Why does the world exist? It just does, without a cause. Could it not have existed? Yes. Could it have existed in a primitive form, such that intelligent beings never came to be? Yes. So why does it indeed possess the property of birthing intelligent worlds? It just does, on its own, an absolutely random property, without which neither we nor these questions would exist.
As an option, a model of the universe could be as follows: it has a beginning, preceded by the Era of Nothing, it emerged with the spontaneous appearance of self-organizing matter and has since evolved. Its structure is a Multiverse or a collection of Multiverses, and its properties enable it to continue to develop and exist eternally. Indeed, at present this assumption, as a comprehensive view on the world's boundaries, lacks a complete and adequate explanation, but as a hypothesis, it warrants recognition, which can be designated by the term "beternism", from the words "beginning" and "eternity".
The universe demonstrates striking mathematical elegance in wondrous equations, and the thought arises that even if there were no matter, these equations would still exist, as the ideal being, which means they have a purpose: the universe, with their help creates intelligent worlds. But the paradox is that if there were no matter, then there would be no such beauty — they only exist due to the presence of matter. The fact that they are so incredible — it's simply their property, and if they were not like this, there would be no us or these questions. They are, as they say in the language of science — supervenient phenomena, not miracles.
Which questions will remain unanswered by scientists? There are no questions that science will not eventually be able to comprehend and explain, it is only a matter of time. There may be certain details that are not crucial for understanding the overall picture of the world. For instance, perhaps, science may never give an exact answer to the question: How much time has passed before self-organizing matter appeared?, but since that period was the Era of Nothing, the concept of time loses its meaning, and therefore the answer to this question is not so important.
Mathematics does not exist in the Universe as the substance of creation; it exists as a language for describing natural phenomena, playing an informative and descriptive role for us. The magnificence of its equations depends on the whimsicality of the physical world, without which the equations would not be so elegant, and we would not exist.
The existence of such a curious creature as humans suggests the existence of a Universe just like ours. And this doesn't mean it was planned this way or that this is the only possible mode of existence. Reality could have had other properties that would not allow for the emergence of any kind of intelligent beings. Yet, fortunately for us, reality is just as it is.
