math as art, and the connection to applied versus "pure" fields
In both mathematics and art, there's this tension between the intrinsic value of abstraction and the... functional role in supplementing human needs. Take applied mathematics: it's often created to solve concrete problems: designing algorithms for smartphones, modeling financial systems, optimizing manufacturing processes,etc; but the foundation rests on pure concepts like set theory or topology. Pure mathematics, meanwhile, revels in exploration for its own sake, like museum art that isn't necessarily used but profoundly influences thought, culture, and even other practical developments.
art follows this pattern too. Some art directly connects with everyday objects, (applied art shaping ketchup bottles, cars, and websites) but even museum pieces indirectly feed into applied art by inspiring trends, themes, or techniques. A painting might not be consumed directly but its ideas ripple into creative industries worldwide.
As for proportion, here's an interesting reflection: applied math (or art) might make up the bulk of what people interact with, but pure math (or pure art) is the fertile soil where new concepts and visions are born. Without pure work, applied advances might stagnate... it's this cyclical relationship that keeps both alive.
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intuition acts as the bridge between the abstract and the applied, logic and creativity. ketchup bottle design process example is an apt metaphor. On one hand, statistical analysis, randomization, and iteration provide a scientific method to navigate through infinite possibilities and refine toward the "perfect" design. Yet, the artist's vision seems to bypass that lengthy process, almost as if they cut straight to the heart of it. How do they know?
I think this is where the artistry lies: intuition is a culmination of experience, observation, and pattern recognition at a level it often feels like magic. An artist might unconsciously synthesize thousands of visual experiences and cultural cues, or even the way the braind processes form and symmetry, to arrive at a design that resonates universally. akin to a chess grandmaster spotting the perfect move they aren’t computing every possibility consciously, but rather drawing from years of internalized strategies and patterns.(qb)
mathematicians also rely on intuition. Even in proofs, the aha moments often spring from an intuitive leap rather than grinding calculations. intuition operates as a shortcut, blending the logical and the aesthetic
