Most vaishnavas seems to be of the opinion that the Gita
is many thousends years old. Many authors however disagrees.
They are quite sure that the Gita could not be more than 2400
years old.There are even some authers who argues that the Gita is not more
than 200 years before common era.It seems to me that the Gita
must be at least younger than the so called classical upanishads,
and they are considered to be from the years 700-300 bce.
Phulgenda Sinha argues in his book "The Gita as it was"
that only the first three chapters are authenic,and the rest are
interpolated around the year 800 in common era. He says that
the Gita was written around the year 400 bce by Vyasa, under
the influence of Kapilas samkya philosophy and Patanjalis yoga sutras.
After Vyasas first three chapters the Gita seems to have been
interpolated by two entierly different authers, one of them monist and
the other theist.