TITLE: Mathematical conjectures on which applications depend
QUESTION [78 upvotes]: What are some examples of mathematical conjectures that applied mathematicians assume to be true in applications, despite it being unknown whether or not they are true?

REPLY [22 votes]: Although we have a proof now, I suspect grocers had intuitively stacked oranges in the most efficient way prior to the proof of Kepler's conjecture.  I don't know for sure if any grocer was an applied mathematician.
https://www.newscientist.com/article/dn26041-proof-confirmed-of-400-year-old-fruit-stacking-problem/