NEW YORK — It was just last summer that the Dow Jones industrial average shed 2,000 points in three terrifying weeks. Investors had a host of things to worry about, including the possibility of another recession.

Now the Dow is within reach of the rarefied 13,000 mark — a level it hasn’t seen since May 2008, four months before the financial system almost came apart.

A strong one-day rally — caused by a deal on bailout money for Greece, perhaps, or an unexpectedly positive economic report — could put it over the top.

What’s more, the average is just a 10 percent rally from an all-time high. And 10 percent rallies can happen fast these days.

The stomach-turning summer is a bad memory. Europe appears to be getting its act together, last summer’s downgrade of the U.S.’ credit rating was quickly forgotten, Washington is mostly behaving, and recession fears are gone.

“There are signs that the economy is getting back on its feet and the market is reacting to that,” says John Prestbo, executive director of Dow Jones Indexes. “The mood is just better in this country than it has been for a while.”

On Wall Street, too. The Dow traded Tuesday at 12,878, a 21 percent rally from Oct. 3, its low point for last year. In January, the average rose more or less in a straight line and added 3.4 percent, its best start to a year since 1997.

From here, the record is tantalizingly close — 14,164.53, reached Oct. 9, 2007, when the investment houses Bear Stearns and Lehman Brothers still existed and the unemployment rate was 4.7 percent.

A 10 percent surge may seem like a lot, but it’s really not. The Dow has gained almost 15 percent since Nov. 25, just 10 weeks ago.