Many economists think that much of the criticism the profession has taken in recent years has been unfair. Academic research has moved on from the days before the financial crisis, they protest. Judging from the new material appearing in the profession’s top journals, that looks to be true.

And yet the problems with economics run deeper than the state of peer-reviewed research. More serious are the fundamental ideas economists continue to teach students, who leave university with many questionable convictions in their heads.

Economist Howard Reed of the consultancy Landman Economics recently called for tearing up the foundations of economics and starting anew. Reed argues that that core ideas of “neoclassical” theory are so flawed that policy would often be more sensibly based on no theory at all. Too much of economic theory centers on neoclassical notions of businesses and people who get busy “optimizing “profits and utility; but that’s not how the real world works, he says.

Economist Diane Coyle of the University of Manchester shot back, saying that Reed was attacking economics as it used to be, not as it is now. My Bloomberg Opinion colleague Noah Smith seconded Coyle’s views.

Coyle and Smith are correct, at least partially. I surveyed the first five papers in the latest issues of the top five economics journals, as judged by impact factor: the Quarterly Journal of Economics, the Journal of Political Economy, Econometrica, the American Economic Review and the Journal of Finance. They concerned topics such as an empirical study of income distribution in the U.S. and an analysis of how some economic models can improve the matching of students to schools. None of the papers fit the Reed stereotype – economic models with infinitely wise individuals acting in perfect, complete markets.

Even so, Reed’s criticisms aren’t all off-base. Most importantly, economics teaching shapes the beliefs and thinking habits of students who go on to careers in business, finance, law or public policy. And academics do continue to teach many of the ideas that Reed criticized.

For example, a key element in any university economics training is exposure to the so-called welfare theorems, closely associated with Adam Smith’s idea of the invisible hand. Students learn that economists in the 1950s proved mathematically, in a highly abstract model, that there always exists a market equilibrium that perfectly matches production and consumption, and that this equilibrium is socially optimal, in a certain technical sense. They also learn that any socially optimal economic state can in principle be achieved purely through free trade in a market. And the embedding of these theories doesn’t just start at university: British high school students studying economics will also find they form the core of the curriculum.

Economists admit that these theorems rely on absurd assumptions, and that there’s no reason to think a real economy might ever come to resemble such a state. The theorems teach us about something that is not even remotely like any real economy. Yet bizarrely, economists go on teaching the theorems just the same, and they’re on the curriculum at MIT, Harvard, Berkeley and most anywhere else. They have an iconic status in the profession that is disconnected from any legitimate explanatory power.