We usually know where things come from. The food we buy comes from farms, practically everything else we own comes from factories, and the raw materials to make them come from mines and forests.

But were does it all go once we finish using it or it breaks? We put it on the curb and—thanks to trash collectors—it seems to disappear. Yet in reality, nothing disappears: We just change useful things into trash, just as we change natural resources into things we can use. This article examines how mathematics lets us calculate the amounts of trash we must either divert to beneficial uses or dispose in landfills or incinerators.

Types and Fates of Solid Waste

In general, there are two kinds of trash, or solid waste. Industrial solid waste is generated when factories convert raw materials into products. Municipal solid waste is...