Where creativity comes from in the age of AI

Kim Dae-shik

The author is a professor at KAIST.

On Oct. 16, 1843, Irish mathematician and physicist William Rowan Hamilton was struggling with a problem that had occupied him for months. Often described as a pioneer of modern linear algebra, Hamilton sought to extend complex numbers, expressed as a+bi, into a broader system. While the imaginary unit i is defined by i² = −1, he could not determine the relationships among new imaginary components needed to represent three-dimensional space.

Exhausted, Hamilton stepped out for a walk with his wife, Helen. As they crossed a bridge in Dublin, a sudden insight came to him: i² = j² = k² = ijk = −1. Struck by the clarity of the idea, he is said to have carved the formula into the bridge’s stone.

This new number system, later called quaternions, has become essential in representing three-dimensional rotations in computer graphics and robotics. It also provides one mathematical framework for expressing aspects of relativity. Yet the more enduring question lies elsewhere. How did a solution that eluded Hamilton at his desk emerge during a casual walk? More broadly, where do entirely new ideas come from? Is creativity uniquely human, or could artificial intelligence one day generate insights beyond human imagination?

Human cognition is shaped by perception and action. We see, hear and feel the world, then decide how to respond. The brain has evolved less as a mechanism for distinguishing truth from falsehood than as a system for predicting the future, which is essential for survival. Most predictions rely on past experience. The better one stores and uses memory, the more accurate those predictions become.

A challenge arises when the future no longer resembles the past. If existing knowledge and experience cannot address new conditions, then simply recombining old ideas is no longer sufficient. Truly novel thinking must emerge from a different process.

Many researchers compare creativity to a probabilistic outcome. It is difficult for any individual to produce a groundbreaking idea, but among large populations, a few will. When many people interact in close proximity, exchanging and comparing ideas, the likelihood of innovation increases. This helps explain why major advances throughout history have often occurred in large cities. When such environments also include horizontal communication and diverse participants, creative breakthroughs become more likely. Silicon Valley’s continued technological leadership reflects the concentration of talent from different cultures and disciplines, along with constant interaction.

Why does creativity depend on diversity and interaction? In neuroscience, one hypothesis points to the Default Mode Network. Once thought to be a passive background system active when the brain is at rest, recent studies suggest that this network plays a critical role in generating new ideas.

Knowledge and skills can be acquired through focus and effort. Creativity, however, often requires stepping away from a problem. The process known as mind wandering — a state in which attention drifts across internal thoughts and emotions — appears essential to creative thinking. Hamilton’s insight during his walk illustrates this dynamic.

Over the past 5,000 years, human knowledge has accumulated from early systems such as cuneiform writing. Today, generative AI compresses and processes this vast record to produce new outputs, while agent-based AI systems increasingly solve complex tasks. If machines were to develop a capacity similar to mind wandering, new possibilities could emerge.

Such systems might prove mathematical conjectures that have long resisted human effort or propose entirely new physical theories. The prospect of an AI comparable to Albert Einstein, capable of explaining the origin and future of the universe, may no longer be inconceivable.

In that context, the role of human creativity becomes less certain. In an era when machines can generate ideas continuously, what remains distinctive about human thought? Humans may still rely on conversation, exposure to art and moments of reflection, such as walking across a bridge. Whether these practices retain their value in the age of artificial creativity remains an open question.

This article was originally written in Korean and translated by a bilingual reporter with the help of generative AI tools. It was then edited by a native English-speaking editor. All AI-assisted translations are reviewed and refined by our newsroom.