When the Math Modeling Club approached us in March 2026 about hosting an on-campus exhibition, I immediately thought of classic Renaissance and Baroque paintings. These works, which had pushed the art of human painting to the pinnacle of order, harmony, and beauty hundreds of years ago, were the perfect subject for us to explore their mathematical elegance. And so, the following 18 works came into our sights.
The 18 Oil Paintings We Analyzed
Vitruvian Man
Artist: Leonardo da Vinci
Date: c. 1490
Features: A pen-and-ink drawing (not oil), housed at the Gallerie dell'Accademia, Venice. It depicts a male figure simultaneously inscribed in a circle and a square, embodying the Renaissance synthesis of art and science through the study of ideal human proportions.
Mona Lisa
Artist: Leonardo da Vinci
Date: c. 1503–1519
Features: Oil on wood panel, Musée du Louvre, Paris. Famous for its use of sfumato (soft, smoky transitions), embedded golden ratio composition, and the subject's enigmatic smile. The world's most recognized portrait.
The Last Supper
Artist: Leonardo da Vinci
Date: c. 1495–1498
Features: Tempera and oil on plaster, Santa Maria delle Grazie, Milan. The vanishing point is precisely aligned with Christ's right eye, resulting in a flawless one-point perspective. The twelve apostles are arranged in four groups of three, forming stable triangular clusters.
The School of Athens
Artist: Raphael (Raffaello Sanzio)
Date: c. 1509–1511
Features: Fresco, Apostolic Palace, Vatican City. Depicts an assembly of ancient Greek philosophers with Plato and Aristotle positioned at the golden ratio points. The architectural arches demonstrate masterful linear perspective, a defining work of the High Renaissance.
Sistine Madonna
Artist: Raphael
Date: c. 1512
Features: Oil on canvas, Gemäldegalerie Alte Meister, Dresden. The composition forms a stable isosceles triangle with the Madonna and Child at the Fibonacci spiral's core. The two cherubs at the bottom have become iconic in modern popular culture.
The Birth of Venus
Artist: Sandro Botticelli
Date: c. 1484–1486
Features: Tempera on canvas, Uffizi Gallery, Florence. Depicts the goddess Venus emerging from the sea, featuring a strict bilateral symmetry and a Fibonacci spiral guiding the figure arrangement. A landmark of Early Renaissance mythological painting.
Primavera
Artist: Sandro Botticelli
Date: c. 1477–1482
Features: Tempera on panel, Uffizi Gallery, Florence. Venus serves as the central axis of a bilaterally symmetrical composition. Nine mythological figures are arranged in an orange grove symbolizing the renewal of spring, rendered in a highly decorative, allegorical style.
Ideal City
Artist: Attributed to Piero della Francesca or his circle
Date: c. 1470–1490
Features: Tempera on panel, Galleria Nazionale delle Marche, Urbino. Depicts an empty ideal city square in strict one-point perspective, with a central circular temple. The receding floor tiles converge to a single vanishing point, a textbook demonstration of Renaissance perspective.
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The Ambassadors
Artist: Hans Holbein the Younger
Date: 1533
Features: Oil on oak panel, National Gallery, London. Features an anamorphic skull at the bottom, visible only from a specific oblique angle, symbolizing mortality (Memento Mori). Scientific instruments between the two ambassadors reference the intellectual ambitions of the era.
The Fortune Teller
Artist: Michelangelo Merisi da Caravaggio
Date: c. 1594–1595
Features: Oil on canvas, with versions in the Louvre, Paris, and Musei Capitolini, Rome. Depicts a street fortune-telling scene with dramatic chiaroscuro — figures are directly lit against a plain background. An early example of Caravaggio's radical realism.
Las Meninas
Artist: Diego Velázquez
Date: 1656
Features: Oil on canvas, Museo del Prado, Madrid. Infanta Margarita Teresa forms the apex of the triangular composition. The painter himself appears in the scene, while the king and queen are reflected in a background mirror, creating one of the most complex spatial puzzles in Western art history.
Hunters in the Snow
Artist: Pieter Bruegel the Elder
Date: 1565
Features: Oil on panel, Kunsthistorisches Museum, Vienna. Part of the "Months" series, this panoramic winter landscape shows hunters returning home. Diagonal leading lines guide the eye from the foreground figures deep into a frozen valley, creating a strong sense of atmospheric depth.
The Surrender of Breda
Artist: Diego Velázquez
Date: c. 1634–1635
Features: Oil on canvas, Museo del Prado, Madrid. Also known as "The Lances," it depicts the 1625 surrender of the Dutch city of Breda to Spain. The dense forest of Spanish lances on the right creates a powerful geometric rhythm within the composition.
The Milkmaid
Artist: Johannes Vermeer
Date: c. 1657–1658
Features: Oil on canvas, Rijksmuseum, Amsterdam. Light streams evenly from a left window, with the Fibonacci spiral centering on the pouring milk. The dominant blue-yellow palette exemplifies the Dutch Golden Age mastery of intimate domestic scenes.
The Night Watch
Artist: Rembrandt Harmenszoon van Rijn
Date: 1642
Features: Oil on canvas (363×437 cm), Rijksmuseum, Amsterdam. Depicts a militia company mustering for patrol. Dramatic Rembrandt lighting creates a theatrical chiaroscuro across the massive canvas, breaking the static conventions of group portraiture with dynamic movement.
Girl with a Pearl Earring
Artist: Johannes Vermeer
Date: c. 1665
Features: Oil on canvas, Mauritshuis, The Hague. Against a stark black background, a girl glances back over her shoulder. Light concentrates on her face and the pearl earring, whose highlight is the painting's singular point of maximum luminosity. This painting is often referred to as the "Mona Lisa of the North."
The Arnolfini Portrait
Artist: Jan van Eyck
Date: 1434
Features: Oil on oak panel, National Gallery, London. A milestone of Early Netherlandish painting. The circular convex mirror on the back wall reflects a wide-angle view of the entire room, functioning as a painting-within-a-painting and reinforcing the work's strong bilateral symmetry.
The Music Lesson
Artist: Johannes Vermeer
Date: c. 1662–1665
Features: Oil on canvas, Royal Collection, Buckingham Palace, London. Strict geometric perspective structures the interior space through ceiling beams, floor tiles, and window frames, forming a precise symmetrical grid. A mirror above the virginal reflects the woman's face, extending the composition's spatial depth through mirrored symmetry.
Oil Painting Puzzle Game
To prepare the audience for our presentations and make them more familiar with the 18 paintings we had chosen, as part of a collaborative interactive event with the Math & Modeling Club, I created a jigsaw puzzle game with 18 classic oil paintings related to the event as puzzle targets and multiple difficulty levels. Participants who successfully complete all 18 puzzles will receive the club's grand prize of art and creative merchandise.
Main Content of the Joint Exhibition and Activities
Once the theme and subject matter of our exhibition were decided, our club joined forces with the Mathematical Modeling Society to investigate the mathematical logic—whether intentional or intuitive—embedded within these celebrated paintings. The exhibition was ultimately structured around six modules, each approaching and appreciating the 18 classic oil paintings through one of the following lenses: golden ratio, perspective, Fibonacci spiral, triangular composition, light gradients, and symmetry. We then presented the findings from our research and discussions to the wider school community through a campus exhibition and a series of guided talks.
Photos from the Event
From March 30 to April 3, 2026, Art & Beyond and the Math Modeling Club hosted a joint exhibition and interactive event called "The Beauty of Mathematics in Art" in the teaching building's third-floor atrium. During the interactive activities, we used a mini-program to test human body proportions, engaged visitors with a self-created puzzle game based on the paintings on display, and shared our art history knowledge via an on-site quiz with prizes.
Activity Summary and Findings
The week-long joint event between Art & Beyond and the Math Modeling Club has come to a successful close. During the interactive sessions held at noon on Thursday and Friday, both the jigsaw puzzle activity and the interactive quiz drew the enthusiastic participation of nearly a hundred students each day. While we were heartened by everyone's engagement, we also noticed several phenomena that had previously escaped our attention.
As an art outreach and interdisciplinary collaborative event, we had already lowered the difficulty of both the jigsaw puzzles and the interactive quiz multiple times to reduce the barrier to entry for participants. We strictly drew all quiz questions and puzzle materials from the 18 classic paintings we had selected for display. Nevertheless, after the first day's quiz session, students widely reported that the questions were still too difficult to answer successfully—so much so that we had to adjust the difficulty level again for the second day. What's more, quite a few students were unaware of even the most basic facts about the classic oil painting Mona Lisa—such as who painted it and which museum currently houses it.
These results remind us that, as a student society whose primary goal is to cultivate artistic appreciation and spread aesthetic knowledge, we still have a long road ahead of us.
I attached our knowledge quiz below—feel free to give it a try yourself.
