The Ricardian vice refers to abstract model building and mathematical formulas with unrealistic assumptions. In simpler terms, the Ricardian vice is the tendency for economists to make and test theories that aren't troubled by the complexities of reality, resulting in theories that are mathematically beautiful but largely useless for practical applications. The Ricardian vice is prevalent in economics and is named after David Ricardo, one of the first economists to bring mathematical rigor to the discipline.
Joseph Schumpeter was the first to call out the so-called Ricardian vice and actually coined the term. He implied that Ricardo took a marginalist approach to economic theory, resulting in a sort of push-button economics in which the "right answer" to a particular problem could be solved by simply "pressing the right button" on an economic model.
Schumpeter's criticism notwithstanding, Ricardo was an influential classical economist of similar reputation and caliber as Adam Smith and Thomas Malthus. He came up with many useful theories and laws that defended free trade and sound monetary policies, including them the law of comparative advantage, the labor theory of value, and the law of diminishing returns. As time passed, however, Ricardo depended more and more on model building and large (sometimes erroneous) assumptions to achieve the results he wished.
For example, Ricardo focused on the distribution of income rather than the growth of economic activity to "prove" that everyone but a landlord was doomed to subsistence wages. He also spent time seeking an ironclad measure of value, trying to link it to the cost of labor while calculating out any benefits of machine labor, hence is labor theory of value, which argued that the true economic value of a thing was based implicitly on the socially necessary labor used to produce it.
Even in his law of diminishing returns, Ricardo simplified all agricultural crops into one field all farmed with the same technique and having an equal yield on all sections. Adding to these already sizable assumptions, he factored the cost of wages as being equal to the subsistence level that he believed to be unavoidable. While it yielded a result that showed that tariffs harm the domestic economy, it oversimplified the case.
Even today, many economic models mathematically remove, simplify or fix dynamic components like competition with an arbitrary value. While these exercises in pure deductive reasoning can yield useful clues about how things might work, they need to be held against the way things actually work in the real world to have any value. (See also: How Influential Economists Changed Our History.)