A new research study has examined the mathematical principles governing creativity and innovation, shedding light on how novel ideas emerge. By analysing data across different domains, researchers have identified patterns that could refine the understanding of how individuals and societies generate new concepts. The study investigates two types of novelty—discovering an entirely new element and forming unique combinations of existing elements. The findings could be crucial in fields such as science, literature, and technology, where innovation plays a vital role in advancement.

Mathematical Framework for Creativity

According to the study published in Nature Communications, researchers introduced a framework to model how new ideas emerge. Led by Professor Vito Latora from Queen Mary University of London, the team focused on higher-order novelties—combinations of familiar elements that create something new. Speaking to Phys.org, Prof. Latora stated that the study is part of a broader effort to understand the mechanisms underlying creativity, aiming to identify factors that contribute to the success of ideas, products, and technologies.

A mathematical model called Edge-Reinforced Random Walk with Triggering (ERRWT) was developed to simulate how people discover and combine elements. Unlike traditional random walks, which assume equal probability for each step, ERRWT strengthens frequently used connections and triggers new links when novel combinations occur. This process mirrors real-world discovery, where repeated exposure to certain elements increases the likelihood of making new associations.

Analysing Patterns Across Domains

The research team applied the ERRWT model to three distinct datasets—music listening habits from Last.fm, literary texts from Project Gutenberg, and scientific publications from Semantic Scholar. The findings revealed that while individuals might have similar rates of discovering new elements, the sequences in which they arrange them differ significantly.

For music listeners, certain users developed unique listening patterns despite discovering the same number of new songs. In literature, writers frequently created new word pairings rather than introducing entirely new words. Scientific papers, particularly titles, demonstrated a higher tendency for novel word combinations compared to narrative texts.

Predicting Innovation with Heaps’ Law

The study also highlighted that the process of novelty creation follows Heaps’ law, a power-law relationship describing how new elements and combinations emerge over time. By applying this principle, researchers could predict different rates of innovation across disciplines. The results indicated that while some fields prioritise the discovery of individual elements, others focus on recombining existing ones in unique ways.

Implications for Future Research

The findings suggest that understanding how creative processes unfold could help refine strategies for fostering innovation. Prof. Latora noted that studying novelty creation is essential for identifying factors that contribute to the rise and decline of trends, products, and ideas. Future research aims to expand the model by incorporating a social component, which could provide insights into how external influences shape creative developments.