Let's start with an answer to your comment on the question itself @RabbiKaii.
Yes, logic itself is an effect of a cause, that cause being design. In fact, we can even argue that logic itself is a fundamental guide to creation. Perhaps this is proof that God himself, or even the concept of God itself is nothing but ordered, similar to the understanding that the cosmos is a well ordered whole by definition.
For a moment, let's get "deep":
*Let us "assume" that God is not a singular man, rather, equivalent to the big bang. In this situation, let us say that God is expressed in a mammalian sense. Since we mammals need the masculine and feminine to express creation in regard to biology at the least, let us say that God is the dualistic expression of the masculine and feminine in regard to energy perhaps at the foundational level. This point itself puts any theological connections into question since theology is in and of itself monistic, whereas this point requires dualism.
*Let us say that this dualistic source, of both masculinity and femininity, is in and of itself designed via laws such as the law of attraction and even the law of cause and effect. The law of attraction dictates that opposites can pose a cohesion, whereas the law of cause and effect can be used before and after. The existence of opposites allows for the effect that is the law of attraction, whereas the existence of the law of attraction allows for the effect that is creation via opposites. This of course suggests some sort of cosmic truth in accord with biology on an energetic scale. Surely to be debated.
*If we can fathom that existence itself retains innate design, perhaps we can say energy is the designer. If energy is the designer, it would truly require the law of attraction and even the law of cause and effect to even be fathomable.
*Once we accept the above, even if for a mere thought experiment, we can move forward with the potential understanding of how God designed logic.
*If God designed logic, it must have been within its own image. "its" is used solely to quantify both the masculine and feminine role in creation.
*The formulation of logic in accord with innateness of what God is, is nothing but a metaphorical "glance into the mirror". The quantification itself must be accepted by all, in order to truly be logical. If it is not, it will be logic that is opinionated, thus being what I call "masqueraded logic". Why? Because logic itself is meant to provide clarity. Opinions themselves do nothing but cause muddy notions.
Thus, we can argue that logic is designed, or even a quantification that allows for a concise description of that which is designed itself. While some would argue that creation and design are different things, let us take the following into account:
Creation implies a "from nothing" or "from scratch" notion, saying that we took multiple things and made it something "new", or made something that never could or would exist. The former is more appealing than the latter.
Design implies a "manipulation" or intended order of something that had to be created... perhaps. If something had to be created, then we must reference the former and attend to "design" with reverence to such. If not, then we can say that creation happens because "something" always is. Perhaps this something is energy, and perhaps energy itself can concentrate to the point of something "significant" happening.
Taking all of this into account, yes, we can argue that logic was designed via God, even if we manipulate the definition of God itself. In fact, this notion would suggest that we are at the least exercising a trait of God via ourselves. Perhaps a damning notion but regardless, it seems as if though it is truth, regardless of opinion.
To correlate back to the question itself, in regard to mathematics, we must understand that math itself is seemingly a principle of all existence. Thus, it would be probable that 2 + 2 = 4 is unchangeable. For instance, if there was one concentrated masculine force and one concentrated feminine force, that we could argue is the reason all things, all life exists, we could go further to understand that 1 + 1 = 2 is a foundational truth that allows for the initial two forces of all existence to "look in the mirror" and see themselves as what they are. That simply would be individuals expressing as opposites that are compatible, to simplify it incredibly.
We see that 2 + 2 cannot = 5 because it is laughable, truly. Why? This could be due to the nature of numbers themselves, or creation itself. Biologically, we understand that 1 + 1 = 2 and can even create situations where 1 + 1 + (specific act) = 3. This itself is a numerical equation for creation biologically, perhaps specifically in the mammalian sense. Thus, if energy follows similar laws to mammalian laws, we can see that 1 + 1 + (specific act) = 3 translates to 1 + 1 + 1 = 3. Even further, 1 + 1 + (effect of specific act) + (engagement of specific act again) = 4. Via this "model" it is true that 2 + 2 = 4 total, not even showing the potential for 2 + 2 = 5.