There are many methods for attaining knowledge in this world. They don’t all work very well. Knowledge allows you to more accurately predict the results of any action taken. The scientific method, since it assumes nothing, seems to be the most effective learning method.
Math is just another symbolic language. We use it to analyze various situations. However, it can only go so far in terms of concrete relationships (where an action always results in the same result). Most relationships between actions and results are probabilistic. 40% of the time when I do X, the result is Y, the rest of the time, the result might be Z, A, or B. So don’t worry, there will be no drones. There is much room for interpretation in numbers. There is much that numbers don’t explain.
Just remember that numbers are the same as words. If we didn’t use numbers, we could still describe relationships between things in words. It would just take longer. Numbers can be used to streamline the discussion. They do not bring us any certainty, however.
I guess what I’m saying is that your understanding of science and scientific method, and math and statistics is very incomplete. If you knew more, you couldn’t ask the question you asked.
When you say that there are some questions that can’t be answered by scientific investigation, how can you know that? Sure there are things that we do not yet have adequate explanations for, but this does not mean we won’t ever get such explanations.
Religion is another way of gathering knowledge. In Christianity, for some versions of it, they say all the knowledge they need is in the Bible. The Bible explains everything. Some religions say that there is a lot we don’t know, but our deity knows. We may never be able to know, because we can’t be the deity. If you belong to such a religion, then you look for truth in your holy book, and you distrust information gathered by making hypotheses, gather data to test those hypotheses, and either supporting them (though not proving them completely), or disproving them. Such a system knows too little (although you call it too much). So some religious people need a God to give them the feeling that even though there’s a lot they don’t know, they have a benevolent deity watching out for them, and that deity knows what its doing.
So, to answer your question: No, science is not playing too big a role in the world. In fact, it plays too little a role.