al-Ghazzali and The Allegory of the Cave

1. This selection of mathematics is showcasing the relationship between religion and advancements through means that are naturally more on the irreligious side.  Mathematicians focus on results that have "clearness and solidity of truth" while religion relies on faith.  Because of this. mathematicians stray away from religion/Islamic values.  The Islamic faith does not condemn nor approve of this behavior, but it does allow mathematics to continue.  The Islamic faith embraces the subjects that will aid in the advancement of society and their people; the faith is not one where people are guided on a straight path to God, but a faith that is intended to support the growth of knowledge and guide people to God.

2. al-Ghazzali supports the idea that mathematics and religion should be separated.  Mathematics "proves nothing for or against religion."  Islamic faith does not condemn nor approve of mathematics either.  Because these two do not relate, it would be odd to combine them.  Religion is based on beliefs that do not have any clear evidence.  Mathematics has "clearness and solidity of proof".  Combining religion and mathematics would most likely lead to questioning of faith as they would be in direct contact.  By maintaining these as two separate entities, Mathematics and religion can coexist.

How do al-Ghazzali's works relate to The Allegory of the Cave?
al-Ghazzali's work Deliverance from Error, and Plato's The Allegory of the Cave both deal with the idea that truth is something that deceives us.  We think that they can see the reality of everything through their five senses as both works claim.  But there lies an issue with the use of senses; they often deceive us.  Plato says that the prisoner's of the den have become accustomed to the idea that the shadows are the ones that are speaking.  This is not true; the shadows are what appears of the actual being: the human.  And the sounds that these shadows make are nothing more than echoes that are emanating from the human.  al-Ghazzali says that we use our strongest sense, sight, to determine what is and isn't real.  But here lies the problem.  The stars adorning the sky are smaller than the size of the tip of our fingers, but in reality, their size dwarfs the size of the earth.  In addition, both of these writers emphasize the importance of helping others once you have found the truth.  The Apostle of God came to the people and answered their questions about how to achieve this enlightenment about reality, according to Deliverance from Error.  Socrates tells Glaucon about how once you have reached enlightenment, it is your role to return to the den in which the imprisoned men reside and make sure to help them see the light of reality.  It will be a struggle because they will deny what they are not accustomed to, but it is something that must be done according to Socrates.
The difference between these two works is that al-Ghazzali believes that the enlightenment is brought down from not only the human, but from God.  al-Ghazzali said that 'God Most High cured me of that sickness" which was his skepticism of religion.  Plato's work speaks of the importance of humans.  It is the humans that are in the light, and it is the human who plays the role that God plays in al-Ghazzali's work (this role is bringing enlightenment to those who are struggling to see reality).