Speakpigeon a faculty is a thing presumed in the brain that carries a capacity to perform some, in this case, some ethereal task. In my post I provided significant evidence that the terms insight and intuition where terms of presumption rather than terms describing some material capability that can be found even by aggregating known human brain capacities. They are like God they are presumptions covering numerous sins.
Better that if you read again.
But, point by point here goes.
Mathematicians use externally defined symbols to prove theories and theorems. I'm going to concentrate on the material, ergo, theory.
Tanner explains that
"...a scientific theory is the framework for observations and facts. Theories may change, or the way that they are interpreted may change, but the facts themselves don't change. Tanner likens theories to a basket in which scientists keep facts and observations that they find. The shape of that basket may change as the scientists learn more and include more facts. "For example, we have ample evidence of traits in populations becoming more or less common over time (evolution), so evolution is a fact but the overarching theories about evolution, the way that we think all of the facts go together might change as new observations of evolution are made,"
In every instance materiality continuity is maintained.
A mathematical theorem is
a result that has been proved to be true (using operations and facts that were already known).
from
https://www.mathsisfun.com/definitions/theorem.html note parenthesis conditions.
Intuition is neither an operation, fact, already materially known. It is a cover capturing some presumed ability like those presumed by examination of bumps on one's head. Not a very satisfying way to establish facts a history has shown. May I say falsified?
As for conjectures it's kind of like "I know this is true but I don't have the evidence or knowledge to prove it yet". Time passes, information is gathered, proof generated IAC with operations and facts already known.
For instance we are beginning to understand why self organization of matter occurs.
Self-organization Simply put it's a mechanism for conservation of energy in matter given the structure of our reality.
However this isn't a science forum it's a philosophical forum so I'm done. Now that you have a nice discussion going with
Jokodo I expect I'll learn more. I do see why he chooses to discuss your comments on the proposition you post since the proposition is so unanchored and you aren't. It's in the commentary where one expects to find linkage between immortal and die.