When Ben Bernanke was asked last month what historians would write about his eight-year tenure as Fed chairman, which ends Jan. 31, he gave a characteristically reticent answer: “I’ll be interested to see. I hope I live long enough to read the textbooks.”

The surprising truth is that Bernanke, the modest, balding economics professor from Princeton, may go down as the most radical innovator in the Fed’s history — and also, one of the most successful. To combat the financial meltdown that began in September 2008, Bernanke invented a new tool kit of monetary policy, including the still-controversial strategy of asset purchases known as “quantitative easing.”

Bernanke’s great achievement at the Fed was the way he combined risk-taking and prudence. He understood that as the financial markets buckled, the usual presumption in favor of orthodox policy was reversed. To restore liquidity and confidence, it was necessary to experiment. But in doing so, Bernanke drew on the most basic rule for dealing with financial panics, enunciated by Walter Bagehot in 1873: Lend early and freely to solvent institutions.

Bernanke showered the financial system with money as if he were hosing down a fire: The Fed’s balance sheet nearly quadrupled, growing from $900 billion in 2007 to $3.5 trillion in mid-2013, for a compound annual growth rate of 28 percent, according to a new report by McKinsey & Co. In the process, Bernanke pushed short-term interest rates nearly to zero and 10-year rates to below 2 percent.

This high-voltage monetary stimulus appears to have worked: By Bernanke’s count, real GDP has grown in 16 of the last 17 quarters and by the third quarter of 2013 was 5.5 percent above its pre-recession peak. Unemployment has fallen from 10 percent in late 2009 to 7 percent recently. These gains have come despite restrictive fiscal policy that, according to an estimate by the Congressional Budget Office, reduced output last year by as much as 1.5 percentage points.

One measure of what Bernanke accomplished is to compare his record with that of policymakers during the Great Depression. As recounted by Liaquat Ahamed in his brilliant 2009 book, “Lords of Finance,” the central bankers of the day made disastrous mistakes, especially in sticking too long with a gold standard that plunged the system ever deeper into crisis.

Writing in October 2008, as the financial world was collapsing once more, Ahamed warned in the foreword to his book: “In trying to calm anxious investors and soothe skittish markets, central bankers are called upon to wrestle with some of the most elemental and unpredictable forces of mass psychology.” Bernanke read the book when it was published, perhaps to pass his sleepless nights during the first year of the crisis. But more important, he had written his own version of the same history while at Princeton before he joined the Fed. He had been schooled for financial disaster, quite literally.

“The crisis bore a strong family resemblance to a classic financial panic,” Bernanke explained in a farewell speech prepared for delivery Friday. “Likewise, the tools used to fight the panic, though adapted to the modern context, were analogous to those that would have been used a century ago.”

The challenge for Janet Yellen, Bernanke’s successor, will be to dismantle safely the structure that he so artfully constructed. Bernanke began this “tapering” process in December, announcing that the Fed would reduce its asset purchases from $85 billion a month to $75 billion. That’s still a torrent of cash swirling through the system, and there are skeptics who doubt it can be withdrawn without a sharp spike in interest rates that could devastate financial markets all over again.

Bernanke’s Wall Street rescue, and his broader policy of quantitative easing, has been criticized for helping the wealthy. That’s surely true, in the sense that by keeping the boat afloat, he allowed the richest Americans to hold on to their privileged seats. But the recent McKinsey study notes that those hurt most by ultra-low interest rates have been savers (which by definition means those with spare money). The big beneficiaries have been corporate borrowers, homeowners and the government itself.

Americans have been uneasy about central banks since the days of Thomas Jefferson and Andrew Jackson. But looking at Bernanke’s record, even the skeptics should grant that the country was lucky to have him when the crisis hit.