only if you believe in just reincarnation If you feel there can be new souls added to the existing recycle then no there is not a finite number of souls

It depends what your belief system about souls and reincarnation is. You don't have to believe in a soul to believe in reincarnation, and reincarnation need not be "species dependent": I've heard one buddhist cosmologist claim that as human life expectancy increases, the demand for "souls" must partially be satisfied from the animal world... hence society gets more violent and self-absorbed as each decade passes. Personally -- I would say no. While there is no evidence that "souls" exist -- I see no reason why the source of "soul" is any different than the source of sunlight -- there's enough sunlight for millions of generations of humans. The sun will eventually burn out -- and humankind will burn out with it unless we've figured out how to move to another galaxy by then.

(Tagging on to peter b) Buddhism flatly denies any evidence for the existence of a soul which might be the medium of reincarnation. That isn't to say it doesn't exist, it means "nobody's ever found one if they go looking for it", i.e. no evidence. Many strains of Buddhism have inherited ideas of reincarnation which trace back to it's roots in Hindusim, however these ideas aren't considered central to Buddhism and plenty of Buddhists consider this an archaic notion. Some Buddhist teachers do believe that "rebirth" occurs, which is different -- because this notion doesn't mean that the soul becomes detached from one body and incarnated in the next, it means that the "causal effects" of one life flow into another life. Think of it like a candle flame: if one candle lights a 2nd candle and then the first candle goes out, is it the same fire? Well, it is and it isn't -- the first fire caused the 2nd fire, so there is a continuity of sorts. But to think of the flame as having some sort of independent existence is wrong -- without the candle wax and oxygen there's no flame. In Zen (which is my neck of the woods), we eschew all sorts of metaphysical notions and focus on waking up from the ignorance, greed, and fear that run most of life. It's a here-and-now orientation that's about realizing and expressing true self rather than arguing about things we have no experience with.

the Vedic religion of the Hindus who believe in reincarnation say "Brahman (world soul Athman) is of the nature of truth, knowledge and infinity". Thus soul is infinate.

If so, why are there more souls today than there were 5,000 years ago, or even 100 years ago? Are we therefore reincarnated into more than one soul?

1) No. What would we do if all souls had a body and a new body would come? Find the answer to that other question first, it will help: http://www.answerbag.com/q_view/467508 2) "In this ONE UNIVERSE there may or may not be a finite number of those souls. I would say there probably are only a finite number of souls in this universe, but it may be in an expanding part of its cycle and new souls may be entering it at any time. Also souls are going clear, getting enlightened, reaching Nirvana or what ever you want to call it, so they are probably leaving the universe. Possibly many more are entering at this stage than are leaving it." Source and further information: http://www.lightlink.com/archive/adore/adr316.adr 3) "this objection can also be formulated more forcefully in terms of human souls, i.e., the actual infinity of human souls that would have resulted from an eternal world eternally populated by human beings with immortal souls. Aquinas had considered this form of the objection in his De aeternitate mundi, and had noted that it has not yet been demonstrated that God could not produce an actual infinity of spiritual beings. Godfrey does not adopt this solution, presumably because he is convinced that an actual infinity of entities whether spiritual or material is impossible. Instead he proposes as a possible alternative an eternally populated world involving the transmigration of a finite number of souls to an infinity of bodies, and ordered only to their natural perfection." Source and further information: http://plato.stanford.edu/entries/godfrey/ 4) "There are a finite number of souls in Autochthonia, which has kept the population stable throughout the millennia. Recently, however, the mechanisms used to recycle souls began to malfunction." Source: http://www.answers.com/topic/alchemical-exalted