This needs to be fleshed out more. I’m reminded of the several instances where people have been accusing of engaging in “numerology” instead of science: one famous example is Dirac’s Large Numbers Hypothesis, where Dirac, Eddington, Weyl and others saw some patterns between fundamental constants and thought they gave evidence to some deeper connections, but this never actually developed into a “real” theory. On the other hand, the periodic table and parts of the Standard Model initially also started out as pattern recognition, but eventually people were able to give deeper, structural explanations for why the objects behaved according to these patterns, also allowing them to make new predictions (new elements or new fundamental particles).
From this, I think a “real” scientific explanation is one that has levels of depth: one is able to explain a numerical pattern produced by a phenomenon by appealing to another observed phenomenon(s) and postulating a well-defined law characterizing the range of behavior of these two phenomena. Usually this involves some sort of reduction, namely:
- Postulating that an object/phenomena consists of certain component parts,
- Postulating fundamental properties for each of those components and fundamental laws/principles for how those components interact with each other.
- Showing that the combination of 1) and 2) give rise to the numerical pattern initially observed.
For steps 1)-3) I don’t think complex mathematics is necessary; you just need logical statements referring to well-defined objects in nature.