# How and Why Mathematics Transformed Art

As seen by Plato, the whole universe could be a manifestation of mathematics, and nature itself can be considered an embodiment of mathematical order. Thus, Wigderson suggests that mathematics could provide artists a unique means to transform the intricate natural world into abstract symbols; thereby representing nature and their emotions better. From the art of Renaissance and modern periods, this essay explores the significant role of mathematical development in the evolution of art.

Since the Renaissance, understanding mathematical orders has been fundamental to artistic image creation and driving transformations of the field of visual arts. For instance, in the 15th century, the concept of linear perspective, a mathematical framework that allowed artists to intricately replicate three-dimensional space on a two-dimensional canvas, were introduced. This theory was originally founded by Francesca and Alberti, holding a basic hypothesis that line segments seen within the same angle appear to be equal, and a fundamental result is that parallel lines appear to converge(fig.1). This innovation revolutionized artistic expression, adding new depth and realism to artworks. For example, in Giotto’s work (fig.2), although he represented exquisite painting technique, His painting still lacked realism due to the yet undiscovered linear perspective techniques, whereas Correggio’s works (fig.3) fully utilized linear perspective techniques, immersing the viewer in the religious environment of the Assumption of the Virgin. This illustrates how the development of mathematics has also revolutionized the arts.

Today, integrating mathematics into art is becoming more common. In the field of modern art, the works of Cezanne, who believes that using three-dimensional geometric shapes like cylinders, spheres, and cones best depicts nature, could be a good example. A notable example from Cezanne is the landscape painting “Monte Sainte-Victoire”(fig.4), where he represented farmhouses as cubes, fields as rectangles, and mountains as cones.

In conclusion, as we see from those great artists like Cezanne and Correggio, it’s fair to say that just as mathematical patterns can underpin great symphonies, so they can influence great artworks.

Author
Qunce Shen

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