For handy reference, here is a simplistic table that is good to start with.

This is Iamblichus on the Hepdomad (7):

The reason for the seventh number being an object of reverence is as follows: the providence of the Creator God wrought all things by basing on the first-born One the source and root of the creation of the universe, which comes to be an impression and representation of the highest good, and he located the perfection and fulfillment of completion in the Decad itself, and the Creator God necessarily considered that the Hebdomad was an instrument and His most authoritative limb and has gained the power of creativity. For by nature, and not by our own devices, the Hebdomad is a mean between the monad and the decad, and the means between extremes are in a sense more authoritative that the extremes themselves, because the terms on either side incline towards the means…7 is the arithmetic mean between the tetrad and the decad (ie, in a sense between two decads, one potential, the other actual, since is half of the sum of both).

This excerpt should give a feel for what the Greek Platonists were doing — they believed that the symmetry and harmony of number was directly revelatory, through Reason (intellectual intuition, which we would term the noetic faculty), of the Logos.

In this case, Iamblichus’ short essays are worth reading — pick one of them & read the entire argument, mathematics & all, to get the feel for how they thought. Next week, I will present a summary of each of the numbers, although the above list will give you an idea of what it will look like.

For instance, the number Five represents Life: specifically vegetative Life (Six represents animal Life, and Seven, the living Soul of man). It also incarnates and mediates Justice — the proper balance. One immediately thinks of the “star” of Justice, the shire-reeve’s badge, five-pointed pentagram.

Here is an extract from Boris Mouravieff in Gnosis, Book III, pg 98,99

As we have already indicated, the first of the three symbols that can be obtained from the Circle and the polygons is the Pentagram, or five-branched triple star. The study of this symbol-in-movement requires precise indication of the order in which  the student’s attention and his pen-point should pass from one to the other of the branch-points of the three stars through the intersections of  the lines that form them. This is how our numbered Pentagram is drawn (fig. 8): The Pentagram numbered in this way was revealed by the author during the lectures he gave at the Faculty of Letters in the University of Geneva. It was also published in the Summary of these lectures. We have already said that this symbol, taken as a whole, reflects the real positions of the elements and forces that form the Third Cosmic Octave. The student should apply the meanings of the Major Numbers to the corresponding figures and study them from this point of view. Here, he will come across the first difficulty: that of interpreting the terms characterizing each of the Major Numbers. In order  to interpret them, he must specially train himself to think ‘in harmony’ and not ‘in melody’, if we may put it this way. In other words, instead of a chain of reasoning he should form a bundle of ideas, of which each section should present a harmonious  chord. Then, and only then – keeping the meaning of the whole continually present in his mind – the succession of the figures as it is shown will enable him to make his thought and attention progress according to a precise order and so reach the desired goal. Except in a few rare cases, as long as the student’s mind has not attained the degree of training needed to enable him to pursue his research in an independent manner, this will require outside help. This is one reason why esoteric  teaching has always included an oral Tradition that vivifies the Letter of the written Doctrine.

The Numbers, properly contemplated, or truly contemplated at all, will lead us to God.