There is no sound argument for the existence of god

Ok, let"s start with your first point where we have a confusion. Nature doesn"t obey mathematical laws, but rather physical laws, which are written in mathematical terms. Mathematics is a language to describe aspects of systems, which operate in the rules of logic, which mathematics has to assume in order for it to work. The formulation, that mathematicians discover a separate world, is therefore misleading, as there isn"t a world of mathematics, which has to be discovered. Mathematics is rather concerned with how logic works and how that can be formalized. Therefore it is not surprising that mathematical principles can be predating the discovery of physical laws, which demand them to be formally described. If we take the example of relativity, we can see that Riemann"s theoretical work is not in the slightest dependent on any practical applications, so that even if Einstein had never found relativity, Riemann"s work would still been mathematically correct. It becomes even more clear if we look at Newton. He found out, that the orbits of the planets around the sun represents ellipsis, which is true independent of him finding the method of differential calculus to describe it. He searched for a mathematical description to check that his findings made logical sense and in order to do that, he developed differential calculus, which is logically consistent and also describes the ellipsis of the orbits. He didn"t develop differential calculus to prove that the orbits represent ellipsis, but rather described his findings. In light of the nature of mathematics, the "usefulness of mathematics" is logical, as it serves as a language to articulate a physical concept. What I think you are arguing is, the question, why logic in form of mathematics is fitting to describe the universe we observe. There are different explanations for that which all include the possibility, that the laws of logic and causality, which build mathematics, can be observed to work in nature. As humans now observe it and expand it in the form of mathematics the basis would still be in an observable logic. Such explanations would show that a mere observation of nature would lead humans to base their thinking on logic (as an evolutionary advantage). Any such connection between logic as the basis of mathematics and the observable universe are absolutely independent from any kind of god. Now to say that there are different universes which independently exist, I have already shown to be not very cogent. The point of consciousness, which I will show has certainly a physical grounding, I will pick up on later again. If we take mathematics, we can see, that it is not a "universe in itself" (what ever that is supposed to mean), but rather a language with logical rules. The notion that the physical universe is a "reflection of these prior formal ideals" and that this ideas exist outside of physical reality doesn"t describe the actual nature. While Mathematical truths based on the assumption of logic are in any condition correct, there is no reason to belief that a mathematical language predates the universe in which it is devised. This happens through thinking entities, which are in all the cases we know of physical and therefore part of our universe. To say that mathematics was there before space and time and before there was a brain to devise it, can"t be the case. Therefore is the notion that Mathematics in its descriptive power, hints at a god, false. Let"s now turn to consciousness. There you start by stating that the consciousness has no physical presence in the world, which directly contradicts the observation. Neurology shows that the state of our consciousness is directly dependent on physical state of our brains. To give an example, we can measure how states from deprivation of oxygen to the lack of your morning coffee, which are physical parameters, directly influence the state of the consciousness (from the loss of consciousness to a bad mood). To say that thoughts are non physical and it is mysterious that they can move our physical bodies is just flat out wrong. We can trace our physical actions directly back to the actions of our nervous system. For example if you would lift your arm we could measure the biochemical changes in your brain resulting in an excited neuron, which then brings your muscles to move. As earlier stated, we can also say that the state of the nervous system directly influences the state of our consciousness. While we understand to some degree how our neuronal system is influencing our physical actions, as well as the other way around, science hasn"t so far understood the mechanism by which consciousness arises from our neuronal system. This though doesn"t even in the slightest imply that it is a supernatural way on which consciousness arises, as all we know at the moment points in the opposite direction. I don"t really understand, what "images and thoughts in our consciousness have no measurable dimensions" is actually supposed to mean. If you mean that the processes of consciousness can"t be measured, I have to disagree. Recent neurological methods allow us to measure directly what the thought of a person is, through measuring the electric currents in the brain (2008, California University, Jack Gallant). It is for example possible to reconstruct a picture of which a person is thinking through those measurements. Now while this technology and understanding of neurobiology is at the moment at best rudimentary and we can already show that consciousness is depending on the physical brain and therefore we can conclude that such a thing as a non physical consciousness independent of a brain, is in all we can observe not possible. Therefore to conclude we can see, that even though science hasn"t found the mechanism for consciousness yet, "the supernatural character" of consciousness, is contradicting what we so far now about the relation between brain and consciousness. Let"s now come to evolution where you make two points. Sadly neither "punctuated equilibrium" by Gould nor the ability of organisms to influence their heredity implies the necessity for a god in any way. The first is that "punctuated equilibrium" by Stephen Jay Gould, implies in some way a supernatural supervisor of evolution to work. I can sadly not see any reason to think so. What Gould has found out is that Evolution occurs not continuously but rather in jumps, where first over a longer time only slight adaptation occurred, which then is followed by a comparably small period of time with big changes in form of new species, due to events with an impact on the system. This theory does neither contradict the basic principles of evolution, nor does it state that for such a "sudden" change, there has to be a supervisor. We even have evidence that evolution can be quite fast according for example to Dr. Frans Witte. He has observed the change in the size of the gills of the cichlid H. pyrrhocephalus in the cause of just 20 years. The second point you are describing is, that there is there is a debate under biologists about whether basic Darwinian evolution is sufficient, or whether the ability of organisms to influence their heredity is important. What you exactly mean by a "purposeful "sentience"" guiding micro-evolution I don"t understand, but the statement that organisms influence with their behavior their heredity I can accept. In fact it is actually part of the evolutionary concept where such behavior is also selected and therefore doesn"t imply the supernatural at all. Important to add is that contemporary scientists don"t just agree with Evolution as Darwin proposed it, but expand the concept with new studies. Francis Collins thoughts depend on the definition of god. As long as you are not proposing that this god interferes with evolution I grand that, but to say that recent results of evolutionary biology make god more probable is not true. Therefore I still can"t see an argument for god