The Mathematics Behind Art: Beautiful Mathematical Principles in Art from Da Vinci to Kandinsky
Mathematics is art and art makes us happy. Happiness is the moment the jar falls to the ground and breaks for an ant.
Art and mathematics may seem like two separate worlds, but they are more interconnected than we realize. Many artists incorporate mathematical principles into their work, whether they are aware of it or not. Geometry, for example, plays a significant role in creating symmetry and balance in a work of art. Furthermore, mathematics and geometry can be used to create illusions of depth and movement, which captivate the eye and draw the viewer in.
Art has the ability to bring us happiness in ways we never thought possible. It’s not just the aesthetically pleasing colors or intricate details that make us feel good, it’s the chemical reactions happening in our brains. Neurobiologists in London found that dopamine, a neurotransmitter associated with happiness and pleasure, is released when we see a work of art that we admire. This means that our brains are wired to experience joy and delight when we come into contact with a masterpiece. From a stunning painting to a mesmerizing sculpture, art truly has the power to elevate our moods and make us feel happier.
The beauty of art is its ability to bring us together. Whether we enjoy painting, music, or theater, artistic activities have a way of connecting people who might not have otherwise crossed paths. Art allows us to view the same piece of work with different eyes and interpretations, sparking conversations and discussions that help us explore our emotions and find common ground.
What’s even more incredible is that a work of art doesn’t have to be liked by everyone. As long as it evokes some sort of feeling — be it love, hate, or indifference — it has accomplished its purpose. By engaging with art, we can discover like-minded individuals who appreciate the same forms of expression and, in doing so, we come to know each other on a deeper level. Ultimately, art has the power to unite us all.
And when it comes to the world of abstract art, there is something truly special that happens. Abstract art, unlike representational art, sets our brains free from the constraints of reality.
Research has actually shown that the human mind is particularly drawn to abstract art, as it allows us to forge new cognitive associations and activate parts of our brains that we may not have known existed. By embracing this kind of art, we are able to delve even deeper into the mysteries of our own minds, and discover new ways of thinking and feeling that we never knew were possible.on between mathematics and art, he said:
When my college professor Ali Nesin explains the connection between mathematics and art, he said:
“There is an element of balance in painting. Colors, lines, darkness-lightness, warm-cold colors… This is a kind of mathematics, of course. Both mathematics and art require a lot of thinking and a lot of solitude. I think this is the deepest relationship between them. And I have no doubt that a good artist is good at math. When I say he is good at math, I mean his mathematical way of thinking. He may not know math, he may have forgotten it, but that doesn’t matter. An artist needs to know what he is doing or think about what he is doing…”
Archimedes Thoughtful by Domenico Fetti, 1620
The art of mathematical discovery is as beautiful as any masterpiece hanging on a museum wall. The origins of calculus can be traced all the way back to the ancient Greek mathematician and inventor Archimedes. With his keen mind and passion for numbers, Archimedes laid the groundwork for what would become one of the most pivotal fields of mathematics. Through his discoveries and the countless contributions of those who followed in his footsteps, calculus has forever changed our understanding of the world, both in art and science.
Domenico Fetti’s 1620 masterpiece, Archimedes Thoughtful, is a testament to the beauty and power of art. The painting depicts the renowned ancient Greek mathematician Archimedes lost in thought, his eyes gazing off into the distance. The intricate details in his robes and the subtle shadows cast by his figure are a testament to Fetti’s skill as an artist. But the true wonder of the piece lies in the sense of emotion it conveys. One can almost feel the weight of Archimedes’ thoughts as he contemplates the mysteries of the universe. It is no wonder that this painting has captivated audiences for centuries, proving that true art can transcend time and space.
Death of Archimedes by Thomas Degeorge, 1815
Thomas Degeorge’s 1815 painting, Death of Archimedes, depicts a somber scene of the great mathematician’s final moments. The intricate detailing and masterful use of light and shadow in Degeorge’s work draw the viewer in, capturing the moment’s emotion.
The painting portrays Archimedes, one of the greatest minds in history, at his most vulnerable. Degeorge’s use of color and composition evokes a sense of gravitas, highlighting the significance of Archimedes’ contributions to the world of mathematics. Death of Archimedes is a stunning piece of art that continues to captivate viewers today.
Newton by William Blake, 1795
William Blake’s Newton is a beauty of art transcending its time and medium. The intricate etching depicts the famous scientist sitting naked on a rock, deep in thought and contemplation. With his muscular frame and flowing hair, the intellectual giant appears almost godlike, suggesting the connection between knowledge and power.
The image is both captivating and thought-provoking, inviting viewers to explore the complex relationship between science and religion, reason and faith. Blake’s attention to detail is remarkable, from the delicate lines of Newton’s body to the intricate patterns in the surrounding landscape. It’s a work of art that challenges and inspires, reminding us that even the most analytical pursuits can fuel the creative fire.
Portrait of Luca Pacioli by Jacopo de’ Barbari, 1500
The Portrait of Luca Pacioli by Jacopo de’ Barbari is a masterpiece that captures the essence of one of the most celebrated mathematicians of the Renaissance period. Pacioli is depicted standing behind a table, dressed in the attire of a member of the Franciscan order. His left-hand rests upon an open book, which is believed to be his Summa de Arithmetica, Geometria, Proportioni et Proportionalità or a copy of Euclid.
Noam Andrews also used this painting as a cover for his book, The Polyhedrists: Art and Geometry in the Long Sixteenth Century.
We see him drawing a construction on a board marked with the name Euclides and surrounded by the tools of a mathematician — a sponge, a protractor, compasses, and a pen. Interestingly, the right corner of the table bears a dodecahedron resting upon a book engraved with the initials of Pacioli.
Meanwhile, a rhombicuboctahedron suspends gracefully on the left of the painting. The identity of the young man at the right is uncertain, but many scholars recognize him as the “eternal student” who was instructed by Pacioli. The Portrait of Luca Pacioli is a captivating piece of art that allows viewers to understand and appreciate the ingenuity of this talented mathematician and educator.
The School of Athens by Rafael, 1509
In Raphael’s famous masterpiece, The School of Athens, a group of the world’s greatest mathematicians is brought together in one vibrant scene. We see them all, from the great Pythagoras himself to Euclid and his geometric musings.
The painting is a celebration of not only art but of the beauty of mathematics as well; the subjects are all deeply engaged in their own thoughts and calculations, while the overall atmosphere is one of intellectual curiosity and exploration.
It’s no wonder that this painting has become one of the world’s most iconic and beloved works of art, capturing the very essence of the meeting of minds that occurs when art and math come together in perfect harmony.
Kandinsky at the Bauhaus
The Bauhaus was a revolutionary art school that attracted some of the most innovative minds of the early 20th century. One of these visionaries was none other than Wassily Kandinsky, a Russian painter whose bold and expressive style captured the essence of the modernist movement.
Here are some beautiful books about Bauhaus art school!• Bauhaus: 1919 - 1933 by TASCHEN
• The ABC's of Triangle, Square, Circle: The Bauhaus and Design Theory
• Bauhaus Graphic Novel by Valentina Grande
When Kandinsky joined the Bauhaus in 1922, he quickly made an impact, becoming known for his innovative mural painting techniques and captivating students with his free-painting class. Over time, this class would become one of Kandinsky’s most popular and enduring contributions to the art world.
Through his teaching, Kandinsky inspired countless artists to explore the limits of paint and create avant-garde and emotionally powerful work. Thanks to figures like Kandinsky, the Bauhaus remains a defining force in the history of art.
Circles in a Circle by Wassily Kandinsky, 1923
When you first lay your eyes on “Circles in a Circle” by Wassily Kandinsky, you might not immediately think of geometry. But take a closer look and you’ll see that this piece of art is full of circles and other geometric shapes. Kandinsky was a pioneer of abstract art and he believed that using geometric shapes helped to create a sense of harmony and balance in his pieces. In “Circles in a Circle,” Kandinsky uses circles of varying sizes and colors to create a mesmerizing effect. The circles seem to ripple outwards, drawing you deeper into the piece. It’s a beautiful example of how geometry can be used to create art that is both visually stunning and emotionally evocative.
Bunt Im Dreieck by Wassily Kandinsky, 1927
Bunt Im Dreieck by Wassily Kandinsky, painted in 1927, is a dynamic piece of abstract art that perfectly captures the essence of the artist’s style. The painting features a striking combination of bold triangles and vibrant, contrasting colors, evoking a sense of movement and energy that draws the viewer in.
Kandinsky was a pioneer of the abstract art movement, and his work continues to inspire and captivate audiences all over the world. With Bunt Im Dreieck, he showcases his creative vision and technical skill, creating a masterpiece that is both timeless and unforgettable. It is a true testament to art’s power and the human imagination’s boundless possibilities.
Mental Arithmetic by Nikolay Bogdanov-Belsky, 1895
Nikolay Bogdanov-Belsky’s “Mental Arithmetic” is a masterful work that captures a moment of intense focus and concentration in a classroom setting. The boys in the painting are intently focused on solving a complex math problem, and their expressions convey the mental effort and concentration required to arrive at a solution.
The use of warm colors and intricate detailing further draws the viewer into the scene, inviting us to imagine ourselves among the students as they tackle this challenging problem. This evocative painting is a testament to the power of art to capture the human experience and to inspire us to engage with the world around us in new and meaningful ways.
The math problem the boys are trying to solve on the board is (¹⁰²+¹¹²+¹²²+¹³²+¹⁴²)/365.
Sky and Water I by M.C. Escher, 1938
M.C. Escher was a master! He is known for his captivating pieces that bend reality and challenge the mind. However, there is more to his work than meets the eye. A deeper look into his intricate illustrations reveals a mathematical foundation that helped bring his designs to life.
Escher was heavily inspired by the patterns and structures found in math, and his use of geometric shapes and tessellations transformed his art into a visual representation of mathematical concepts. Perhaps this is why many consider Escher to be both an artist and a mathematician. Regardless of how you view his work, one thing is certain: his pieces continue to mesmerize and inspire viewers to this day.
M.C. Escher’s Sky and Water I is a stunning depiction of the intertwining relationship between the sky and water. Beyond its striking beauty, this piece is also a masterpiece in geometry and tessellation. Escher’s use of precise mathematical shapes and patterns creates a mesmerizing optical illusion as one’s eye shifts between the billowing clouds and the flowing waters.
The clever manipulation of these shapes allows for the seamless integration of the two elements, reminding us that in nature, everything is connected. It’s through Escher’s artistic and mathematical brilliance that we are able to see the complexity and harmony of the world around us.
The Starry Night by Van Gogh, 1889
Vincent van Gogh’s iconic piece, The Starry Night, is a breathtaking representation of the artist’s imagination. The swirling blues and yellows perfectly capture the brilliance of a starry sky on a clear night. The texture and depth of the painting transport the viewer to a serene and peaceful place, where one can almost feel the gentle breeze blowing through the cypress trees.
Van Gogh’s use of color and movement in this piece has made it one of the most recognizable paintings in history, inspiring countless artists and dreamers alike. It is a true masterpiece that continues to captivate and inspire people worldwide.
On the other hand, the human brain possesses a remarkable ability to recognize and describe patterns, including the complex concept of turbulent flow in fluid dynamics. While this phenomenon remains difficult to understand mathematically, art has provided a means to visualize its appearance. Vincent van Gogh’s “The Starry Night” is a striking example of this, utilizing circular brushstrokes to create swirling clouds and an array of twinkling stars.
Through the use of luminance, Impressionist painters depicted the movement of light in a unique way, capturing its motion across various landscapes. Though our understanding of turbulence has evolved through scientific study, the field remains a mystery.
Physicist Werner Heisenberg said, “When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first.”
However, researchers studying Van Gogh’s works have discovered a distinct pattern of turbulent fluid structures hidden within them that closely aligns with a mathematical equation proposed by Russian mathematician Andrey Kolmogorov. Despite Van Gogh’s inner turmoil, he was able to perceive and represent one of nature’s most complex phenomena in a way that captivates and inspires viewers to this day.
Number 14 by Jackson Pollock, 1951
Jackson Pollock’s art has enraptured both art enthusiasts and mathematicians alike for years with its unique style. His chaotic and unconstrained paintings have brought a fresh perspective to modern art, incorporating seemingly random patterns and splatters that create a mesmerizing visual effect.
While some argue that Pollock’s works are genuine examples of fractal geometry, others debate whether his art can truly embody this complex mathematical expression. Regardless, Pollock’s art remains a source of inspiration today, showcasing unconstrained creativity that will continue to fascinate and intrigue art enthusiasts for generations to come.
Vitruvian Man by Leonardo da Vinci, 1490
The Vitruvian Man, created by the legendary artist and inventor Leonardo da Vinci in the year 1490, is a work of art that strikes the perfect balance between beauty and mathematical precision. The incredibly detailed drawing of the human figure is based on precise measurements and ancient mathematical theories gathered from the work of the Roman architect Vitruvius.
The artwork is a stunning example of how da Vinci used his incredible knowledge of science and art to create something truly extraordinary and unique. The Vitruvian Man is not only a masterpiece but also a testament to the genius of Leonardo da Vinci, who integrated two seemingly unrelated fields of study to produce a work of unparalleled beauty and significance. The Vitruvian Man remains an important symbol of the Renaissance period and a testament to the power of human creativity and ingenuity.
Mona Lisa by Leonardo da Vinci, 1517
The Mona Lisa is perhaps Leonardo da Vinci’s most famous masterpiece and has captivated art lovers for centuries. However, beyond its enigmatic smile and the mystery surrounding the identity of the portrait’s subject, this artwork also has a fascinating mathematical aspect.
Leonardo da Vinci was a man of many talents, including mathematics. It is widely believed that the artist used geometry to create the composition of the painting, using the mathematical “Golden Ratio” to establish the dimensions and positioning of each element in the artwork. Indeed, the Mona Lisa has been analyzed in detail by mathematicians, who have uncovered a variety of intriguing geometric patterns and connections.
It’s truly amazing to consider the complex interplay between art and mathematics in this iconic piece of art.
Golden Ratio by Rafael Araujo
The Golden Ratio, a mathematical pattern that’s been used in artwork and architecture since ancient times, has always sparked fascination among artists and mathematicians alike. One artist who has taken this fascination to a whole new level is Rafael Araujo. His intricate illustrations showcase the beauty of the Golden Ratio and how it’s present in the natural world.
What’s unique about Araujo’s art is that he doesn’t use a computer to create his designs. Instead, he draws each line and curve by hand, bringing a sense of organic authenticity to his work. When viewing his pieces, it’s impossible not to appreciate the intricate dance between art and math and how the two seemingly separate subjects can harmoniously coexist.
The Alhambra Palace
As you wander through the corridors and courtyards of The Alhambra Palace, it’s impossible not to be taken aback by the intricate, awe-inspiring geometry that surrounds you. The attention to detail in every aspect of the architecture is simply breathtaking; from the carved stucco patterns to the interlocking star-shaped designs, every inch of the palace seems to have been crafted with care and precision.
Even the simple act of walking through a doorway becomes an experience in itself, as the elegant arches and layered motifs draw your eye upwards to the perfectly symmetrical domes and ceilings. It’s no wonder that The Alhambra Palace has been called one of the most beautiful examples of Islamic art in the world — its stunning geometry truly is a masterpiece of design.
So the next time you’re admiring a piece of art, take a moment to appreciate the mathematical precision that may have gone into its creation. The elegance of mathematics may just be the underlying beauty that you’re experiencing.
Note 1: Beyond Euclid! is my weekly newsletter that brings you only high-quality math and science stuff to ensure you are having a good week. Please do yourself a favor by subscribing to Beyond Euclid and enjoy it! And if you can be a member and support my work, that would be awesome! Thank you!
Note 2: I get commissions for purchases made through Amazon links in this post.
