The isosceles theorem put forward by the Greek mathematician Euclid became a test in medieval times of one's ability to master more difficult matters. Greece this week faces such a test.

It must convince the European Union, the International Monetary Fund and the European Central Bank of three things: fiscal measures will put its debt load onto a sustainable path heading toward 120 percent of gross domestic product by 2020; Greek politicians will abide by deep budget cuts even after their April elections; and a 200 billion euro debt swap with private creditors can be completed by March 20, the deadline for Greece to make 14.5 billion euros in debt payments.

Only if Athens meets these tests will Greece win a second round of international loans from the EU and IMF to avert a disorderly default, financial officials say. A decision is expected on Monday when euro zone finance ministers meet.

Clearing this hurdle would open the way for Greece to take on the still more difficult task of restructuring its economy - far beyond the initial steps it has taken so far.

The urgency is painfully evident. The latest data shows its economy in a freefall. GDP contracted at annual pace of 7 percent in the fourth quarter. Economists forecast a similar plunge in 2012. Unemployment is 21 percent and half of its young people under 25 are out of work.

Richard Parker, professor of public policy at Harvard University and an adviser to the Greek government until December, said Greece has to reform its family-based business and retail sectors and overhaul its wage and cost structure to make its primary industries, tourism and shipping, internationally competitive - a process that can often take decades.

"Because there is not a growth plan - austerity is not a growth plan - Greece faces a long, dark path," he said.

While Greece might avert a March default, its economy is unraveling so fast that new funds may only delay its collapse by a few months, Wall Street analysts said. Northern European politicians are equally skeptical.

Germany's finance minister, Wolfgang Schaeuble, calls Greece a "bottomless pit." Greeks angered by German demands are burning effigies of Chancellor Angela Merkel in Nazi uniform.

"Political tensions in Greece, and between Greece and the rest of Europe, may have reached a point of no return," said Erik Nielsen, global chief economist at Unicredit.

"Short of a big pro-reform, pro-Europe vote at the Greek election in April, the program may run off track within months, which could well cause Greece to start an unintentional and messy exit from the euro zone," he warned clients.

CENTRAL BANKS TO THE BARRICADES

In the meantime, major central banks are taking no chances, given a tentative global economic recovery.

Although the U.S. economy has shown signs of strength recently, with surprising improvement in the labor market, Europe is still seen flirting with recession after the euro zone economy contracted in the fourth quarter.

Some central banks have quietly unleashed a fresh flood of money in recent weeks.

The ECB has pumped half a trillion euros of three-year ultra-cheap money into its banks with more to come on February 29. The Bank of Japan and Bank of England are printing fresh money with new bond-buying programs, and Sweden's Riksbank surprised with an interest rate cut last week. And last month the U.S. Federal Reserve extended until late 2014 its pledge to keep rates ultra low.

James Rickards, an investment banker at Omnis, called the latest central bank measures a risky inflation strategy "to scare us into spending." Neal Soss, chief economist at Credit Suisse, sees them as a wise investment to secure a vulnerable upswing.

"The massive expansion of central bank liquidity should better prevent and insulate the real economy from financial shocks. If that's the case, the current upswing in cyclical momentum may prove more sustained than previous speed-ups," Soss said.

G20 BUILDS FIREWALLS

Central banks are not alone in bolstering the defenses against the risk of an eventual Greek default.

When financial policymakers from the Group of 20 major advanced and developing economies meet in Mexico City next Saturday and Sunday, they will discuss an IMF request to build up its war chest.

The international firefighter wants an extra $600 billion to handle any further sovereign crises, a risk that would mount should Greece abandon the euro. The United States is unwilling to chip in, so the IMF is looking to emerging economies with current account surpluses, notably China and the Gulf states.

China has said repeatedly it will not give money before Europe has dealt with its problems, a way of piling pressure on Europe to enlarge the European Stability Mechanism, the 500 billion euro emergency fund designed to backstop troubled countries and banks.

Once these funds are in place, the IMF and the EU would be better equipped to cope with any financial firestorm spreading from Europe's southern perimeter.

Given the enormity of the tasks ahead, no wonder mastering Euclid's isosceles theorem in medieval times was called crossing the bridge of fools.