Leonardo da Vinci’s creative escape through geometry

Home > Opinion > Meanwhile

Leonardo da Vinci’s creative escape through geometry

Published: 05 Jun. 2025, 00:05

Audio report: written by reporters, read by AI

Lee Woo Young

The author is an HCMC distinguished professor at the Korea Institute for Advanced Study.

In ancient Greek mythology, King Minos of Crete was dissatisfied with the size of his son’s tomb. The monument, shaped like a cube, seemed too small for the king’s pride. He ordered it to be doubled in size, and the tomb’s designer mistakenly assumed that simply doubling the side length would suffice. This miscalculation introduced what became known as the “Problem of Minos,” an early geometric challenge to double a cube’s volume while preserving its cubic form. The problem remained unsolved until the 19th century, when it was formally proved to be impossible using classical geometric constructions.

“The Last Supper” (1495-98) by Leonardo da Vinci, at Santa Maria delle Grazie. [WIKIPEDIA]

More than a millennium later, this puzzle unexpectedly resurfaced in the life of Leonardo da Vinci. In the late 15th century, da Vinci was commissioned to paint “The Last Supper” (1495-98) as a mural in a monastery dining hall. The project took three years to complete, and da Vinci was repeatedly chastised by church authorities for his delays. Some interpreted his slow pace as laziness, but the real reason lay elsewhere.

During this period, da Vinci formed a friendship with Luca Pacioli, a Franciscan friar and mathematician. Pacioli introduced him to Euclidean geometry and proportion theory. For da Vinci, who already had a deep interest in numbers and forms, the encounter was transformative. He became absorbed in geometry, especially the Problem of Minos, and began writing extensively on the subject. His obsession with mathematical theory often led him to neglect his painting duties — not out of idleness, but due to intellectual curiosity.

Painting of Luca Pacioli, attributed to Jacopo de' Barbari. [MUSEO DI CAPODIMONTE]

There is, however, an ironic twist. Depictions of Jesus’ final meal were popular during the Renaissance, but none left as lasting an impression as “The Last Supper.” What set his version apart was not only the composition or expression but the subtle infusion of mathematical precision. Central to the painting is the use of linear perspective, anchored by a single vanishing point located just behind Jesus' head. The meticulous use of symmetry and proportion animates the scene with a lifelike presence. These principles — mastered during his mathematical interlude with Pacioli — helped elevate the work beyond a religious tableau to a study in harmony and balance.

Had da Vinci not briefly abandoned his canvas for geometric speculation, his masterpiece may never have taken such a vivid form. His journey into abstract space suggests that moments of intellectual escape — however distant from the task at hand — can ignite lasting creativity. It is a reminder that stepping outside routine can sometimes bring us closer to enduring brilliance.

Translated from the JoongAng Ilbo using generative AI and edited by Korea JoongAng Daily staff.