Do pheromones influence human behavior?
Many animals use airborne chemicals to communicate, particularly when mating. Controversial studies have hinted that humans too use pheromones. Identifying them will be key to assessing their sway on our social lives.

How do general anesthetics work?
Scientists are chipping away at the drugs' effects on individual neurons, but understanding how they render us unconscious will be a tougher nut to crack.

What causes schizophrenia?
Researchers are trying to track down genes involved in this disorder. Clues may also come from research on traits schizophrenics share with normal people.

What causes autism?
Many genes probably contribute to this baffling disorder, as well as unknown environmental factors. A biomarker for early diagnosis would help improve existing therapy, but a cure is a distant hope.

To what extent can we stave off Alzheimer's?
A 5- to 10-year delay in this late-onset disease would improve old age for millions. Researchers are determining whether treatments with hormones or antioxidants, or mental and physical exercise, will help.

What is the biological basis of addiction?
Addiction involves the disruption of the brain's reward circuitry. But personality traits such as impulsivity and sensation-seeking also play a part in this complex behavior.

Is morality hardwired into the brain?
That question has long puzzled philosophers; now some neuroscientists think brain imaging will reveal circuits involved in reasoning.

What are the limits of learning by machines?
Computers can already beat the world's best chess players, and they have a wealth of information on the Web to draw on. But abstract reasoning is still beyond any machine.

How much of personality is genetic?
Aspects of personality are influenced by genes; environment modifies the genetic effects. The relative contributions remain under debate.

What is the biological root of sexual orientation?
Much of the "environmental" contribution to homosexuality may occur before birth in the form of prenatal hormones, so answering this question will require more than just the hunt for "gay genes."

Will there ever be a tree of life that systematists can agree on?
Despite better morphological, molecular, and statistical methods, researchers' trees don't agree. Expect greater, but not complete, consensus.

How many species are there on Earth?
Count all the stars in the sky? Impossible. Count all the species on Earth? Ditto. But the biodiversity crisis demands that we try.

What is a species?
A "simple" concept that's been muddied by evolutionary data; a clear definition may be a long time in coming.

Why does lateral transfer occur in so many species and how?
Once considered rare, gene swapping, particularly among microbes, is proving quite common. But why and how genes are so mobile--and the effect on fitness--remains to be determined.

Who was LUCA (the last universal common ancestor)?
Ideas about the origin of the 1.5-billion-year-old "mother" of all complex organisms abound. The continued discovery of primitive microbes, along with comparative genomics, should help resolve life's deep past.

How did flowers evolve?
Darwin called this question an "abominable mystery." Flowers arose in the cycads and conifers, but the details of their evolution remain obscure.

How do plants make cell walls?
Cellulose and pectin walls surround cells, keeping water in and supporting tall trees. The biochemistry holds the secrets to turning its biomass into fuel.

How is plant growth controlled?
Redwoods grow to be hundreds of meters tall, Arctic willows barely 10 centimeters. Understanding the difference could lead to higher-yielding crops.

Why aren't all plants immune to all diseases?
Plants can mount a general immune response, but they also maintain molecular snipers that take out specific pathogens. Plant pathologists are asking why different species, even closely related ones, have different sets of defenders. The answer could result in hardier crops.

What is the basis of variation in stress tolerance in plants?
We need crops that better withstand drought, cold, and other stresses. But there are so many genes involved, in complex interactions, that no one has yet figured out which ones work how.

What caused mass extinctions?
A huge impact did in the dinosaurs, but the search for other catastrophic triggers of extinction has had no luck so far. If more subtle or stealthy culprits are to blame, they will take considerably longer to find.

Can we prevent extinction?
Finding cost-effective and politically feasible ways to save many endangered species requires creative thinking.

Why were some dinosaurs so large?
Dinosaurs reached almost unimaginable sizes, some in less than 20 years. But how did the long-necked sauropods, for instance, eat enough to pack on up to 100 tons without denuding their world?

How will ecosystems respond to global warming?
To anticipate the effects of the intensifying greenhouse, climate modelers will have to focus on regional changes and ecologists on the right combination of environmental changes.

How many kinds of humans coexisted in the recent past, and how did they relate?
The new dwarf human species fossil from Indonesia suggests that at least four kinds of humans thrived in the past 100,000 years. Better dates and additional material will help confirm or revise this picture.

What gave rise to modern human behavior?
Did Homo sapiens acquire abstract thought, language, and art gradually or in a cultural "big bang," which in Europe occurred about 40,000 years ago? Data from Africa, where our species arose, may hold the key to the answer.

What are the roots of human culture?
No animal comes close to having humans' ability to build on previous discoveries and pass the improvements on. What determines those differences could help us understand how human culture evolved.

What are the evolutionary roots of language and music?
Neuroscientists exploring how we speak and make music are just beginning to find clues as to how these prized abilities arose.

What are human races, and how did they develop?
Anthropologists have long argued that race lacks biological reality. But our genetic makeup does vary with geographic origin and as such raises political and ethical as well as scientific questions.

Why do some countries grow and others stagnate?
>From Norway to Nigeria, living standards across countries vary enormously, and they're not becoming more equal.

What impact do large government deficits have on a country's interest rates and economic growth rate?
The United States could provide a test case.

Are political and economic freedom closely tied?
China may provide one answer.

Why has poverty increased and life expectancy declined in sub-Saharan Africa?
Almost all efforts to reduce poverty in sub-Saharan Africa have failed. Figuring out what will work is crucial to alleviating massive human suffering.

The following six mathematics questions are drawn from a list of seven outstanding problems selected by the Clay Mathematics Institute. (The seventh problem is discussed on p. 96.) For more details, go to www.claymath.org/millennium.

Is there a simple test for determining whether an elliptic curve has an infinite number of rational solutions?
Equations of the form y2 = x3  ax  b are powerful mathematical tools. The Birch and Swinnerton-Dyer conjecture tells how to determine how many solutions they have in the realm of rational numbers--information that could solve a host of problems, if the conjecture is true.

Can a Hodge cycle be written as a sum of algebraic cycles?
Two useful mathematical structures arose independently in geometry and in abstract algebra. The Hodge conjecture posits a surprising link between them, but the bridge remains to be built.

Will mathematicians unleash the power of the Navier-Stokes equations?
First written down in the 1840s, the equations hold the keys to understanding both smooth and turbulent flow. To harness them, though, theorists must find out exactly when they work and under what conditions they break down.

Does Poincaré's test identify spheres in four-dimensional space?
You can tie a string around a doughnut, but it will slide right off a sphere. The mathematical principle behind that observation can reliably spot every spherelike object in 3D space. Henri Poincaré conjectured that it should also work in the next dimension up, but no one has proved it yet.

Do mathematically interesting zero-value solutions of the Riemann zeta function all have the form a  bi?
Don't sweat the details. Since the mid-19th century, the "Riemann hypothesis" has been the monster catfish in mathematicians' pond. If true, it will give them a wealth of information about the distribution of prime numbers and other long-standing mysteries.

Does the Standard Model of particle physics rest on solid mathematical foundations?
For almost 50 years, the model has rested on "quantum Yang-Mills theory," which links the behavior of particles to structures found in geometry. The theory is breathtakingly elegant and useful--but no one has proved that it's sound.