From ancient times to this day, people have been incessantly arguing about the possibility or impossibility of the existence of God the Creator, but what does the science of sciences of mathematics say about this?
Back in the first half of the 20th century, the brilliant German mathematician Kurt Gödel proved two theorems that in fact prove the fundamental limitations of human thinking.
Human thinking
Mathematical logic is the pure embodiment of how human intelligence works.
And Gödel proved that formal arithmetic (as well as any other, formal language, which is also our "ordinary" human language - for example, Russian) has fundamental boundaries, beyond which it is impossible to go in principle.
There are only two types of formal systems
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In the first case, it is an “incomplete” system, a system of axioms (initially given concepts) with the help of which it is possible to make an assertion that cannot be proved or disproved by means of this system (“incompleteness”).
In the second type of systems, it is possible to derive a statement that can be simultaneously proved and disproved ("contradictory" system).
Other systems of formal logic simply do not exist. And the concept of God in theistic religions certainly falls into both the "incomplete" system of human formal thinking (including human language, for describing thoughts), and into the "contradictory" system, if we allow "miracles" as an integral element of many religions and ideas about God.
Thus, the dispute about the existence of God, which has been going on for many centuries and even millennia, is simply insoluble within the realities in which we all exist - having our brains, which are arranged exactly as they are, and which have their own formal language means of communication and dispute.
Our concepts
And this despite the fact that we do not even touch on the "axiomatics" of the concepts that we use in language or in any dispute, including about God.
The exact meaning of each of the abstract concepts of the human language - such as life, love, beauty, reason - cannot be precisely defined, which means that it is simply impossible to find absolute truth, since we have to use concepts whose truth and even accuracy we ourselves only understand to a certain extent, we understand very conditionally and only in general terms.
You can find conventional and relative truth, and be content with it, as long as it does not cause contradictions in the field of its application. Truths of this kind include open and reliably verifiable laws of nature, some agreements about how we live in society (state laws).
It is possible (and even necessary) to argue about these relative truths endlessly and achieve some results: changes in the laws of society, clarification or discovery of new laws of nature. There is simply no point in arguing about the absolute truth, under the definition of which the idea of God certainly falls.
Thus, the refusal to reason about the "proof of the existence of God" by means of logical argumentation and our linguistic, conceptual apparatus is the only possible scientific worldview, and this is precisely what is called agnosticism.
Everything else is questions of faith, whether a person believes in God, the spontaneous generation of life, or some lack of logical knowledge to explain existence, and this lack of knowledge will always be, according to Gödel's proven mathematical theorems.
And if you so want to convince
This is really often desired and it is quite a human desire, regardless of whether you are a believer or not.
However, if you are a believer, then you can simply share the calculations of your faith with an interested person, while respecting the God-given freedom of a person (including unbelief).
If you are an unbeliever, then it will be enough just to understand ethics and all the same freedom of each person to adhere to any views and believe in anything, as long as the actions of this person do not violate the law.
In addition, the dispute about the fundamentally unprovable always saves a lot of time, effort and energy (including health).
Why Believers Like It
Still, the dispute between a believer and an atheist is an unequal dispute. The atheist always demands proof. And since proofs are simply impossible, then, as it were, the believer wins automatically.
Because the victory of an atheist in this dispute would be the absence of proof of the existence of God. There really is no evidence - within the framework of human logic, human language and human thinking.
However, God, and a believer of any religion will tell you about this, clearly goes beyond these boundaries and all religions claim that God is fundamentally unknowable … And here, moreover, the queen of sciences proves the fundamental possibility of the existence of something that definitely remains unknowable in principle. Is it only God …? However, this is already a rhetorical question.