Premise, Pi, Playfulness and the Polymath

In August 2024, a young boy stood in the Museo Interattivo Leonardo da Vinci in Florence, Italy, his face awash with awe. The museum dedicated to the renowned Florentine polymath housed a life-size recreation of his fighting machine, a prototype of what would become the modern tank. Constructed from birch plywood and reinforced with iron plates, the armoured vehicle featured an enclosed dome mimicking the shell of a tortoise, with a conical shape intended to deflect enemy fire. Inside, a system of cranks and gears powered by soldiers would rotate the vehicle, allowing it to move in any direction. The original sketches contained a flaw in the gearing, which some believe da Vinci introduced deliberately to prevent its misuse. However, modern reconstructions, including the one in this museum, have made minor adjustments to render the design fully operational (apart from the cannons, of course). 

The machine towered over the boy, casting a shadow so large that he might have been swallowed by the darkness if not for the glow of a nearby projection. Illuminated on the wall beside him was Lady with an Ermine, one of da Vinci’s masterpieces, now housed at the Czartoryski Museum in Kraków, Poland. Painted with oils on a panel of walnut wood, the portrait is striking in its composition. Unlike the rigid, frontal poses common in paintings of the time, da Vinci introduced a sense of movement by positioning Cecilia Gallerani’s body at an angle while her gaze turned in another direction, creating a natural sense of dynamism. He developed and employed the sfumato technique, using subtle gradations of light and shade to soften Gallerani’s features rather than relying on the harsh outlines typical of earlier works. This allowed him to achieve a lifelike quality with seamless transitions between light and shadow. It was considered revolutionary for its departure from traditional portraiture. The light from the painting’s display caught the boy’s expression, reflecting the wonder in his eyes. 

An  enormous war machine, an exquisite portrait: both creations born from the same mind nearly 550 years ago.

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I first heard about da Vinci when I was around ten. He was a character in a video game my older brother was playing and I wanted to delve deeper into his story. What I found sparked a fascination that has lasted fifteen years. It was the beginning of a lifelong admiration for those who can excel across different fields.

The foundation of my formal education was in the sciences. I studied for a mathematics degree. I have also worked professionally as a comedian, trained as a theatre director, and served as Youth Trustee for a theatre - but mathematics and performance never seemed to intersect. They never seemed to intersect because the systems were designed to keep them separate. Whenever I had the opportunity to advance in one path, the best way to succeed was to suppress the other. I was strongly encouraged not to study both maths and English at A-Level (little content overlap). Career advisors told me to remove major achievements from my CV (irrelevant). At every stage, the message was clear: pursuing multiple paths would not enhance my success, but hinder it. Sitting in that museum in Florence, I had never felt more divided or more pressured to choose just one path. I had just been let go from my role in a tech start-up, one that had initially promised excellent development opportunities and the chance to combine the performing arts with deep analytics. Those promises never came to fruition.

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Leonardo da Vinci was a polymath in the truest sense of the word. His curiosity knew no bounds and his mind refused to separate disciplines. His notebooks, filled with sketches, theories, and observations, show that he viewed art and science as complementary tools for understanding the world. Whatever task he put his mind (or hand) to, his approach remained the same: to study, to question, and to experiment.Da Vinci did not simply paint or sketch. He engineered his compositions with mathematical precision. His fascination with proportion is best exemplified by the Vitruvian Man, a drawing that exhibits, par excellence, the balance between logic and beauty. Inspired by the Roman architect Vitruvius, da Vinci used geometry to scrutinise the ideal human form, believing that mathematical harmony underpinned all of nature’s designs. This obsession with proportion was carried through to his paintings, from the carefully structured perspective of The Last Supper to the symmetry present in the Mona Lisa.In The Last Supper, da Vinci used linear perspective to direct the viewer’s eye. The vanishing point of the painting, where all receding lines converge, falls precisely on Jesus’ right cheek, reinforcing his centrality in the composition. The disciples are arranged in four groups of three, a deliberate structuring that enhances visual balance. 

Some scholars have speculated that da Vinci used the Golden Ratio when composing the Mona Lisa. This is a mathematical proportion of approximately 1.618:1, often associated with aesthetic harmony. While there is no direct evidence that this was deliberate, his close connection to mathematician Luca Pacioli, who wrote extensively on the topic, suggests familiarity with its principles. The proportions of Mona Lisa’s face, as well as the positioning of her eyes and hands, align with this ratio, creating a sense of natural balance that feels intuitively pleasing to the viewer.Beyond proportion, da Vinci’s understanding of light and vision shaped the way he approached realism. He pioneered techniques such as atmospheric perspective, using gradual shading and colour shifts to create the illusion of depth. In the Mona Lisa, much like in Lady with an Ermine, da Vinci’s soft blending of tones and edges allowed him to create a face that feels almost alive. His anatomical studies played a crucial role in this pursuit of realism. Through dissection, he developed an unmatched understanding of musculature which gave his subjects a lifelike quality few before him had achieved. Da Vinci didn’t just paint the human body - he reconstructed it from the inside out.

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Da Vinci’s scientific work was just as influenced by his artistic eye. His engineering designs were not simply technical schematics but intricate illustrations of possibility. There was an elegance to his designs, a sense that beauty and utility were not mutually exclusive. Fascinated by the natural world, he produced studies of the movement of water that were both scientific analyses and works of artistic expression. His Deluge Drawings, chaotic swirls of ink depicting stormy waters, are not just representations of turbulence but reflections of his technique. Each brushstroke becomes a microcosm of the larger composition, fluid, dynamic, and imbued with motion. This same attention to natural detail is evident in his paintings. The backgrounds of both versions of The Virgin of the Rocks are carefully observed geological studies. The plants in The Annunciation are rendered with botanical accuracy; da Vinci sought to understand the underlying structures governing plant growth, from the curvature of petals to the way light interacted with leaves. Among them, the carefully detailed irises and lilies stand out, each painted with an attention to form and texture that mirrors real botanical studies.

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Da Vinci’s work stands as testament to a mind that refused to be confined. He did not work in silos. Each pursuit informed and enriched the others. His willingness to experiment, to play with ideas before fully realising them, allowed him to innovate in ways that few others could.In today’s world, where specialisation is often valued over breadth and the boundaries between disciplines are more rigid than ever, da Vinci’s ability to excel across so many fields feels almost impossible. His genius was not just in his skill but in his refusal to see divisions where others did. It raises an important question: why is this kind of fusion so rare today? And what might we gain by embracing a more holistic way of thinking, one that does not force us to choose between logic and creativity, but instead allows us to discover the full spectrum of our abilities?

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Looking at da Vinci’s work, one trait stands out above all else: playfulness. This was not just a tool for exploration, but a mindset that allowed him to bridge disciplines. Playfulness is often dismissed as something frivolous, but for da Vinci, it was the foundation of his most remarkable achievements. Whether sketching fantastical flying machines, dissecting human cadavers to understand anatomy, or blending mathematics with portraiture, he approached each pursuit with curiosity and an openness to experimentation. At its core, playfulness is about engaging with the unknown. It is the willingness to try new ideas, push boundaries, and step outside rigid structures to see what might emerge. For both artists and scientists, it is a necessary tool. It allows for trial and error, for making unexpected connections, and for finding solutions that would not have been possible through logic alone. Da Vinci’s legacy is a reminder that the greatest minds do not just work - they play, test, tinker. His approach shows that innovation happens when we embrace the connections between disciplines.

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In improvised comedy, playfulness is the foundation of the entire art form. There is no script, no safety net, and no predetermined structure to fall back on. Scenes are built in real time through spontaneous collaboration, and the best improvisers are those who are willing to take risks and follow unexpected paths. The principle of "Yes, and..." is central to this. Accepting whatever your scene partner offers and building on it keeps the momentum going. Without that openness, the scene stalls. The moment an improviser tries to control too much, clings to a plan, or refuses to adapt, the energy collapses. Play is what keeps the scene alive.

Stand-up comedy, though more structured, relies on the same fundamental principle. Comedians might walk on stage with a set, but the performance is never static. The audience is a living, reacting presence, and no two performances are ever identical. The best stand-ups do not just recite material. They adjust their timing based on the crowd, riff on unexpected interactions, and allow room for spontaneity. Some of the best moments in comedy come from these unscripted detours, where playfulness takes over and a joke evolves in real time. Few comedians embodied this better than Robin Williams. His sets felt like an explosion of energy, shifting between voices, impressions, and wild improvisations at breakneck speed. He could take the smallest audience reaction and turn it into a five-minute bit, crafting new jokes in the moment rather than relying solely on pre-written material. Williams treated stand-up as a playground, proving that the most memorable moments often come not from what is planned, but from what is discovered in the moment.For me, this sense of play is what makes performing so fulfilling. Standing in front of an audience, testing ideas, finding new rhythms, leaning into the unpredictable, and learning from it is what keeps the work exciting. Comedy is an iterative process: it thrives on the willingness to experiment, to fail, and to try again.

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Mathematics is often misunderstood as a rigid, rule-bound discipline. People who don’t engage with it past their school years often imagine formulas, strict procedures, and cold logic. But at its core, mathematics, too, is an act of play. It requires curiosity, creativity, and a willingness to investigate beyond what is immediately obvious. In mathematics, problems are not just solved; they are explored. The best mathematicians approach their work not as a mechanical process but as an open-ended puzzle, where unexpected connections and insights can emerge through experimentation. When I was studying for my mathematics degree, I was struck by how often breakthroughs came from toying with an idea rather than simply following a prescribed method. Whether it was visualising problems in new ways, trialing different approaches, or using intuition to guide formal proofs, playfulness was always present.One of the best examples of this is combinatorics, a branch of mathematics that studies counting, arrangement, and structure. It often involves trying different arrangements and imagining new patterns. Another example is mathematical logic, which requires flexibility of thought and the ability to see how small changes can completely shift an argument. It is no coincidence that famous logician Charles Dodgson, better known as Lewis Carroll, was both the author of Alice’s Adventures in Wonderland and a mathematician at Christ Church, Oxford. Much of Carroll’s writing embraces nonsense, but beneath the absurdity lies a deep understanding of mathematical structures, from logical paradoxes to wordplay rooted in formal reasoning. He applied a sense of play to all aspects of his work, using seemingly illogical ideas to unpack logic itself.

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For me, the connection between my mathematics and my comedic practice lies in this shared need for play. In both fields, rigid thinking leads to dead ends, while an open mind leads to discovery. Whether working on a proof or crafting a joke, the most exciting moments come from the unexpected.It is easy to feel that pursuing multiple disciplines will dilute success, rather than concentrating it. Yet da Vinci’s life proves otherwise. His brilliance did not come from choosing a single path but from allowing himself to explore freely, from seeing the value in both precision and imagination. He thrived at the intersection of structure and spontaneity, and in doing so, he reshaped what was possible.

Playfulness is not just for artists or scientists. It is for anyone navigating an uncertain world. It is what allows us to adapt, to rethink, and to approach challenges with curiosity instead of fear. In an era where everything seems increasingly structured and predefined, where education systems reward rote learning over exploration and career paths often demand specialisation from an early age, the ability to play, to remain open to potential, is more valuable than ever.

That trip to Italy did not provide me with all the answers about where my future lies. But perhaps I do not need them yet. If da Vinci’s legacy teaches anything, it is that progress is not always linear. It comes from trialing and learning, and from staying engaged with the process rather than fixating on the outcome. If I allow myself to remain playful, then perhaps I, too, can build something meaningful in the space between logic and creativity.

By Oliver Johnson for CRoB Digital, edited by Francesca Gardner

Artwork by Holly Poynter