Correctly speaking, an algebraic number is a complex number
which is a root
of a polynomial
with integer coefficients
. A complex number which is not algebraic
is called a transcendental number
For example, the square root of 2 is a root of the
polynomial: x^2 - 2 = 0, so it is an algebraic number.
On the other hand, e and pi are transcendental, as
was proved by Hermite and Lindemann. This is the basis
for the fact that squaring the circle is impossible.
Algebraic numbers are not to be confused with a rational numbers, which is a number which is a quotient of two
integers, like one-half.