Every year or two I teach a Fall multivariable calculus class. The enrollment in these classes is typically at least 40% freshmen. These freshmen must have earned a 5 on their high school AP BC calculus exam to be eligible to enroll in this class. Despite this credential, I often give a diagnostic quiz the first day of class. Question 1: define a derivative. Question 2: define an integral. Most of the students fail this quiz, even though a high school AP BC calculus class spends a semester studying derivatives and their applications and a semester studying integrals and their applications. I always find it disturbing that the students spend so much time computing derivatives and integrals but don't know what they are.
I suspect that one aspect of mathematics is not well known to the general public: mathematics is a language - the most precise language known to man. Mathematicians are obsessed with definitions and the precise use of words. Of course when we venture outside mathematics to the real world, all definitions become fuzzy, but we can think more clearly when we use and understand precise language.
In the war of words between tea partiers and liberals, we hear the tea partiers calling Obama a socialist and liberals deriding them for this rhetoric. Let's consider the substance of this exchange. As a mathematician, I begin any such discussion with a definition.
Definition: Socialism is an economic system in which the government owns or controls the means of production.
Fundamental elements of production which the government might wish to control are choice of what to produce, how much to produce, and at what price to sell. In a capitalist economy these elements are decided by the profit seeking owners responding to individual choices made by suppliers, workers, and thousands of consumers. In the socialist ideal, these decisions are made by a central planning body, motivated not by profit, but by the government's perception of the greater good of the society.
Because centralized planning need not reflect the desires of the suppliers, workers, and consumers, the classic liberal (now called conservative) contends that the government must coerce suppliers, workers, and consumers to supply, labor, and purchase at the rate the government desires. The outcome is a loss of individual freedom in order to achieve the "greater good."
Does this description fit Obama's signature achievement, Obamacare? The legislation mandates purchases of health plans, provides for government control of the content of health plans, and dictates limits on what medical providers receive for their services. Clearly this meets the criteria for a socialist enterprise. Obama has in fact moved a sixth of our economy to the centrally planned column. The left only disputes this because socialism has negative connotations for the majority of Americans. They have no argument on the merits. The much derided tea partiers are on the winning side of this exchange.