Final answer:
Finding a paradigm entirely devoid of mathematics is difficult, as even language contains mathematical elements. While mathematics fundamentally aids in structuring our world, there are areas, like narrative storytelling, where it is less prominent, allowing for more qualitative analysis.
Step-by-step explanation:
The quest for a paradigm without mathematics is indeed challenging, as maths intricately weaves itself into nearly every aspect of learning and understanding our world. Nonetheless, there can be disciplines or contexts where mathematics might not be as explicitly employed, such as in certain aspects of linguistics or narrative storytelling. But even in language, we can find that mathematics plays a background role, as syntax often follows patterns that can be analyzed and understood through mathematical principles like probability and combinatorics.
Historically, mathematics has always been intertwined with its practical applications, as seen in ancient civilizations using it for everything from agricultural planning to religious rituals. Thus, mathematics forms an innate part of our understanding of the universe. Whether we look at the constructs of language, the assumptions in economic models, or the simple tasks of addition, the influence of mathematics is omnipresent. While there are disciplines where mathematics is not the primary focus, it's hard to find an area of study completely isolated from mathematical reasoning or problem-solving skills.
However, the appreciation for the beauty of math and its underlying logical rigor doesn't negate the importance of qualitative analysis. Narrative forms and qualitative reasoning offer nuances and complexities that may not be captured in pure mathematical models. They allow for different perspectives and can accommodate the subtleties of human emotion and behaviour that mathematics may not fully express.