Truth is tricky. If I state "The sky is blue", I can look out of the window, the sky is blue, my statement corresponds to the state of the world, my statement is true, right? But in mathematics there is no window, everything is internal, abstract, so what does "truth" mean when there is no state of the world with which to compare? More importantly, would the mathematics be any different if the axioms are declared to be true? No, it wouldn't make any difference at all. So let's leave "truth" to the physicists and philosophers.
This is perhaps not all that relevant to your point, but "the sky is blue" so often being used as an example of an obvious truth is amusing to me, because very often the sky is not all that blue at all.
If I look outside right now, the sky is probably better described as cyan; quite obviously a different colour from the blue exercise mat that happens to be on my floor.
The sky can also be described by many of the other colours depending on weather or the time of day.
