Every branch of science has at some point been confronted by a daunting question that stumps progress for years, even decades. How did the continents form? What causes fever? Is there intelligent life beyond Earth? Solutions may accrue incrementally or arrive in a flash of inspiration. Sometimes it seems they are destined never to come at all. Here are four disciplines in need of a modern-day Einstein.

WHERE WE ARE NOW In 1998 astronomers discovered that the universe is expanding ever faster over time, driven by a mysterious force they dubbed dark energy. Is dark energy the result of countless virtual particles being created and destroyed in empty space? Will it eventually rip spacetime apart, or might it wither away? Physicists have no clue.

Calculations show that empty space should bubble with virtual particles, theoretical objects that produce so much energy that they should have blown the universe apart long ago. Since this hasn’t happened, theorists had figured that the energy of some of those particles must perfectly cancel the energy of the rest, leaving space as calm as flat soda. Yet observations, based on the brightness of distant exploding stars, show levels of dark energy that are tiny but not zero. If the virtual particles thought to inhabit space are truly the source of dark energy, it’s a conundrum: They should produce either huge amounts of dark energy or none at all. “We really, totally are in the dark,” says theoretical physicist Lawrence Krauss of Case Western Reserve University.

Explain what dark energy is.

The so-called anthropic principle holds that different parts of the universe each have dark energy of a particular strength and that we just happen to live in, and hence observe, a part of the universe with a low level of dark energy. If that sounds like a cop-out to you, you’re not alone. The anthropic principle makes no predictions, Krauss says, and thus goes against the grain of four centuries of physics, during which theories have ultimately won out or lost based on how their predictions matched the world. To build support for the anthropic principle, physicists must show that dark energy could take on different values and then calculate the odds that it would have the value that astronomers measure.

WHERE WE ARE NOW Experts have identified most of the genes in the strands of DNA curled inside our cells, but between those genes are long, apparently nonsensical stretches known as “junk DNA.” This wilderness makes up as much as 98.5 percent of the human genome. But recently, as the intricacies of gene functioning have become clear, geneticists have begun to wonder whether junk DNA might have some subtle purpose, such as influencing when genes are turned on and off.

Last May a team at the University of California at Santa Cruz found that humans and rodents share nearly 500 identical sequences of junk DNA. If that DNA were truly useless, it should have become garbled by random mutations over evolutionary time. Many of the conserved sequences cluster near genes that are crucial for embryonic development, and others may be causing nearby genes to ramp up protein production. A few hundred sequences are just a drop in the junk-DNA bucket, though. “It’s frustrating because there’s so much of it, and there seems to be at least some that’s fairly tightly conserved between species,” says Alan Guttmacher, deputy director of the National Human Genome Research Institute. “It’s an attractive target to try and understand.”

Find out what junk DNA does, or ascertain that it is useless.

The National Human Genome Research Institute’s new project, Encode, will probe junk DNA’s possible functions-in part by comparing the genomes of various mammals to reconstruct their evolutionary history.

WHERE WE ARE NOW Current simulations of the global climate break the world into a grid and ask how the temperature, wind and moisture of each square on the grid affects its neighbors. These simulations ably predict the activity of big atmospheric features, such as jet streams, but they fumble when it comes to finer details, such as the formation and behavior of clouds. That’s an important omission, because clouds both reflect light and trap heat, so they could add to or diminish global warming.

The updrafts of air that form clouds are only hundreds of meters across, whereas the smallest units of climate models are some 200 kilometers wide. Calculating interactions among smaller units requires more power than today’s computers possess. Climate experts expect to have the computer power to solve the cloud problem in a few decades, but they want answers now. “It’s the single largest uncertainty in predicting climate change,” says Chris Bretherton of the University of Washington.

Model clouds more accurately.

Though as yet untested, simulations of life-size clouds dotting an Earth that’s one tenth its true dimensions promise to yield realistic climate data. Such models require one thousandth the computing power of a full-scale model of global cloud cover, says Bretherton, who took part in the research. “That brings the cost down to something we can do with a powerful university computer.”

WHERE WE ARE NOW Scientists know how memories form: When something noteworthy happens, certain brain cells branch out and connect to one another. If the event is intense and long-lasting enough, the connections, called synapses, become durable. If not, the memory is lost (which explains why an inopportune interruption will keep you from memorizing a phone number). From there, though, things get more mysterious.

Recent work by neuroscientist Karel Svoboda of Cold Spring Harbor Laboratory in New York reveals that 40 percent of the synapses in a mouse’s brain change over the course of a few weeks. Still, the mouse retains earlier memories-but scientists don’t know how. Perhaps memories migrate to new groups of brain cells or become stored in some more efficient way. “How can we have a memory that lasts for years when the underlying synapses are no longer there?” ponders Karim Nader, a neurobiologist at McGill University. “I’ve got no clue.”

Learn how memories are stored.

Observe brain cells’ changing connections in living animals. One new technique is to manipulate a mouse’s genes so that its brain cells produce a green fluorescent protein when they’re active. Peering through a microscope, investigators will then be able to track changes in brain cells and synapses as the animal uses its memory, simply by following the green signal.