Of course, by this, we could only mean financial models. Frankly, we thought the wizardry of our advanced market tools was supposed to protect us humans from, well, ourselves. And while we’re glad to say it turns out we were right in that rather humble assumption, it doesn’t seem we properly anticipated the equipment being superior to the operator. (Ahem, the operators, in this case, being us.) The take-away from some of the world’s brightest minds on why the very departments designed to minimize risk somehow fouled up.

Today’s economic turmoil, it seems, is an implicit indictment of the arcane field of financial engineering — a blend of mathematics, statistics and computing. Its practitioners devised not only the exotic, mortgage-backed securities that proved so troublesome, but also the mathematical models of risk that suggested these securities were safe.

What happened?

The models, according to finance experts and economists, did fail to keep pace with the explosive growth in complex securities, the resulting intricate web of risk and the dimensions of the danger.

But the larger failure, they say, was human — in how the risk models were applied, understood and managed. Some respected quantitative finance analysts, or quants, as financial engineers are known, had begun pointing to warning signs years ago. But while markets were booming, the incentives on Wall Street were to keep chasing profits by trading more and more sophisticated securities, piling on more debt and making larger and larger bets.

“Innovation can be a dangerous game,” said Andrew W. Lo, an economist and professor of finance at the Sloan School of Management of the Massachusetts Institute of Technology. “The technology got ahead of our ability to use it in responsible ways.”

That out-of-control innovation is reflected in the growth of securities intended to spread risk widely through the use of financial instruments called derivatives. Credit-default swaps, for example, were originally created to insure blue-chip bond investors against the risk of default. In recent years, these swap contracts have been used to insure all manner of instruments, including pools of subprime mortgage securities.

These swaps are contracts between two investors — typically banks, hedge funds and other institutions — and they are not traded on exchanges. The face value of the credit-default market has soared to an estimated $55 trillion.

Credit-default swaps, though intended to spread risk, have magnified the financial crisis because the market is unregulated, obscure and brimming with counterparty risk (that is, the risk that one embattled bank or firm will not be able to meet its payment obligations, and that trading with it will seize up).

The market for credit-default swaps has been at the center of the recent Wall Street banking failures and rescues, and these instruments embody the kinds of risks not easily captured in math formulas.

“Complexity, transparency, liquidity and leverage have all played a huge role in this crisis,” said Leslie Rahl, president of Capital Market Risk Advisors, a risk-management consulting firm. “And these are things that are not generally modeled as a quantifiable risk.”

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