Unsurprisingly, number theorists are interested in the properties of numbers! In particular, the relations between the additive and multiplicative structures of integers are so fascinating that they make number theory a vast and fertile field of mathematical research. Gauss, who is often known as the 'prince of mathematics', called mathematics the 'queen of the sciences' and considered number theory the 'queen of mathematics'.

Many
problems
in
number
theory
can
be
formulated
in
a
relatively
simple
language.
For
example,
the
famous
last
theorem
of
Fermat
states
that
there
exists
no
non-trivial
integer
solution
of
the
equation
x^{n} +
y^{n} =
z^{n} for
n
≥
3.
The
twin
prime
conjecture
is
to
ask
if
there
should
be
infinitely
many
primes
p
such
that
p+2
is
also
a
prime.
Although
these
questions
are
easily
stated,
they
are
so
deep
that
they
have
withstood
attempts
to
prove
them
for
centuries.
Fermat's
last
theorem
was
only
proved
in
1995
by
A.
Wiles
after
the
cumulative
effort
of
many
mathematicians
for
more
than
350
years,
while
the
twin
prime
conjecture
remains
open
even
today.

The great difficulty in proving relatively simple results in number theory prompts many new concepts in mathematics. Over the centuries, this discipline has grown very much with close connections to other areas of mathematics: algebraic geometry, representation theory, combinatorics, cryptography and coding theory, probability, harmonic analysis and complex analysis.

The Pure Mathematics department teaches number theory courses at various levels. The elementary number theory course is offered twice per year. The analytic number theory and the algebraic number theory course are available every other year. We also teach advanced topic courses on a regular basis. Major areas of interest for number theorists in the Pure Mathematics department include Diophantine equations and Diophantine approximation, arithmetic geometry, L-functions and random matrix theory, representation theory, computational number theory, and additive and probabilistic number theory.