Define "G-d", define "existence", and you'll have answered your own question, no matter what those definitions are. We live in a material world, call it World or Earth. We experience sensations through our organs into our brain, where the little electrical flashes go like crazy. We see others like us, we were raised by others like us, mother and father, who from infancy told us through language (which somehow we've managed to learn!) what things are like and what to expect. It's amazing how humans do not differ that much. There is a novel "The Black Cloud" by astrophysycist Fred Hoyle which describes the arrival to the solar system of a cloud of some sort. Eventually people understand it's alive (?) and it's inteligent (?). The book touches this sensitive point: what is to be alive?, what is to be inteligent? An inteligent non organic life form not attached to a planet? Eventualy the astrophysycist of the story manages to engage communication with the cloud (?). The cloud seems to be a quite relaxed being who doesn't worry much about anything in particular, not even his own life, his destiny, whose only interest in life is to study and understand the Universe (see World, Earth). The cloud doesn't have children, at some point in life it splits in two who totally relaxed continue their travel through the Universe. After some talk with the scientist, the cloud notes the oddity that humans, though different individuals, seem to feel exactly the same about the same pheonomenon they experience. So, we all feel roughly the same when our organs sense the same thing. This is what makes Science possible: common experience and reasoning. "Existence" is synonymous with "existence in the real world, ie Universe, Earth", which means, in the current state of Science, to emanate some kind of field, either gravitic, or electromagnetical or a probability field as in quantum physics. "G-d" is what? I don't know. You say "G-d exists", show me a field of some sort so that I can identify its source, and then we can stick the label "G-d" to it. But whenever you look for a definition of the word "G-d" you hit this: it is something that does not exist in the real world. So G-d doesn't exist, period, by the definition of the word. You'll say: but I think about it! Yes, you do think about G-d: that means there are little electrical flashes going like crazy inside your cranium. Is there the place where we should look for the source of the field to which we should stick the label "G-d"? No, you say. So, what?, says I. I don't know, says you. And we can go round and round with this throughout the ages of the World. No, G-d, by the definition of the word "G-d" doesn't exist, scientists are right. Not just scientists, also philosophers, the mailman, anyone who has a head, a reasoning, and stops for a while to think about it. At this point atheists always rejoice hearing me saying this. Caught you! Either you're a hypocritical atheist who goes around praying and eating kosher for no rational reason at all, or you're a hypocritical religious man who goes around saying G-d doesn't exist. Nothing of it true. G-d (we'll not define this word at this point) made the World/Earth on one side and Heaven on the other side. The Earth goes by these rules, Heaven by those. Among the rules of Earth is reasoning, let's say a present from G-d to mankind. Man can walk around the Earth using his reasoning to grasp the rules by which the Earth goes by. But no matter how much man struggles with his brain to grasp the rules of Heaven, he can't. Man was given a key which doesn't open that lock. Simple as that. G-d, soul, Heaven, things for which we have words and electrical flashes in our craniums, can't be grasped by reasoning. But you can be conscious of them. Being conscious of them is what people usually call "believing", "faith", etc. You can extend the meaning of "existing" from "existing in Earth only" to "existing either in Earth or in Heaven", and then you can say G-d exists. But someone will always come along saying Middlearth and Narnia also exist. And then you start with him the childish conversation no it doesn't, yes it does, not, yes, not, etc. The only definition of "exists" that suits everybody (as long as we're talking with a rational person) is "exists in the Earth". Answering to your question: why being religious is a duty? Ie, why living according to the Torah is a must? Because. But what if I don't, says you, then you scramble the whole setting of the cosmic wheels and G-d knows what no good will come out of that, says I. No I won't scramble anything, says you, yes you will, says I, not, yes, not, yes. Yes, yes, you must live by the Torah, and you may lay to that.
