Why do plants follow mathematical rules to grow their leaves, stems, and roots?
In short: The natural world is filled with stunning geometric precision, from the elegant Fibonacci spirals of leaves to complex fractal-like patterns in roots. These structures are not random; they emerge from simple, reproducible rules. Mathematician Alain Goriely explores how biological growth can be understood through the lens of mathematical theory.
The plant kingdom displays a remarkable degree of regularity in its physical architecture. Whether observing the symmetry of a stem or the intricate arrangement of leaves, one finds that these biological forms are governed by underlying mathematical principles. Alain Goriely, the Gresham Professor of Geometry, argues that these structures are created through processes that we can fully describe and understand using mathematics. This intersection of biology and geometry reveals that the complexity we see in nature often arises from surprisingly simple, repeatable rules.
Goriely’s work focuses on the mathematical theory of biological growth, a field that seeks to explain how living organisms develop their specific shapes. His research extends far beyond botany, applying dynamical systems and mechanics to diverse phenomena such as the coiling of plant tendrils, the formation of seashells, the structure of umbilical cords, and even the modelling of the human brain. By treating growth as a mechanical and mathematical process, he provides a framework for understanding how reproducibility is achieved across such vastly different biological systems.
This approach highlights the power of applied mathematics to demystify the natural world. By identifying the simple rules that dictate how plants grow, mathematicians can predict and explain the emergence of complex patterns that might otherwise seem chaotic. Goriely’s lecture, recorded on 11th November 2025 at Barnard's Inn Hall in London, serves as a testament to the utility of mathematical modelling in biology. It underscores the idea that the beauty of nature is deeply rooted in the logic of geometry, offering a bridge between the abstract world of equations and the tangible reality of the living environment.
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Sources
- Summary by Intellect · source: The Shape of Plants: Why Plants Love Mathematics and Mathematicians Love Plants - Alain Goriely
- Also: The Shape of Plants: Why Plants Love Mathematics and Mathematicians Love Plants - Alain Goriely - Gresham College Lectures
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