The cutting edge of modern physics examines some of
the most fundamental
questions in science. These questions address the very structure and
origin of the universe, the nature of the constituents of all matter and
their interactions and the mathematical structures that are necessary
for a quantitative formulation of the fundamental laws of nature. Two
concrete goals of current focus in fundamental physics are to find a
quantum theory of gravity that avoids the inconsistencies that arise
from trying to reconcile Einstein's general theory of relativity with
quantum mechanics and to find a unified theory which encompasses of all
the forces of nature and describes all of the particles which are
subject to those forces.

String theory provides a promising candidate for a
physical theory that
could simultaneously achieve both of these goals. String theory is a
physical model which is postulated to describe fundamental interactions
at exceedingly small distances where quantum mechanical fluctuations of
the geometry of spacetime would become important. As such, it should
offer an explanation for the conjectured phenomena which should occur
when quantum effects and gravity combine. In fact, string theory has had
some spectacular successes in this direction. It has given a microscopic
explanation to the apparent thermodynamic properties of black holes and
suggested a source of Hawking radiation. It has also been used to
understand the structure of some space-time singularities. A current
active research area centers on attempting to quantize strings in the
background of an expanding universe, possibly with an initial
singularity. The goal is to understand whether the microscopic physics
described by strings could be imprinted on spacetime in the form of some
observable features of the cosmos.

There are solutions of string theory which are
tantalizingly similar to
the standard model of elementary particle physics which describe the
presently observed non-gravitational interactions of elementary particle
physics. String theory is the ultimate unification of particles and
forces -- the only fundamental object is a string -- different particles
are strings with different modes of internal vibration -- and all
interactions are simply explained by the splitting and joining of those
strings. And, not only does this unify the forces of the standard model
in an elegant way, it incorporates gravity in a way which is apparently
consistent with quantum mechanics.

As a physical dynamical system, string theory is
still not completely
understood. It is clear that its full power will only be realized once
significant progress has been made in understanding its mathematical and
dynamical structure. This will undoubtedly involve the development of
radical new physical ideas and new mathematics. This development will be
an important frontier area for both mathematics and physics in the
foreseeable future.

One of the most interesting features of string theory
is duality.
Duality is the phenomenon where apparently different theories describe
the same dynamics with different mathematical variables. In string
theory, dualities take a few different forms. One is duality between
different kinds of string theories. It is now known that the five
apparently consistent kinds of superstring theory are related by
dualities and they are now thought to all be limits of an underlying
theory called M-theory. Another example is mirror symmetry, which is
currently an active subject of investigation in mathematical string
theory. It relates string theories which live on different space-times.

A different kind of duality is holography. It relates
string theory
living on a particular space-time to an ordinary quantum field theory,
usually living on a boundary of the space-time. These later dualities
have been used to find string theory duals of various gauge field
theories. Being a strong-weak coupling duality, it can give information
about either gauge theory or string theory in the strong coupling
regime. This subject is currently undergoing vigorous investigation. It
promises to progress our understanding of string theories by studying
their dual descriptions as field theories. It also yields a string
theory dual of the field theories involved and gives a new window for
quantitative description of their behaviors.