Burdens ... and Proofs

Christian: ...God...
Atheist: You refer to this "God" as if it exists. I'm skeptical. Prove it.
Christian: Excuse me?
Atheist: You seem to be making the positive claim that God exists. That means you have the burden of proof. 
Christian: You refer to this "burden of proof" as if it exists. I'm skeptical. Prove it.
Atheist: Cute.
Christian: Seriously: you seem to be making the positive claim that positive claims require bearing the burden of proof. But you don't seem inclined to bear its burden of proof.
Atheist: Hold on.
Christian: Besides, a "burden of proof" is not a thing. It is often just a rhetorical device used to avoid the responsibility of engagement.
Atheist: But you have no proof that God exists. 
Christian: And we have no proof that other minds exist. But here we are in conversation.
Atheist: The existence of other minds is a pragmatic necessity.
Christian: The existence of God is an ontological necessity.
Atheist: So you assert.
Christian: Are you familiar with Fermat's last theorem ?
Atheist: Sure: no three positive integers x, y, and z satisfy the equation xn + yn = zn for any integer value of n greater than 2.
Christian: Very good. Are you familiar with its proof ?
Atheist: Well, I understand that Andrew Wiles took almost a decade of work to come up with it, and the proof is formalized in 129 pages.
Christian: Quite so. Do you suppose mathematicians used the theorem in the 358 years between Fermat and Wiles?
Atheist: Perhaps they did.
Christian: Without a requirement to bear the burden of proof?
Atheist: I suppose.
Christian: But about Wiles' proof. I'll confess that its mathematics is inaccessible to me. Are you able to track it?
Atheist: Not at all. It is, frankly, over my head. Why do you ask?
Christian: Well, Wiles claims that his proof required what he calls an "indescribably beautiful revelation" to discover. If proofs of mathematical theorems that any child can understand can be so far over our heads, what makes you imagine that proofs of transcendence (something already over our heads, by definition) should be easily accessible? Perhaps, rather than a proof, you need an indescribably beautiful revelation ?