**Sir
Isaac Newton** stated
that "If
I have
seen further
it is by
standing
upon the shoulders of giants." Newton's
extraordinary abilities enabled him
to perfect the processes of those who had come before
him, and to advance every
branch of mathematical science then studied, as well
as to create some new subjects. Newton
himself became one of those giants to whom he had
paid homage.
**Newton's
image** is
set against
the cover
of a tome
easily
recognizable
to those
familiar
with the
history
of mathematics
-- his **Principia
Mathematica**,
The Mathematical Principles of Natural Philosophy, first
published
in 1687.
Its
first two
parts,
prefaced
by Newton's
"*Axioms,
or Laws
of Motion*",
dealt with
the "Motion
of Bodies".
The third
part dealt
with "The
System
of the
World"
and included
Newton's
writings
on the
*Rules
of Reasoning
in Philosophy*,
*Phenomena
or Appearances*,
*Propositions
I-XVI*,
and *The
Motion
of the
Moon's
Nodes*.
**Inscribed
over Newton's
image** is
Newton's
*binomial
theorem*,
which dealt
with expanding
expressions
of the
form (a+b)^{ n.
} This
was Newton's
first epochal
mathematical
discovery,
one
of his
"great
theorems".
It was
not a theorem
in the
same sense
as the
theorems
of Euclid
or Archimedes,
insofar
as Newton
did not
provide
a complete
"proof",
but rather
furnished,
through
brilliant
insight,
the precise
and correct
formula
which could
be used
stunningly
to great
effect.
Newton
is widely
regarded
as the
inventor
of modern
**calculus**.
In fact,
that honor
is correctly
shared
with Leibniz,
who developed
his own
version
of calculus
independent
of Newton,
and in
the same
time frame,
resulting
in a rancorous
dispute.
Leibniz's
calculus
had a far
superior
and more
elegant
notation
compared
to Newton's
calculus,
and it
is Leibniz's
notation
which is
still in
use today.
Newton's
portrait
shares
a color
palette
with Leibniz,
the other
acknowledged
"inventor"
of calculus,
Lagrange,
a pioneer
of the
"calculus
of variations",
and Laplace and Euler,
two of
those who
built
on what
had been
so ably
begun. |