How do mathematicians handle it when there are tantalizingly close relationships between purely mathematical numbers? I fell down this particular rabbit hole th

How do mathematicians handle it when there are tantalizingly close relationships between purely mathematical numbers? I fell down this particular rabbit hole through the musical entrance (just intonation intervals), but I mean look at all this, it's clearly a setup. https://en.wikipedia.org/wiki/Mathematical_coincidence https://en.wikipedia.org/wiki/Mathematical_coincidence