“is nothing sacred?” is spoken used to express shock when something you think is valuable or important is being changed or harmed (more) Human groups often unite via agreeing on what to treat as “sacred”. While we don’t all agree on what is how sacred, almost all of us treat some things as pretty sacred way. Sacred things
Euclid alone has looked on Beauty bare.Let all who prate of Beauty hold their peace,And lay them prone upon the earth and ceaseTo ponder on themselves, the while they stareAt nothing, intricately drawn nowhereIn shapes of shifting lineage; let geeseGabble and hiss, but heroes seek releaseFrom dusty bondage into luminous air.O blinding hour, O holy, terrible day,When first the shaft into his vision shoneOf light anatomized! Euclid aloneHas looked on Beauty bare. Fortunate theyWho, though once only and then but far away,Have heard her massive sandal set on stone.
Edna St. Vincent Millay
Sacred things are especially valuable, sharply distinguished, and idealized, so they have less decay, messiness, inhomogeneities, or internal conflicts.You might be fitting your premise to your conclusion here, when you say that sacred things have less messiness or internal conflicts. "Sacred" is most often used in relation to religion, and other uses of the word "sacred" derive from its use in religion. In the context of religion, what is sacred is roughly defined as what your religion tells you is important. For example, Christians consider the Bible to be sacred. But the Bible has plenty of messiness and internal conflicts. Even if you do not admit these to be outright contradictions, there are at least a lot of rules in the Old Testament that a Christian would say are no longer applicable, creating some messiness and conflict between what God said then and what he says now. Don't wear mixed fabrics, take slaves from neighboring nations, don't eat shellfish, etc. However, this messiness does not diminish the sacredness of the Old Testament in the view of a Christian.
Many people consider marriage to be sacred. But a marriage certainly has a lot of messiness and conflict.
Zen koans are inherently contradictory.
The holy trinity - that God is at the same time three, and one - involves holding two contradictory statements in mind.
The miracle of transubstantiation is similarly contradictory, where Catholics both acknowledge that the bread and wine chemically remain bread and wine, and believe that they become the body and blood of Christ in a metaphysical way "surpassing understanding."
We might greatly (although not permanently) harm our ability to use math, but that ability is not the thing that has all the properties you described (not created, clear lines, independence of cultural context).
I think of it this way. If I read a detailed description of an ancient religion or a social norm once treated as sacred, there is no way I'll convert to it. Once people stopped holding it sacred and raising their children to hold it sacred, it lost virtually all of its power.
If, on the other hand, I read a correct proof of a theorem by a long-dead author, it will have about as much power to convince me as it had originally. It won't matter if that theorem was forgotten for a hundred years, or if any mention of its author was illegal. It will have kept its power through all of it passively, without a need for anyone to continually defend its sacred status.
We might greatly harm math if, for example, we put too much weight on political loyalty or DEI criteria in choosing our math priests. Of if we erased and forbade the use of math results from long dead authors who once committed offenses in our eyes.
There is another important quality math lacks: the sacred has to be fragile. When we see an offence against it, we fell outrage and prioritize defending it over everything else not because the sacred is immortal and unassailable – that would make no sense – but because we fear the consequences of a failure to defend it. Because it can only continue to exist due to our fierce suppression of blasphemy. Not the case for math, obviously.
Asimov's Foundation consisted of all kinds of scientists (except psychologists, so they wouldn't figure out the Seldon Plan). In Prelude to Foundation Seldon is supposed to be a mathematician, but in the original trilogy it's emphasized that he was a social rather than physical scientist (so the prequel, which I read first, appears to have been a retcon).
The helps us to use math is a good sign about mental ability, care, and clarity, especially re the young.That doesn't seem grammatical, and I'm not sure what you're intended sentence was.
Though that did happen long ago.When?
I think this fits with history and also fiction. Pythagoreans built a quasi religious community around math. Famous works of fiction such as Herman Hesse’s Glas Bead Game and Asimov’s Foundation series both feature monastic communities that center around math.
Moreover, mathematicians have been fairly mystical (such as Kurt Godel) and even claimed to be prophets (Ramanujam claimed he received his proofs from a Hindu goddess).