There could never be another “Iron Lady.”

That was the first thought that came to some minds today with the news that Margaret Thatcher, the U.K.’s great prime minister, had died.

This is an odd reaction. Women in the developed world now routinely hold more top jobs than they did in 1975, when the 49-year-old Thatcher first assumed leadership of the Conservative Party. The No. 1 bestseller on the New York Times list is “Lean In,” by a woman holding one of the highest of those positions, Sheryl Sandberg, the chief operating officer of Facebook Inc.

A look at what Sandberg, the granddaughter of a retailer, recommends and what Thatcher, a grocer’s daughter, did, reveals similarities. But there are also such great differences between the two women that you wonder whether a Thatcher might make it today in politics or at a publicly traded company.

Sandberg advises women to learn from female mentors, and Thatcher certainly did. Her tutor at Oxford University, the scientist Dorothy Hodgkin, encouraged the young Margaret Roberts to logically work through problems to their conclusion. That is so Sandberg: Sheryl plans her career moves in an Excel spreadsheet.

Taking Risks

Sandberg admonishes younger women to “lean in,” to push harder at work, in order to advance. Thatcher did lean in, and up, ascending by force the lowest rungs of the Tory ladder, starting with the Oxford University Conservative Association as a student. Sandberg specifically counsels women to take risks early and Thatcher certainly did that, too. While still in her 20s, Thatcher dared to run twice for office in a Labour Party stronghold, Dartford, and lost both times. Nor did Thatcher temper her risk-taking as she rose.

Her party tended to cave and reverse policy under political pressure, but not Thatcher: “This lady’s not for turning,” she famously declared.

As a Cabinet member or prime minister, she pushed for budget cuts when her advisers, including influential U.S. supply-siders, advised her to emphasize tax cuts. “Pennies don’t fall from heaven,” Thatcher said in 1979, the year she took office. “They have to be earned here on Earth.” Under her guidance, the U.K. cut spending with a vigor that Ronald Reagan admired.

“Sit at the table,” is another key Sandberg precept and Thatcher did a splendid job at that. A genius at political timing, Thatcher very early sensed that the moment to grab a power seat was when the table was in disarray, as in the 1970s, when the Tories were flailing.

Thatcher also ruled at the diplomatic table, and even served as a kingmaker. “I like Mr. Gorbachev,” she said in 1984, when Mikhail Gorbachev was still merely an influential Politburo member. “We can do business together.”

We don’t know how much the Thatcher seal of approval contributed to Gorbachev’s elevation to general secretary of the Politburo a few months later, but it undoubtedly helped. Her partnership with Gorbachev, in turn, made it possible to bring about the end of the Soviet Union. Her encouragement to President George H.W. Bush -- “George, don’t go wobbly on me” -- helped the allies conclude the first war in Iraq.

But if Thatcher knew how to take her place at the table, she also knew how to walk away. The most spectacular instance of her doing so was in Bruges in 1988, when she made it clear the U.K. wasn’t willing to join the nations of continental Europe in building up the social welfare state.

Resisting Europe

“We have not successfully rolled back the frontiers of the state of Britain only to see them reimposed on a European level with a European super state exercising a new dominance from Brussels,” she said.

Thatcher paid gloriously little heed to social fashion. She was known as a man’s man, and even one who harassed men she suspected might be vulnerable: When I worked in the U.K. in the 1980s, more than once I heard a male Tory say of another, “she made him cry.”

That same rough style might disqualify a rising Thatcher today. Over and again, today’s leaders counsel their pupils, especially the female ones, to network and get along, and focus on discrimination. “Many people believe that the workplace is still a meritocracy,” writes Sandberg, suggesting that the people who hold such beliefs are blind or wrong.

“It’s heartbreaking,” Sandberg also maintains, “to think about one woman holding another back.” Indeed it is, but an emphasis on woman-to-woman help tends to reward the get-along women rather than the aggressive ones.

Which brings us to the largest obstacle to today’s Iron Ladies: the emphasis on corporate or government process. As Sandberg laboriously notes, Harvard Business School, which already famously focused on teamwork and consensus, has lately emphasized teamwork even more. It’s hard to imagine Thatcher (“Defeat? I do not recognize the word”) thriving at HBS.

The result of the collaborative culture is that corporations or government institutions focus intensely on internal culture and pour their energy into achieving minuscule policy changes relating to workplace efficiency, gender or race. The great victory with which future Thatcher biographers are likely to open their accounts is her winning back the Falkland Islands from the Argentine junta. The great victory with which Sandberg opens her book was getting Google Inc. to establish reserved parking for pregnant women.

The one area in the U.S. where new Thatchers might arise is private companies, especially ones they themselves found. That is where they won’t be bogged down by process or political correctness. To these future Iron Ladies, one can imagine Thatcher advising: “The goal is not to lean in, though certainly that’s necessary. The goal is to move mountains.”

(Amity Shlaes, director of the Bush Center Four Percent Growth Project, is the author of “Coolidge,” published by HarperCollins, and a Bloomberg View columnist. The opinions expressed are her own.)

To contact the writer of this article: Amity Shlaes at amityshlaes@hotmail.com

To contact the editor responsible for this article: Max Berley at mberley@bloomberg.net