“There’s a whole neoliberal agenda,” she said, referencing the received free-market wisdom that cutting public budgets spurs economic growth. “And then the way that traditional theory has fomented it or not contested it — there’s been kind of a strange symbiosis between mainstream economic thinking and stupid policies.”

Dr. Mazzucato takes issue with many of the tenets of the neoclassical economic theory taught in most academic departments: its assumption that the forces of supply and demand lead to market equilibrium, its equation of price with value and — perhaps most of all — its relegation of the state to the investor of last resort, tasked with fixing market failure. She has originated and popularized the description of the state as an “investor of first resort,” envisioning new markets and providing long-term, or “patient,” capital at early stages of development.

In important ways, Dr. Mazzucato’s work resembles that of a literary critic or rhetorician as much as an economist. She has written of waging what the historian Tony Judt called a “discursive battle,” and scrutinizes descriptive terms — words like “fix” or “spend” as opposed to “create” and “invest” — that have been used to undermine the state’s appeal as a dynamic economic actor. “If we continue to depict the state as only a facilitator and administrator, and tell it to stop dreaming,” she writes, “in the end that is what we get.”

As a charismatic figure in a contentious field that does not generate many stars — she was recently profiled in Wired magazine’s United Kingdom edition — Dr. Mazzucato has her critics. She is a regular guest on nightly news shows in Britain, where she is pitted against proponents of Brexit or skeptics of a market-savvy state.

Alberto Mingardi , an adjunct scholar at the libertarian Cato Institute and director general of Istituto Bruno Leoni, a free-market think tank, has repeatedly criticized Dr. Mazzucato for, in his view, cherry-picking her case studies, underestimating economic trade-offs and defining industrial policy too broadly. In January, in an academic piece written with one of his Cato colleagues, Terence Kealey , he called her “the world’s greatest exponent today of public prodigality.”

Her ideas, though, are finding a receptive audience around the world. In the United Kingdom, Dr. Mazzucato’s work has influenced Jeremy Corbyn, leader of the Labour Party, and Theresa May, a former Prime Minister, and she has counseled the Scottish leader Nicola Sturgeon on designing and putting in place a national investment bank. She also advises government entities in Germany, South Africa and elsewhere. “In getting my hands dirty,” she said, “I learn and I bring it back to the theory.”