You do realize military and intelligence leaders are the ones that made the recommendation not to shoot it down immediately, right? It's a bit of a political cheap shot to try and lay the blame on the sitting President. Unless he were to say, ignore the advice of those leaders, which the article makes clear he didn't.
When people withhold answers to reasonable questions in order to probe for some hidden or more "real" intent of the asker. This is a ubiquitous problem polluting sites like Stack Overflow, but can also happen within an org. Always start with the simple answer first, and go from there.
> But I ultimately think of mathematics as a just an invented tool whose only reason for existence is to solve concrete problems.
This might be the source of disconnect. I frequently encounter this perspective and worry there's a fundamental problem with how mathematics is taught if so many people walk away believing this. Whether or not humans ever mastered mathematics, what is and isn't mathematically true would not change. Humans can create notation and formalisms, but they do not invent the truths those mathematics represent.
That's self-evidently untrue. The properties that make a circle would be true regardless of whether a human ever set eyes on a perfect circle. Us identifying those properties is an act of discovery via research. Codifying those mathematical truths into a written notation is the only component of the process that could really be called invention.