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The question is clearly asked “from the point of view of art”=))
I'll move it a little:
In this setting, the answers seem obvious, but take your time…
Theoretically, they can. But it is much more interesting for them to exist together. For example, Gaudi learned analytical geometry and designed an entire Sagrada Familia. And Professor Subramanian came up with a new paint for artists and is now one of the most respected chemists in the States.
Both are based on the creative work of the mind, so the Greeks in ancient times did not separate them at all.
A certain distinction in the modern understanding has arisen due to the impression of the rigor of the scientific method of research, which cuts off a significant share of free creativity, and often even recognizes this freedom as sabotage.
But in general, all the sciences and all the arts have their origin in creative effort, the only difference is where it is directed.
Science and art are different spheres, but they can co-exist. Science is a logical knowledge of yourself, the world and the universe. Art is a sensory knowledge of the world based on inner feelings and emotions, while art is a kind of knowledge of everything (yourself, the world, the universe).
Art and science can coexist without each other, but without art, it is difficult for people to express their emotions, feelings, and ideas.
Science and art are repetitions of each other. Scientists always strive for the beauty of their theories. For example, to the beauty of a mathematical description of a phenomenon. People of art also strive for the beauty of their works. In art, beauty is achieved through allegory.