An Online Lecture Series on Mathematics for Planet Earth

The Mathematics for Planet Earth online lecture series commenced on 20 August 2026 with its inaugural lecture, “Mathematics of Planet Earth: A Wide Spectrum of Ideas and Possibilities.” The session was delivered by Prof. Christiane Rousseau, Professor Emerita in the Department of Mathematics and Statistics at Université de Montréal, Canada. An internationally recognised mathematician and former President of the Canadian Mathematical Society, Prof. Rousseau was also the international coordinator of the Mathematics of Planet Earth 2013 initiative. The lecture series has been conceived with the larger objective of encouraging students, faculty members and mathematics enthusiasts to look beyond the conventional boundaries of mathematics and recognise its presence in the world around them. The inaugural session set the tone for this vision by demonstrating how mathematical ideas can help us understand ecosystems, climate, biodiversity, cooperation, natural resources and some of the most pressing challenges facing our planet. Prof. Rousseau began by presenting the broad vision of Mathematics of Planet Earth, explaining its connections with fields such as meteorology, geophysics, ecology and the structures of civilisation. A central idea of the lecture was that the Earth is a complex system and that mathematics provides powerful ways of describing, modelling and understanding the interactions taking place within such systems. One of the most engaging examples discussed during the lecture was the concept of tipping points in ecosystems. Using clear and turbid lakes as an example, Prof. Rousseau demonstrated how feedback mechanisms can maintain an ecosystem in a stable condition. However, increasing external pressures, such as excessive phosphorus entering a lake through agricultural runoff, can eventually push the ecosystem beyond a critical threshold. Once such a tipping point is crossed, returning the external conditions to their earlier levels may not necessarily restore the ecosystem immediately. This led to an explanation of hysteresis, illustrating how mathematical models can help us understand both ecological collapse and the difficulty of recovery. The lecture also explored the fascinating mathematics behind patterns in vegetation. Prof. Rousseau discussed how mathematical models involving diffusion, water availability and feedback mechanisms can generate patterns such as spots, labyrinths, gaps and strips. Remarkably, similar patterns can be observed in vegetation in semiarid regions, providing an excellent illustration of how mathematical structures can emerge visibly in nature. Moving from individual ecosystems to the planetary scale, Prof. Rousseau discussed potential planetary tipping points, including concerns surrounding Arctic sea ice, the West Antarctic ice sheet, the Gulf Stream and the possibility of the Amazon rainforest transitioning towards a savanna-like state. The lecture also brought the discussion closer to the Indian context by referring to the melting of Himalayan glaciers and the importance of understanding the stability of the Indian monsoon. Another important part of the lecture examined biodiversity, competition and cooperation. Prof. Rousseau explained that simple competition models alone cannot adequately account for the coexistence of a large number of species. Spatial and temporal heterogeneity, along with cooperation, are important ingredients in understanding complex ecosystems. This discussion naturally led to game theory and the Prisoner’s Dilemma. Through examples ranging from natural systems to arms races, trade tariffs and climate negotiations, the lecture demonstrated how decisions that appear individually advantageous can result in poorer outcomes for everyone involved. The example of cleaner wrasse fish further illustrated that cooperation is not merely a human social construct but is also observed in nature. Prof. Rousseau discussed repeated interactions and strategies

that can encourage cooperation and produce mutually beneficial outcomes over time. The session then turned to weather and climate modelling. Prof. Rousseau emphasised that mathematical models are necessarily simplifications of reality. Their purpose is not to reproduce every detail but to capture the essential components and interactions required to understand a system. Climate models must therefore consider the interconnected behaviour of the atmosphere, oceans, ice, vegetation and soils. She also highlighted how advances in data availability, computing power and data assimilation have contributed to significant improvements in meteorological forecasting. Since atmospheric systems are chaotic and sensitive to initial conditions, modern forecasting relies on results from multiple simulations and models rather than a single prediction. The role and limitations of

Artificial Intelligence in meteorology were also discussed. While AI offers valuable possibilities for forecasting, Prof. Rousseau pointed out the challenge of predicting unprecedented extreme events when models depend heavily on patterns learned from historical data. This highlighted a broader message of the lecture—the importance of validating models and recognising uncertainty rather than treating mathematical or computational predictions as absolute truths. The final part of the lecture connected mathematics with sustainable development and resource management. Prof. Rousseau discussed how economic models focused heavily on short-term returns can contribute to resource depletion. She emphasised the need to recognise the wider value of ecosystem services, including water regulation, carbon sequestration, soil protection, medicinal resources and human well-being, when making decisions about natural resources. The lecture concluded with an engaging question-and-answer session, during which participants raised questions about climate modelling, interdisciplinary research, model validity and uncertainty. Prof. Rousseau emphasised the importance of mathematicians working closely with experts from other disciplines, understanding the problems they seek to model, and communicating mathematical findings in language accessible to scientists, policymakers and the wider public. She also encouraged young people to explore areas that genuinely interest them and use their expertise to contribute to global well-being. The inaugural session thus provided an inspiring beginning to the Mathematics for Planet Earth lecture series. Through examples drawn from ecology, climate, game theory, economics and sustainability, the lecture demonstrated that mathematics is not confined to equations and classrooms; it is deeply embedded in the systems and relationships that shape our planet. The session encouraged participants to view mathematics not merely as a technical discipline, but as a powerful language for understanding the world and contributing meaningfully to its future.