The Mathematical 'Other'

I am proving a theorem I have understood. I am writing out the proof. To whom is a theorem being proven and for whom? For posterity? For the ideal mathematician? For an invisible mathematician who is always there? A ghost. Now it is true I want to win the trust of this ghost whether the future reader is convinced or not. To never cheat the ghost and hope that some such correct proof is a key to secret code of transcendence.

You may ask :what a strange kind of ghost that stays mute until the end of the theorem , that does not ask me questions at every step and seek clarifications of every proposition because what in the world is not potentially ambiguous? Or the case could also be that I have complete empathy for said ghost, that I could envision it taking hostage of my own self. That all the mid-proof surprises, doubts, affirmations,jolts of sarcasm it goes through, I too can feel . The ghost can feel the same relief of reaching the end of a proof and shaking hands with me that , thank God, the business was finite , well just enough.

A finite business of discrete, discreet acts. For Heyting, the ghost and I construct every mathematical object through dialogue and we midwife it silently out of the womb of history . For even language is not necessary for this holy act. We can say this ghost is necessary to my own existence and I carry it like a hallucination worth my affection.

To live with the ghost may seem so eerie. And yet it is not a burden throughout the day. Instead our proofs are less lonelier. Those were the days when we proved things for our own clarity. We proved the same theorem again and again and again. To prove a theorem again and again , to win the trust of the ghost every single time and yet you may ask: Who am I? If I am not a mathematician who invented the theorem, then this I is ghost-like in its pretense.  The ' I ' is exceptional only because of its ability to have absolute and perfect empathy with the Ghost which may sadly be suspected to be its own creation. May every Calvin truly understand the innermost feelings of his Hobbes.

 There is, thus, no mathematical 'other'. The proof divides us temporarily into two entities skeptical of each other . The only true stranger is the mathematical object and all the secrets it hides, and which it may soon reveal . And yet it is our child.