When will humans outstrip the carrying capacity of the Earth, or numbers of a pest, such as rats, blow out to plague proportions in an agricultural region?

The mathematical description of such thresholds has vexed the best minds around the world for 100 years. If mathematicians could predict when systems will be pushed over the edge, action could be taken before irreversible damage is done.

Fundamental research by ANU mathematician Florica Cirstea promises to formalise such problems, clearing the way for more accurate predictions about the physical world. Cirstea, whose research takes her to the institutions of her collaborators in France and Italy, says she was attracted to mathematics because ``it lies at the foundation of everything that surrounds us".