Keys of Heaven

So this Sunday's Gospel reading was about Jesus giving the keys of the kingdom to Peter, Mt 16:13-20. The first reading is the preimage of this scene where the Lord tells the master of the palace Sheba that Eliakim will replace him, Is 22:19-23. From this story we derive many things but mostly the role and founding of the Church.

So one might ask why is this mathematical, but I want to contend that this story eludes to the very philosophical structure of mathematics and then relate it to the Church. First, what I ask what does a key that opens doors and locks doors do? For one it allows people to see into the room, it also allows for people to enter the room, it sometimes even allows someone to change the decorations of the room or use the room for storage. One thing it does not do is allow the shape of the room to be changed, nor does it change the view from the windows. My point is that keys will allow us to do minor things to rooms but the structure and fundamental elements of the room is already in place.

This is largely how I view mathematical research. Academics is the pursuit of knowledge by opening doors and seeing if we find an answer there. Sometimes we take problems to different rooms to discover potential solutions and other times we just curse the room we are in since it isn't helping us at all. The structure of the palace is the foundations of mathematics that has been set up through the centuries of studying. These things are unlikely to be changed, there will always be an infinite number of prime numbers, there will always the be same number of integers as rationals, etc. Of course the rooms that researchers open do more than just light their own path. By opening new ideas and areas mathematicians are able to drive the field into new directions allowing others make use of the newly opened rooms. This is why we have so many theorems that are discovered at the same time (not to mention that the Communists didn't let people publish freely). So in many ways the mathematician is just a keeper of the keys to mathematics.

This observation gives me new insight (to my very limited sight) into the Church's role with Her keys. In the same way, Jesus has set the foundations of the Church for us to discover by viewing, using, and closing rooms. Thus we are able to discover what seem to be new truths but are actually new use of the same truths. Furthermore, this gives the mandate for the leaders of the Church to open doors that will bring new fruits to the people of our time. The leaders are able to set the sight of all the Church in a direction that will allow our Church to proceed together towards God's Kingdom.

Now there are other things to get from these passages but I just wanted to take a moment to look at the beauty of our Scriptures in relation to mathematics.