D'Arcy Wentworth Thompson

A Scottish biologist and classicist whose 1917 book On Growth and Form examined how mathematical and physical processes shape biological structures.

On Growth and Form: A 1917 book by D'Arcy Wentworth Thompson on mathematical and physical explanations of biological form. This book develops the ideas that made Thompson’s approach distinctive.
Diffusion: The net movement of particles from regions of higher concentration to regions of lower concentration. Thompson considered diffusion as a physical process capable of shaping biological patterns.
Gaspard Monge: A French mathematician whose work helped establish descriptive geometry and the mathematical study of surfaces. Thompson invoked geometric methods associated with Monge to analyze biological form.
Darwinism: The broad family of ideas explaining biological diversity through descent with modification and natural selection. Thompson emphasized physical and mathematical causes of form rather than selection alone.
Allometry: The study of how an organism’s traits scale in relation to its size. Thompson used scaling relationships to connect growth with changes in biological form.
Surface tension: The tendency of a liquid surface to minimize its area because of cohesive molecular forces. It helps explain why cell aggregates and other soft structures take particular shapes.
Foraminifera: A group of mostly marine single-celled organisms that commonly build chambered calcium-carbonate shells. Their varied shells let Thompson connect growth patterns with geometric forms.
Evo-devo: The study of how evolutionary change relates to developmental processes and gene regulation. It investigates developmental mechanisms with tools unavailable to Thompson.
Dimensional analysis: A method for checking physical equations by comparing the dimensions of their quantities. It exemplifies the quantitative reasoning Thompson brought to biological questions.
Reaction–diffusion system: A mathematical model in which interacting substances react and diffuse through space, sometimes producing patterns. Later pattern-formation models extend the physical approach Thompson advocated.

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Mathematical and theoretical biologyRelated: His work argued that physical forces and geometry help explain organismal shapes.