An honest and sincere question deserves an honest and sincere answer:

Gatekeeping: Simply suggesting that others need to read more, or that they need to "look into" one of the largest and most controversial philosophical topics in history is a haughty and disdainful way of saying "I'm right, I'm not going to cite my sources, and anyone who disagrees with me must carry the burden of proof". Don't leave the justification for your argument as an "exercise for the reader" involving the entire canon of published thought, since that insinuates that they are simply too uneducated to understand how correct you are. THAT is gatekeeping knowledge.

I didn't say maths was from Europe: Not directly, but you supported your argument for the statement

"[The scientific] method is predicated on European Enlightenment avowals of what constitutes an acceptable boundary of truth... [etc.]"

with nothing but the statements

"2+2 does equal 4. That doesn't mean valuing 4 as an answer or valuing the act of valuing of the certainty of 2+2=4 is an objective position."

as exemplary evidence. You are, quite literally, stating that the "valuing" of 4 as an answer to 2+2 is a question of science (otherwise it's a non-sequitur), and that this is an example of how the scientific method privileges European Enlightenment ideals over others. That is saying that the precepts of mathematics are based on European enlightenment ideals, Q.E.D.

"Where's the disdain": I believe that a reasonable person would read this argument and conclude that the disdain is implied, given that you clearly seem to be complaining that the European enlightenment ideals have somehow "privileged" certain perspectives. Now, I happen to agree with that statement, but clearly in a very different way than you do:

It seems to me that, until the likes of Karl Popper's contribution of the principle of falsifiability as the chief hallmark of scientific practice, the entrenched belief in strict empiricism was being privileged as a leftover of European Enlightenment traditionalism. Perhaps another will come along soon who similarly unseats Popper. To claim, however, that the scientific method itself is somehow predicated on enlightenment ideals appears, to me, to miss the entire point of this original post: that science changes, just as much as how we do science, because science is all about constantly holding ourselves, and our ideas, to ever-higher standards. Most of the principles of the modern scientific method have been around for more than a thousand years, slowly building on one another. The idea of a strict "scientific method" is as much an illusion as the entirety of reality may be, but that's just because we are always developing new ways of knowing.

*Edited for readability and clarity.