It is fairly obvious to readers of the Bible that there are
'special numbers' such as 3, 7, 12 etc. They are special
because they relate to sequences of events, groups
of people, or other aspects of the narrative (i.e. not some
magical power in the numbers themselves). For instance,
the days of the week should remind of of various aspects
of nature as announced in Genesis 1. (It is unfortunate
that we adopted pagan names for the days of the week,
which really should be named to celebrate aspects of
creation: earth day, light day, sea day, etc.)
The Pythagoreans, centuries before Christ, developed
a whole religion based on numerology. They gave us some
major contributions, such as the Pythagorean theorem
and the muscial scale, as well as a lot of arcane nonsense.
Kepler was (as pointed out by Koestler in The Sleepwalkers)
a watershed figure who sought to find patterns in nature
in both ways: the ancient Greek way, such as by fitting
the Platonic solids into the spacing of planets in the solar
system; and the "modern" empirical way, by letting Tycho's
data force him to the conclusion that the orbits are elliptical,
not perfect circles. The latter approach ushered in what
we think of today as scientific.
There is a long tradition among the Jews and some Christians
of relating numbers and names, based on the ancient
system of using letters to represent numbers. There is
perhaps one direct reference to such a relationship in
the Bible -- in the reference to 666 in the Revelation.
I don't recall any other such direct references to numerology,
although maybe there are some.
In recent times there has been an increased interest in Bible
numerology, with the publication of an article showing
high correlations of modern names with the OT text; this
kind of thing was also published recently in a book, The Bible Code.
Computer technology has enable the progress in this work.
Of course the intent of this work is apologetic: if the
probability of some pattern occurring by chance is negligible,
this may imply that the text had a miraculous origin, or at
least a hidden but deliberate origin. (You can see a similarity
between this and the argument from design in nature).
Skeptics might point out that all the numbers involved are
small, which increases the likelihood that interrelationships
will exist. If there were a trillion letters in the alphabet, there
would be far less instances of matching. And how probabilities
are calculated depends on some assumptions. There don't
seem to be a lot of 'controlled' experiments such as
attempts to find similar coincidences in secular books.
Christians generally have not been as excited about
numerology as Jewish scholars. Perhaps this is because
they are not as good at math. Or perhaps it is because they
see it as a distraction from the real message of the Gospel,
which has to do with moral and spiritual life, not calculations.