In explaining your question, you have stated only a series of your "beliefs":
Everything relies on mathematics!?
Everything can be calculated/predicted!?
Maths is a fundamental explanation to everything!?
How and what you think is dependent on the chemicals present in your brain!?
We can effectively run a simulation of the human mind and the interference of all these chemicals to determine/predict each and every action of an individual!?
You are actually telling us your "religion" because you correctly conclude: "Religion is basically what you believe in." It means that you are currently, just at the beginning of cognition, answering your question! Therefore, following your task is to "refute or confirm" your beliefs!
From my point of view, your "beliefs" are not grounded at all because you overlooked the fundamental fact that your question was asked by "your Mind - our Mind" and which also posed the postulates of the Mathematics (logic) you are talking about, so your answer is imposes on its own - that "It Is Mind To Determine Everything In The Universe." This is the fundamental postulate of Kant's "Copernican Turn" in Philosophy!
Our Mind recognizes both us and the world around us, thus creating within ourselves an image of our world - "woven of ideas" - of knowledge and belief, which it then tests in reality to transform them into a new truth, that is, a new knowledge! So the Mind creates its knowledge in the interaction of itself and its environment, not how you believe in the interaction of some chemicals. Chemicals (or electromagnetic states) are not thoughts (ideas) they are just a means of remembering ideas and thinking!
Imagine now your a "very powerful computer", which you dream of, which would predict "everything"! That computer, in its working memory (soul), must have all the knowledge, beliefs and delusions of our Minds, and in its hardware (body) the entire Universe! So why would someone build such a computer when we and our Mind already live in one of these already?!
And as for predictions: the past is what no longer exists, the present is what our Mind just realizes, and the future exists only in our Mind as our belief! Reasonless predictions don't even make sense! Our Planet revolves around its axis and around the Sun, whether we predict it or not. Much more important than predicting is to understand the "causes" of the phenomena! Just look at what evil in the world was created by people and their movements that "predicted a better future." Just look at what misery and chaos in the world right now is being created by false sciences such as economics and epidemiology that misuse mathematics for their "predictions", all for the purpose of one's "private interests"!
The most interesting, and probably "the most wrong" of your belief is: "Maths is a fundamental explanation to everything"! This belief is currently prevalent in the natural sciences, and especially in Physics where it causes the greatest "damage"! This belief has led to the fact that many "physical theories", without any physical foundation, work very well and evolve on postulates of pure mathematics. But Physics and Math are not the same! Physics is our objective - truth, and Mathematics is only our instrument - a tool! In Physics, every member of the equation must have its "reason", and in Mathematics it is - whatever!
Thank you for the opportunity to exchange opinions!