The importance of numbers becomes even more mysterious if you begin to think about their limits. For all the things that numbers can do for us, they are dwarfed by the things that numbers can't do for us. Often
There is also the limit disguised as a need for large amounts of numbers. For instance, consider music CDs and their relation to actual performances. Although with good equipment a recording can really involve the listener, the experience of listening to a recording is worlds apart from being physically present at a performance. It would be easy to claim that the difference is in not having enough data - enough channels of music, the full sound (echoes etc.) of the performance site, the visual data presented to the eyes, etc. But in fact no amount of recording, no number of microphones and cameras, can duplicate the experience of a live in-person performance.
Another related issue - chaos, sensitive dependence on initial conditions.
Another - Numbers being unable to plumb human personality, morality, dignity, self, religious questions, etc.
Another - signals from within math - when infinity comes up.