1. Comments on the Mathematics of Sustainability Science Louis J. Gross National Institute for Mathematical and Biological Synthesis (NIMBioS) The Institute for Environmental Modeling Departments of Ecology and Evolutionary Biology and Mathematics University of Tennessee Supported by NSF Award EF-0832858 NIMBioS.org

2. Overview Definitions A few examples Interdisciplinarity and sustainability Potential problems to be addressed by an Institute of Mathematics and Sustainability Closing remarks

3. Sustainability definitions Hypothesis: If D = f N where N = number of people you ask, D = number of different definitions of sustainability you will get f = definition multiplier then f > 1. To avoid floundering on the shoals of definitional overload, I suggest we take the usual modeling approach of choosing the definitions/criteria so the model/approach has utility.

4. “ meets the needs of the present without compromising the ability of future generations to meet their own needs.” Brundland Report 1987. "improving the quality of human life while living within the carrying capacity of supporting eco-systems.” IUCN/UNEP/WWF 1991. “the simultaneous pursuit of economic prosperity, environmental quality and social equity”. World Business Council. “the process of building equitable, productive and participatory structures to increase the economic empowerment of communities and their surrounding regions.” Interfaith Center on Corporate Responsibility. A sample of definitions:

5. http://www.sage.wisc.edu/pages/datamodels.html World arable/grazing land

6. THE SCIENTIFIC BASIS FOR ESTIMATING EMISSIONS FROM ANIMAL FEEDING OPERATIONS, NRC 2002

7. Carpenter et al., PNAS 2009

8. Rockstrom et al., Nature (2009)

10. Interdisciplinary Research and Education : (from Jim Collins, NSF) How we were educated What happens when two of us get together What many of us have done In math/biology linkages What sustainability science might foster

11. www.eds.com A challenge of linking sustainability to human actions and policy

12. Possible components of a proposal for an Institute of Mathematics and Sustainability: What resolution of agents/objects are essential to capture the diverse components of sustainability - are there generalities? Develop a general procedure for “back-of-the- envelop” estimates of impacts. Is there any general guidance for when scenario rankings are robust to uncertainties? What methods are usable to evaluate the robustness of spatially-connected economic and environmental models? Develop new methods for multi-modeling, connecting models at multiple scales using multiple mathematical approaches.

13. “systems-modeling approaches yield an informative and normatively more adequate conceptualization of sustainability, one that gives us a better sense of what we are shooting for, one that helps us better understand what our adjustments,approximations and ameliorative strategies should be striving toward.” From Chapter 11 - Sustainability: What it is and What it is not. University Press of Kentucky

14. A cautionary note: Mathematicians can’t claim to be solely theoreticians anymore. Models and analyses we carry out can directly impact sustainability policy, natural resource management, public health policy, etc. While it is exciting that our efforts can have direct impacts, this potentially opens up numerous ethical questions. We need to enhance our political/social assessment skills - no longer can we claim we are simply doing “science”.