Is poverty a mathematical necessity?
American economic theorist Henry George wrote about precisely this issue in his famous work Progress and Poverty published in the late 1800s, and based on his observations on the economic development of San Francisco during the gold rush.  His argument was that increasing economic development primarily benefitted landowners, at the expense of both capital and labor.  (However, since landowners were often also holders of large amounts of capital, it was primarily labor that ended up losing out.)  In a nutshell, the leverage that landowners held over the workers allowed them to push wages ever lower, creating poverty as a result of economic progress.  He theorized that taxing economic rent (at/near 100%) would eliminate speculation and thus stop the boom/bust cycle endemic to market economies, as well as providing ample revenue to the government to fund social welfare programs and to develop infrastructure.