I learned and heard of panpsychism from Eastern religions and Leibnitz, who as a universalist was well aware of and very interested in eastern mythology and religions. In Leibnitz later years he developed Monadology as a final summary to depict his panpsychism view using his famous monad, which I suspect is derived from the old indo-european word "Manas", very similar in meaning to English's word "Mine".
In his view, certain higher level monad like animal soul and human rational mind with reasoning/abstracting capabilities can have consciousness. Only monad is real substance in this world and monads exist everywhere, but one person can only have one distinctive soul-monad which is self-conscious. Plants also have monads but they're of bare type without consciousness. A math entity is only a very abstract concept only found to be in human mind level monad, thus the math concept itself has no consciousness, but the containing mind has.
A computer's memory also can have math entities, but computers are material composites which can be infinitely divisible without a unifying consciousness, thus according to him, this computer can not have consciousness. it can manipulate and compute these math entities faster than any human mind, but it simply does not "understand" any meaning of its computation. And I totally agree with him on this question.
There are many different approaches to pansychism.
In Buddhist Yogacara philosophy, subjectivity is seen as fundamental, with all phenomena occur in the intersubjective space of shareable experiences. That is, no pure objective reality, because no one can experience that, but no pure subjectivity or isolated thinker either because that arises interactively - as illustrated in the metaphor Indra's Net. In this framework, relations between minds would be fundamental, with material experiences like geometry occuring within that, ie within the alaya vijnana, or space of mentalising/narrative possibility.
In physics, symmetries and conservation laws have been shown to be equivalent. If the set of fundamental constants has been determined by the Strong Anthropic Principle, then the symmetries and arising of minds are intimately related, and perhaps equivalent in our patch of all possible universes. That is not all mathematics being a kind of entity, but maybe E8.
It generally does not. According to panpsychism consciousness is intrinsic to matter, it is in rocks or rivers. The more advanced forms of the human-level of consciousness arise due to complex combinations of particles and their specific properties intrinsic to matter (i.e. spin, charge, mass).
mathematical entities, like numbers and functions and sets, are conscious entities
Can be metaphysically speculated under idealist panpsychism where ideas are themselves, conscious agents. I do not recall a variant of panpsychism that asserts just that, however, I find Donald Hoffman's conscious agent theory close.
Namely, Don Hoffman proposes that all experience in so-called reality is constructed by qualias which are themselves, agents. Those agents (i.e. the qualia of red apple) degrade from complex agencies down to simple binary agents at Planck scales. Agents are networked through Markov's kernels and operate via state transitions.
Mathematical ideas are not conscious. However there is a craving to hold on to numbers and mathematics in general. Craving gives rise to grasping. Grasping gives rise to becoming(a Mathematician). Becoming gives rise to birth of ,numbers , mathematical equations , concepts and understanding. However given the birth , the mathematician and mathematical ideas are subject to ageing and death.
Therefore ideas of maths take birth ,and, they age ,and ,they die. If there is a craving left while dying ,then there is a rebirth of mathematician and the related ideas.
Panpsychism doesn’t mean that the numbers themselves are alive. It takes a mathematical mind to become conscious of numbers. Not everything conscious is capable of discerning mathematical ideas.