Semi-strong agnosticism states "it is probably the case that I cannot know whether a deity exists or not, and neither can you, but there is a possibility that my mental model of the certainty of information is flawed, and hence there is a possibility that it is possible to know for certain whether a deity exists or not".
My belief in strong agnosticism stems from my general stance on what I can know (I first thought this after spending some time thinking about Descartes' I think therefore I am):
That which I perceive exists, but I cannot know the nature of its existence.
So, I perceive myself, but I cannot know the nature of my existence, for example I cannot know whether I have free will. I perceive the world around me, but I cannot know whether it is real, a dream, an illusion or a simulation.
Hence, I may perceive a deity but given that I cannot be certain that I'm not in a dream, I cannot be certain that the deity is not merely a figment of the dream.
However, I have to accept the possibility that my general stance on what I can know might be wrong, and therefore have to accept the possibility that there could be some kind of mathematical proof of the nature of what I perceive, and hence of a deity.