If there is no absolute proof that there is G-d, then why should anyone believe this and actually keep Judaism? Thanks, Al

Answer:

You ask how we can believe in G-d if His existence is not proven. Believing in G-d is just that - a belief. Something proven requires no belief, so if we could prove G-d, then we would no longer need to have faith in His existance.

Nevertheless, Judaism does not espouse 'blind faith'. As Jews we ask, study, seek, find, and ask again. There is a Jewish saying that 'where knowledge ends, faith begins'. The further we push ourselves to know G-d intellectually, the better. This will never mean precluding the need for faith. But we will have replaced that which was once faith with knowledge, and then move on to the next level of faith.

As to why should we keep Judaism based on our faith in G-d: I guess there are many things we do even without understanding or proving them. We take medicine without being a chemist or physician. We fly on planes without understanding aerodynamics. We decorate our house even though we can't prove beauty. We  have children even though we can't prove love and trust, and even if this means inconveniencing ourselves for a good couple of decades.

Living a Jewish life promises eternal benefits both in this present world and in the next world. Living Jewish brings us closer to G-d and allows us to achieve personal potential and fulfillment. Even if you have doubts, isn't it better to possibly 'err on the side of caution' (and spiritual advancement). Besides which the obligations of Jewish life itself will, G-d willing, bring you immense joy and meaning in themselves.