It may be helpful to keep looking at this issue from a variety of related perspectives.
So in stressing the need for the both quantitative and qualitative aspects of interpretation (in science and mathematics) the role of the unconscious needs to be equally incorporated with conscious type interpretation.
Though the unconscious is now accepted as an integral aspect of psychology, its counterpart complementary equivalent is not however yet recognised (especially in mathematical terms).
In physical terms this counterpart equivalent of the unconscious would be the recognition of an unmanifest hidden (potential) dimension that continually interacts with actual manifest phenomena in nature. We could perhaps fruitfully refer to the unmanifest aspect as the holistic ground (or holistic dimensional ground) of reality.
So whereas in direct terms, traditional conscious rational type interpretation would directly relate to the manifest features, unconscious intuitive type appreciation would characterise the unmanifest holistic aspect of reality.
And from a scientific perspective, such intuitive understanding can be indirectly represented through a circular logical approach (with various degrees of increasingly refined expressions available).
Admittedly there is already some recognition of the holistic nature of physical reality at the highly interactive dynamic level of sub-atomic particles. However an equal recognition of the need for explicit incorporation of an unconscious aspect with respect to an appropriate paradigm has not yet been admitted.
This problem is of a more fundamental nature with respect to Mathematics where the unconscious aspect of understanding likewise urgently needs to be explicitly incorporated in an altogether more comprehensive approach.
Putting it bluntly the somewhat absolute nature of mathematical appreciation is ultimately grounded in a paradigm that fundamentally misrepresents the true dynamic nature of mathematical experience and thereby is greatly limited in scope.
So once we accept the need to (explicitly) incorporate the role of the unconscious (with conscious interpretation) then we must likewise accept that underlying all manifest mathematical phenomena is an unmanifest or hidden holistic universal ground with which these phenomena continually interact. Now this might seem like a million light years away from the cold abstract view of static absolute mathematical forms that currently exists but this really indicates how rigid - and indeed unrepresentative - is the current mathematical paradigm (based solely on mere conscious rational interpretation).
Now we have already seen with respect to one key area of investigation i.e. prime numbers what the dynamic nature of this activity might entail!
However though mathematicians are indeed coming to accept that prime number behaviour (at a deep level) is not what they expected, there is absolutely no recognition yet of the central issue i.e. that the existing method of approach ultimately is not fit for purpose.
So if we are to talk of the prime numbers in this new light we are led to accept that their behaviour - necessarily - is of a merely relative nature, reflecting the continual interaction of its manifest features with a universal (unmanifest) holistic ground. Seen in this light we cannot divorce the (actual) finite nature of the prime numbers from their (potential) infinite nature so that in a sense prime numbers - from a dynamic interactive perspective - are in a continual state of becoming (exhibiting at any time a merely approximate identity).
So as we have seen the primes and the non-trivial zeros are mutually encoded in each other. Though from an isolated perspective when we freeze this interaction they both show quantitative features, their mutual interdependence depends on the equal incorporation of their hidden holistic features (which reflects qualitative understanding).
Putting it more simply we can say that the prime numbers dynamically vibrate (with this vibration necessarily reflecting both quantitative and qualitative aspects of interpretation).
When we look carefully at our actual experience of number, it necessarily entails both quantitative and qualitative aspects pertaining directly to (rational) conscious and (intuitive) unconscious aspects of appreciation.
The infinite nature of the number concept (as potentially applying to all numbers) is strictly holistic (pertaining to unconscious intuitive type appreciation).
We then give the number concept a reduced finite nature as applying to all actual numbers (pertaining to conscious rational interpretation).
Likewise we have actual individual number perceptions (again pertaining to conscious rational interpretation).
And finally we have the sense of such perceptions in some way embodying the potential number concept (i.e. as members of the number class that is potentially infinite). So this points once more to the unconscious aspect of understanding.
So in actual experience we have the dynamic interaction of both finite and infinite notions of meaning (pertaining to conscious and unconscious appreciation of both number concepts and perceptions respectively).
And yet in interpreting numbers, mathematicians attempt to view them in merely conscious rational terms. And the key casualty in this is a highly reduced notion of the infinite, which effectively is considered as a linear extension of finite notions.