What is a casual thought that you cannot explain in math?
That question makes no sense. You can explain anything in math, because math is a language and lets you define whatever terms and axioms you need at a given moment.
(Whether or not such explanation is useful for anything is another issue entirely.)
Can you explain how intuition led you to try a certain approach?
Is it enough if I hand-wave it with probability distributions, or do you want me to write out adjacency search in a high-dimensional space?