Jainism's beliefs are at least 2900 years old and are born out of the Gangetic Indo-European beliefs in reincarnation, the concept of maya and rejection of Aryanic deities like Indra/Thor and Varuna/Dyaus Pita/Zeus/Jupiter.
By 900 BC, the Aryans had been in northern India, in the Gangetic plains for 800+ years and had been moving towards demoting their ARyanic gods like Indra (who in the Rig Veda (c. 1700 BC) is mentioned quite often as the War/Storm God and get high praise and yagnas (sacrifices etc.) of worship, yet in modern-day Hinduism is practically ignored along with the rest of the pantheon bar the Hindu trinity (Shiva-Vishnu-Brahma).
Shiva seems to be more a Dravidian god (if one connects the pictures of the ascetic with a cobra protecting his head that are depicted on Harappan coins to Shiva), while Vishnu seems like a convenient way to add in different gods to the pantheon -- functioning in the same way as Osiris did, so both Rama and Krishna are incarnations of Vishnu (and also 8 other incarnations from Narasimha, the half-man, half-lion to the dwarf who could step across worlds) and Brahma is the creator but ignored)
Indra seems to have retained his place until the time of Emperor Asoka (300 BC) who proclaimed Buddhism as the theme religion of his Empire (which stretched over all of what is now Afghanistan, Eastern Iran, TAjikistan, eastern Uzbekistan, Turkmenistan, all of Pakistan, India except what is now southern Tamil nadu, Bangladesh, Nepal) -- this act destroyed Vedic Hinduism and even when Hinduism reclaimed ground under the Nandas (post Christ), it was Brahmanical Hinduism with Manu rated highly and a Hinduism influenced by Mahavira and GAutama Buddha's rejection of the old gods.
This is reflected in the Jatakas and that era writing where there is a story of Indra attempting to disturb Shiva and shiva cursing him to have his body covered with va... (well, woman's private parts) -- and India from that point on becomes an object of ridicule in Hindu religion (he was already ridiculed in Jainism and Buddhism).
Jainism, with it's rejection of Vedic Hinduism also added in the concepts of ahimsa and vegetarianism --> Jains will not eat any meat or eggs or fish or any vegetable that grows under the ground.
The Jain idea of the universe is
They believe that EVERYONE on this diagram except the Siddhis/Adinaths (conquerors of death) i.e. those who live in Siddhasila are subject to death and reincarnation -- the gods may have powers, but they are just another one of those subject to the law of reincarnation.
They believe in endless cycles of time, and cycles within cycles (the hindu ability to generate high numbers is truly amazing -- their cosmology relates to billions of years).
To answer betty's question -- the Jains argue that all are subject to the laws of the universe and that it is illogical to argue for a being that exists out of it. While Maths did originate in the EAst (from the Babylonian concepts of 360 degress of a circle to the Hindu discover of 0, Natural Sciences too had their origins in the Near East - India, with the extensions into Greece (mainland Greece didn't get civilised until the fall of the Minoans on Crete c. 1700 BC IMHO). The Indians concentrated on maths, metallurgy and medicine.
To answer boatbums -- no one is needed to keep score in their theory as what you do influences your internal "aura" or whatever. This is completely alien to the Christian concepts so it is not Pelagianism either as this is not "doing good" but "cleansing your aura". Also, do note that in the Hindu system, at least the modern one, there is a higher god above the trinity called Ishwara (of whom Shiva is supposed to an embodiment of -- I don't quite follow that). Presumably he keeps score. however, Hindus believe that the universe ends when all (including the gods) are absorved into Ishwara and everything ends.
This ties in to their concept of maya (or that the entire universe is an illusion) which is what influenced the Gnostics from the Paulicians to the Cathars.