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Insolvability of the quintic in radicals
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Insolvability of the quintic in radicals
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Description
Identifier
Thesis
2192
Author
Kielski, Michael Edward, 1983
Title
Insolvability
of the
quintic
in
radicals
Publisher
Central Connecticut State University
Date
2011
;
*
Resource Type
Master's Thesis
Notes
The
goal
of this
thesis
is
to
trace
the
development
in
mathematical
theory
that
led
to the
proof
of the
insolvability
of the
quintic
. That
is
, there
does
not
exist
a
general
formula
in
radicals
for
equations
of the
form
[not
reproduciblesee
full
text
document
for
equation]
for
[not
reproduciblesee
full
text
document]
. There are of
course
solutions
to
equations
of this
form
, in
fact
the
fundamental
theorem
of
algebra
guarantees
it
, but a
formula
using
only
radicals
to
find
the
roots
of the
equation
is
an
impossibility
. The
question
as to
why
this
is
so
has
remained
an
allusive
gem
of
mathematics
until
the
early
19th
century
.
Even
then
it
was
disputed
for
another
forty
years
after
being
proven
because
of the
seemingly
unlikeliness
of there not
being
a
“nice”
formula
.
After
all
, there were
general
formulas
to
find
the
roots
of
quadratics
,
cubics
, and
quartics
so
the
question
must
be
asked
as to
why
there
isn’t
one
for
equations
of the
fifth
degree
and
higher
. This
question
has been a
driving
force
behind
the
creation
of
Galois
Theory
which
has
ultimately
redefined
the
way
mathematics
is
structured
. The
ideas
formed
in
order
to
find
the
roots
of
equations
have
permeated
almost
all
areas
of
mathematics
.
Some
mathematicians
,
such
as
Felix
Klein
, have
suggested
that these
ideas
,
particularly
group
theory
, be
placed
at the
center
of
mathematical
research
because
of their
far
reaching
consequences
.
It
is
for this
reason
that the
developments
in
early
equation
theory
be
closely
examined
and
understood
.
Subject
Quintic equations
Equations, Roots of
Department
Department of Mathematical Sciences
Advisor
Waiveris, Charles
Type
Text
Digital Format
application/pdf
Language
eng
OCLC number
804653035
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