Johann
Carl Friedrich
Gauss reportedly
believed
that there
had been
only three
'epoch-making'
mathematicians:
Archimedes,
Newton,
and one
of his
own students.
While there
is puzzlement
as to why
Gauss would
accord
this singular
honor to
his student,
many would
Gauss himself,
sometimes
referred
to as the
"prince
of mathematics",
the
rightful
third member
of his
list.
Gauss,
a stickler
for perfection,
lived
by the
motto "*pauca
sed matura*"
(few
but ripe).
He published
only
a small
portion
of his
work.
It is from
a scant
19 page
diary,
published
only
after Gauss's
death,
that
many of
the results
he established
during
his lifetime
were posthumously
gleaned.
**Gauss
is portrayed** with
one of
his most
important
results
-- the
refutation
of Euclid's* fifth
postulate*,
the '**parallel
postulate**',
which posited
that parallel
lines would
never meet.
Gauss
discovered
that valid
self-consistent
geometries
could be
created
in which
the *parallel
postulate* did not
hold. These
geometries
came to
be known
as 'non-Euclidean
geometries".
**The
parallel
lines which
begin in
the portrait
of Euclid**,
**end
and meet
in the
portrait
of Gauss**,
the two
portraits
also sharing
a common
color palette.
Gauss
chose
not to
publish
his
results
in alternative
geometries,
and credit
for the
discovery
of 'non-Euclidean
geometry'
was accorded
to
others
(Bolyai,
and Lobachevski)
who arrived
at
similar
results
independently.
**In
the Gauss
portrai**t,
above
the parallel
lines which
meet, what
has come
to be known
as "**Gauss's
Equation**"
(for the
second
derivatives
of the
radius
vector
r), is
inscribed.
Gauss
did pioneering
work
on differential
geometry
(the
specialized
study
of manifolds),
which
he did
publish
in *Disquisition
cica
superticies
curvas*.
**Overlying
Gauss's
portrait
the ***Gaussian
distribution* curve is
incised.
This probability
distribution
curve is
commonly
referred
to as
the "*normal
distribution*"
by statisticians,
and, because
of its
curved
flaring
shape,
as the
"*bell
curve*"
by social
scientists.
The Gaussian distribution
has found wide application in numerous experimental
situations,
where it
describes
the deviations
of repeated
measurements
from the mean. It has the characteristics that positive
and negative deviations are equally likely, and small
deviations are much more likely than large deviations.
Gauss
is also
known for
Gaussian
primes,
Gaussian
integers,
Gaussian
integration,
and Gaussian
elimination
-- to name
only a
few of
the achievements
directly
named after
an individual
who was,
perhaps,
the most
gifted
mathematician
of all
time. |