One can find depictions of mathematical symbolism in several of our major religions. Either through a conscious effort (in the case of Hinduism) to simplify profound philosophical concepts whose core ideas are mathematical. Or through mathematical interpretations (in the case of Christianity & Islam) of the religion's fundamental icons that seem to suggest that there may be more to the choice of the religion's symbols than mere theological history and opportunistic proselytization. Here only Hinduism is studied since more than any other religion, Hinduism abounds in such symbolism.
Here only a few striking examples are discussed.
In Hinduism, MahaVishnu, the Deity responsible for the preservation of the Universe is often represented as Lord Padmanabha reclining on the magnificent snake Anantha as shown in the picture below:
It is interesting to note that the other two Deities in the Hindu trinity, Brahma & Shiva responsible for the creation and dissolution of the Universe is also represented in this image. Brahma, sits on a lotus that emerges from Vishnu's navel, while Shiva in the form of Shiva Linga is almost touching Vishnu's reposing right hand. In His left hand, He holds a lotus to His nose.
Now, Anantha literally means "endless" in Sanskrit, or in other words, infinite. Thus infinity is aptly represented by the many layered coiled snake. Vishnu, the Preserver of the Universe is reclining on this Infinity, while sprouting from His navel, which is physically in the middle, is Brahma the Creator. It shall be recollected that prior to Creation, the only thing that existed was Nothingness. This Nothingness is beyond Time and Space. And from the womb of this Nothingness sprang forth the infiniteness of the Universe during Creation. This Nothingness is Brahma, who is shown as an ancient (beyond time) Man with four heads looking into the four directions : +, -, +i, -i (Positive, Negative, Positive Imaginary and Negative Imaginary). The origin of the lotus on which Brahma sits is the positional indicator of Nothingness (Zero) in the infinite number line. The roles of Brahma and Shiva are hinted by the hands of Vishnu: if Creation (the lotus, symbol of Brahma) is in the left hand, Dissolution (Shiva Linga) must be in the right hand.
One may also note the manner in which the three deities, Brahma, Vishnu & Shiva are set out in this picture with reference to their respective backdrop. The backdrop, as you may note, is partly sky and partly water. Sky, in Sanskrit, is synonymous to Shunya or Nothingness, while water is synonymous to Maya or illusion. Brahma, the Creator, seems to be hovering in a backdrop of empty sky, suggesting creation started with Nothingness. Thus Creation in the form of Brahma leads into the Created Universe in the form of the reclining Vishnu on the majestic Anantha floating on the ocean of Maya. In the Hindu scriptures, the created universe has often been depicted as nothing but a grand illusion. It is now needless to say that the hand of Vishnu leading to the Shiva Linga represents the final dissolution of the Universe. It is also worthwhile to note the relative sizes and the positioning of Brahma, Vishnu & Shiva in this picture. While Vishnu occupies the major portion of the image and sits between the Nothingness of the sky and the Universe of illusion (water), Brahma & Shiva are but tiny specks perhaps implying instants in time.
This is a wonderfully symbolic representation of the duality of the Universe/Nature -- the Male/Female, the positivity/negativity, the static/dynamic, the sublime/horrific aspects of the universe are all represented here symbolically in a way the common man can understand.
Shakthi, in the form of the primeval mother Kaali, stands over the inert Shiva. Mathematically, this represents the positive and negative aspects/energies of the Universe. The static Shiva, stretches from left to right, with an expression of total tranquillity, while the horrific Shakthi, which literally means energy, stands over Him with Her hands (originally four) pointing in all directions.
This may be considered the Hindu equivalent of the Yin & Yang. Shiva & Shakthi complement each other and in totality represent the entire universe. Here, everything that is not Shiva is Shakthi and vice versa.
Another similar representation of the duality of the universe is the depiction of Shiva in the form of Ardhanaarishwara; containing the male and female aspects of the Universe as shown below:
There are several websites that discusses the symbolism behind the ancient tale in the Hindu scriptures of the churning of the ocean of milk. There is an excellent interpretation of the symbolism behind this tale at this website.
Here, an attempt is made to look at this story from a mathematical perspective.
The picture above shows a photograph of a temple sculpture that depicts the above story. In the story, the Devas (gods) & the Asuras (demons) got together to churn the ocean of milk to extract the elixir of immortality that lay hidden in the depths. In the picture, the Devas are on the right holding the head of Vasuki, the snake god who was used for the churning, while the Asuras are on the left, pulling at his tale. They used the mountain of Mandhara (supported by Vishnu in the form of Kurma, the tortoise) as the pole to churn the ocean.
As the story goes, after many days and much effort by this strange team, the ocean yielded an extremely potent poison that had the power of destroying the three worlds. Shiva lost no time in trapping this poison in his throat thus saving everyone.
After much more strenuous and incessant churning the ocean began to yield many treasures one by one, which was distributed by the gods and the demons. Finally, the sage Dhanvantari stepped out of the ocean holding the one thing that everyone was eagerly waiting for -- Amrith, the elixir of immortality. There is more to this story, which is not discussed here for the sake of brevity.
Now, coming to the mathematical interpretation. This story wonderfully represents Man's ultimate goal in life -- the journey to self-realization. Mathematically, the journey to self realization can be considered analogous to mortal Man's journey to Godhood, and thus immortality -- the freedom from rebirth. As seen before, Godhood is essentially Nothingness and Man, mathematically, is a matrix of non-zero values. Therefore in order for Man to reach this liberated state of Nothingness, he must strive such that the elements of his matrix must approach zero. When Man starts this journey to mergence (with the Absolute), using the tools of meditation, inquiry, bhakthi etc. the elements within his matrix approach zero, overshoots, thereby fluctuating like a pendulum between positivity & negativity. This is akin to the churning motion. The constant effort by the positive (Devas) and negative (Asuras) aspects of his consciousness leads the ocean of milk that is his mind to release the poisons of his desire and Karmic history that were until then obstacles to progress. An animated explanation of this is given below (please click on "Play/Resume"):
The swastik symbol is a direct derivative of the Gaussian plane that represents the Universe complete with its real and imaginary axes. The four spiralling arms at the tip of the axes represent the dynamic nature of the Universe -- from Changelessness at the centre (point 0) to Continual Change.
Please refer to previous discussion on Om titled the Primal Word. It is also interesting to note that the Christian crucifix and the Islamic crescent can be combined to form the Hindu Om as shown below. Please click on "Replay" to re-load the animation: