here is a list, whic h is at bes t partial , o f topics Euler worke d o n in his lifetime ,
many o f whic h wer e founde d b y hi m an d i n almos t al l o f whic h hi s wor k wa s
pioneering:
Differential an d integra l calculu s
Logarithmic, exponential , an d trigonometri c function s
Differential equations , ordinar y an d partia l
Elliptic function s an d integral s
Hypergeometric integral s
Classical geometr y
Number theor y
Algebra
Continued fraction s
Zeta an d othe r (Euler ) product s
Infinite serie s an d product s
Divergent serie s
Mechanics o f particle s
Mechanics o f solid bodie s
Calculus o f variation s
Optics (theor y an d practice )
Hydrostatics
Hydrodynamics
Astronomy
Lunar an d planetar y motio n
Topology
Graph theor y
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