the mathematical methods that we need to do this effectively along with some of
the challenges we face. For example, we need to be able to precisely quantify
natural capital as well as human and natural well-being, to understand how our
activities affect natural capital, to calculate how quickly nature can regenerate, to
develop ways we can adapt to a changing environment, and to make responsible
decisions balancing the needs of people today with the needs of future
generations and balancing the needs of different people around the world.
The second group focused on Human-Environment Systems as ComplexAdaptive Systems. The interactions between humans and the environment are
both extraordinarily complex and constantly changing, with interacting feedbacks
between different parts of the system. For example, humans farm, which affects
the health of the soil; the health of the soil then affects where humans farm,
which in turn affects the health of the soil. The science of complex adaptive
systems has been developing to understand interactions like these. This group
looked at how the mathematics of complex adaptive systems can illuminate the
interactions between humans and their environment.
The third group discussed Measuring and Monitoring Progress towardSustainability. To learn to live sustainably, we’ve got to know how well we’re
doing. But measuring the health of a forest or an ocean is an extremely complex
task: You have to collect a huge amount of data, get the most information
possible given limited resources, and then make sense of the data you get. Every
step raises mathematical and statistical challenges.
The fourth group examined Managing Human-Environment Systems forSustainability. The central point of sustainability science is to guide decision-
making. This group examined this final step. For example, given current
trajectories, society might have to double food production in the next 40 years
while reducing pollution impacts on lakes and rivers and reducing the rates of
biodiversity loss associated with land-use change and overfishing. How are we
going to do it? This group laid out the mathematical sciences tools needed to put
together what we know into a precisely defined set of questions and into a
practical course of action.
The fifth group examined Mathematical Challenges in EnergySustainability as an in-depth case study that touches on all four previous groups.
The energy system needs a radical transformation, fast, and so does the relation