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