“What is the relationship between mathematics and the environment?”

 Anyway, to pick a few examples, mathematics provides a number of ways to describe relationships among elements of the environment, such as the weather [1], the flow of water and nutrients in streams [2], the volume of water in a flood, behavior of wind and water currents in the atmosphere, and calculating a water balance between downward flows (rain), surface flows (runoff, soil penetration), and upward flows (evaporation from water bodies, transpiration from biomass) [3]. Maths can be used to describe the difference between current conditions and historical conditions, such as droughts and floods [4].

Maths are also used to describe and estimate complex interactions among components of the natural environment. These are often called models. A simple model is a thermometer: some colored liquid rises and drops within a very narrow glass tube based on temperature. The thermometer is not “the temperature” but rather a close estimate of the temperature based on physics and thermodynamics. Complex models for various aspects of the environment are described with computer programs [5] (as with the previous USGS and NOAA examples).

Maths are really part of the foundations for all the natural sciences, including chemistry (mass balances and interactions of elements and molecules), physics (fundamental relationships between particles, forces and motion), thermodynamics, and electromagnetics, which includes properties and behavior of visible light, radio waves, and other wave-based phenomena. Possibly the hardest aspects of natural science to model with maths are biology and ecosystems, because of their complexity. One of the most ambitious projects I’ve seen is about the description and accounting of the embodied energy (called emergy) in any natural process, system or system of systems, including human systems such as capital flows, markets, and education [6].

One other avenue for maths’ relation to the environment is in the area of Geographic Information Systems (GIS). These computational tools can solve for spatial relationships such as intersection, containment, adjacency (geometric math), useful for computing and applying spatial, statistical, topological, and other measures to movements of animals, people, and business. The maths in GIS allow you, for example, to determine that natural corridors for wildlife trying to move from one end of Florida to another are reduced to less than a quarter mile in places. One can study the effects of, say, edges of urban areas on populations and behavior of birds and other wildlife.

What I’ve just described is just the “tip of the iceberg” of ways that maths relate to the environment. You can spend a life learning any one of them, and you can save many lives by understanding and applying them.