The contemplatives have always known there is a discipline of removal. Meister Eckhart called it Abgeschiedenheit, which translates roughly as detachment or releasement: the practice of stripping the self of everything that is not the ground of being. It was not emptiness for its own sake. It was the condition under which something could arrive that could not arrive into a full vessel.
The problem with this account is that Eckhart was describing a chosen spiritual method. What the mathematician experiences in the period before the next arrival is not chosen. It is an absence that arrives without being invited, and persists without explanation, and ends, when it ends, without clear cause.
The Zen tradition speaks of beginner's mind, shoshin: the openness of one who does not yet know, as opposed to the closedness of an expert who believes they do. Suzuki Roshi: in the beginner's mind there are many possibilities; in the expert's there are few. This is useful as a corrective to expertise. It does not address what happens when the mind is emptied not by practice but by circumstance, when you did not choose to become a beginner again.
The Sufi concept of fana, the annihilation of the self in divine presence, is the most radical version of this pattern. Fana is a death and a transformation. What comes after is not the original self but something that has been through absence.
None of these traditions provide a timeline. None guarantee that something arrives after the emptying. They are accounts of the experience, not explanations of the mechanism. They say: this has been reported, across cultures and centuries, by people of serious practice. They do not say: wait thirty days and you will receive.
The mathematician in the fast does not have a tradition that claims him. He is experiencing something that has been named, obliquely, in other contexts, but not his. The closest practice is the apophatic method, which says: the way forward is through. What you are living is not a problem to be solved but a passage to be crossed.
The traditions do not say how long the crossing takes.