In 1967, the nuclear strategist Herman Kahn—one of the inspirations for Dr. Strangelove—coedited a volume called The Year 2000. Kahn and his collaborators predicted high-speed data processing, the fax machine, and, maybe—just maybe—mobile phones. Not bad as prognostication goes. Then again, they also predicted that the new millennium would bring interplanetary travel, giant supersonic jets, cheap nuclear power, dream-control machines, artificial moons, automated supermarkets, and undersea colonies.

Yes, there has been mind-blowing progress in information technology over the past four decades—in short, the Internet—but that progress may be blinding us to a major innovation slowdown in important scientific and technical areas. The Boeing 747, which first flew commercially just three years after Kahn’s book was published, remains the dominant long-distance plane. Our progress toward a cheap, safe, low-carbon form of energy has been glacial. In 1984, President Reagan’s health secretary promised an HIV vaccine within two years. We’re still waiting.

The reason for this lag, according to economist Tyler Cowen, is that we have burned through all of the relatively easy innovation. The low-hanging fruit has been plucked, as he argues in The Great Stagnation. Making progress in areas such as transportation, energy, and medicine now requires more complex efforts on a much larger scale, efforts that are unlikely to emerge without some smart prodding by government and the private sector.

Fortunately, there are two solid models that have already proven effective at cracking problems and pushing past plateaus. The first approach is for governments to fund large prizes for successful innovations. This is an old idea: The French government used a prize to spur the invention of canned food; the British government established the famous Longitude Prize in 1714. Innovation prizes can provide serious money while preserving a pluralistic, “anyone can try” quality. Everyone assumed the astronomers of the Royal Observatory would find a way for ships to determine their longitude; in fact, the solution came from a village carpenter with a gift for making accurate clocks.

Prizes made a comeback in the ’00s. Their modest scale but outsize success only show how much potential the model has. The Ansari X Prize helped inspire a private flight into space, and now Virgin Galactic is taking orders from space tourists. Netflix used a $1 million reward to upgrade its recommendation engine, while similar statistical challenges are hosted by the website Kaggle. These proofs of concept suggest that huge innovative gains could be made if governments got involved and put billions on the line.

In this era of tighter fiscal belts and diminished objectives, that hasn’t happened—with one ambitious exception: In June 2009, five national governments, along with the Bill & Melinda Gates Foundation, put $1.5 billion into a program that rewards the developers of a new cost-effective vaccine against pneumococcal disease. The result is now being used to protect poor children against this mass killer. And the program’s proponents hope to establish far larger incentives to encourage the development of vaccines for even more-challenging diseases: malaria and HIV.

The second approach to goading innovation is simpler. Research funders such as the National Institutes of Health should set aside a larger chunk of their budgets for highly speculative projects. That is what one private foundation, the Howard Hughes Medical Institute, already does, explicitly seeking projects that are too risky for anyone else to fund, “even if it means uncertainty or the chance of failure.”

Three economists, Pierre Azoulay, Gustavo Manso, and Joshua Graff Zivin, have rigorously evaluated the Hughes approach. They found that once scientists received HHMI funding, they produced more failures—but also far more highly cited “blockbuster” research papers. In other words: more risk, more reward. Yet HHMI research grants, big as they are, are substantially less than one-tenth of 1 percent of global R&D.

But change has begun. NASA and other government agencies are recognizing the power of innovation prizes and starting to introduce relatively small awards. The NIH, meanwhile, is establishing more risk-friendly grants. The past 150 years have made us complacent about how new technologies actually happen. That has to end. Innovation must be painstakingly nurtured and generously funded. With the right tools, it will be.

Tim Harford (@timharford) is a Financial Times columnist. His book Adapt: Why Success Always Starts With Failure was published in May.