The principal cause
It was published the other day that a group of scientists had found a plant to be performing arithmetic division. The plant would control the speed at which it converts its accumulated starch reserves into energy at night, so as to not run out before the sunrise.
Whether humans "invented" or "found" mathematics is one of the oldest philosophical questions that have been recorded in history. In the case of the dividing plant it is arguable whether the plant really implements a division algorithm or not. But regardless of how it does this feat, it still uses the abstract mathematics behind the arithmetic division for its own purpose, for controlling its energy consumption. The mathematical idea of division implies certain properties for it, and the plant applies these properties for a seemingly unrelated purpose. Therefore, it "knows" mathematics.
But the plant cannot have invented its mathematics. It doesn't have a culture nor the capability of thinking about the most appropriate way to balance its energy use. It cannot invent an algorithm by planning ahead how to modify itself. Given what we know of the plant chemistry and physics, we can say that it must be that this feature has emerged in it, produced by numerous mutations of its DNA over the course of years. The chaotic, fractal process of evolution has produced variations for all available mutations, they have been tested, and this one has remained over the others.
It is also well known that the very same underlying chemical processes that enable DNA-based biological evolution, exist in both plants and animals, and thus also in us humans. Our existence as such is not any different from the existence of the other forms of life we're aware of. You can say that the world peoples; it took a while for us to appear, but we're here.
On the other hand the advent of particle physics made us realize that we're all made of the same stuff, same particles, regardless of whether we're of flesh or of cellulose (or of silica). The atoms we all share don't change their function based on the biological status of the chunk of matter they're part of. If we combine this thought with what has now been found to be a fact, that mathematics cannot be simply a human invention, it must be that mathematics is something shared by the whole universe, and that it is a property of the universe itself that it finds ways to apply mathematics.
Taking mathematics and the concept of evolution together as a whole opens many interesting questions. Generally evolution and natural selection are thought of as processes of living organisms, but the most central concepts, variation and natural selection, can be extended far beyond that. For example, you could consider the fact that life has emerged on planet Earth as a result of natural selection: the universe is full of planets, but "life" could not emerge and maintain itself on planets that were not sufficiently hospitable. Taking this idea still further, we can go even as far as to say that the universe as we know it is a result of natural selection of certain mathematical constructions, in particular those that define the physical environment in which the known particle physics emerges. This logical outcome has often been disregarded in the past as circular reasoning: it's not useful to claim that the universe exists only because we think it exists. But since mathematics is apparently not be a product of the universe, rather the opposite, there is no logical fallacy. The universe exists, not because we observe it, but because there is mathematics behind it.
It seems that all the way from the most basic physics, the universe itself is the implementation of different mathematical expressions. It is a fractal universe that composes more and more constructs on top of each emergent feature, combining each useful byproduct in most miraculous ways. The underlying principles must look like they got selected "for us humans", just because otherwise we wouldn't be here to observe it. With "intelligent" life, the universe has found a way to make use of the fractal complexity of itself to help find interesting expressions and to implement them withing the system itself, automatically, with this particular set of fundamental choices for "physical laws". We are smart enough to realize the value of mathematics, and we're capable of categorizing and combining mathematical expressions to produce results that compete in beauty with physics itself.
This is not a religion, and does not rule out religion as a guide. It is not the basis of a moral code, nor does it exclude the value of moral codes in general. It does not give purpose to the existence of life as such, but I feel that it does define a clear framework for why the world as we know it exists and how it came to be.
Where does that leave us? The universe itself starts to look like a deterministic system, trying out all possible evolutionary steps. If so, it should really be possible to calculate the same steps with a big computer.
One of the greatest inventions of the humankind were algorithms: methods of evaluating rules for finding results to mathematical problems. If a problem can be represented sufficiently unambiguously in the human-made language for mathematics, often it is possible to find steps of calculations, or a mathematical proof, to find the answer to the problem. We have also figured out that there is a certain group of very difficult mathematical problems that cannot be solved effectively using normal step-wise calculation. These are called "NP hard" problems. The known algorithms for computing the answers to this group of problems are too expensive to execute. It simply takes too much time, too many computing steps, to find the final result for any such problem of practical size. Theoretically the correct results can still be found.
To simulate the universe, you don't need a fast calculator; you need one that runs for eternity without stopping. And running for an eternity may not be impossible at all. Think about the planet we're living on. It has been alive for a long, long time before we came to inhabit it. Surely even that time interval is finite, but it's not over yet.
For us, inside the system, it's easier. The universe itself does computations for us, whether we think we're in control or not. Throughout the history of physics it has been seen that if you implement the problem in just the right way, the universe itself finds the result for you, just like it did for the dividing plant. It is still unknown whether this also applies to NP hard problems, but we've already seen that self-sustaining subsystems are able to grow, mutate, and to live on in a framework like this, and we haven't reached that point with our own computers yet.
I would propose that the same applies to the universe itself. It's growing and learning all the time, and it wants you to help it grow, to find new, yet undiscovered mathematics, and to apply it in all the different ways you can think of. We're all "it", and boy what a ride it is!