An American scientist won the 1982 Nobel Prize in physics yesterday for a mathematical theory explaining the odd changes in the behavior of materials at high temperature and pressure. The prize for chemistry was won by a scientist in Britain who developed a method of deciphering the shapes of many biologically important molecules.

The American physicist is Kenneth Geddes Wilson, 46, of Cornell University, whose work is theoretical, but may be useful in studies as varied as the work on quarks, the building blocks of atoms, the study of weather and hurricanes, and the mixing of metals.

The scientist working in Britain is a native South African, Aaron Klug, 56, who has worked for the past two decades at the Medical Research Council, Britain's equivalent of America's National Institutes of Health. The awards committee of the Royal Swedish Academy of Sciences said his work might one day be crucial in the fight against cancer.

Wilson is the 46th American to be awarded the Nobel Prize and the only American to win a Nobel Prize in the sciences this year. The prize, first awarded in 1901, is named after Alfred B. Nobel, who invented dynamite.

Wilson developed a mathematical theory that allows physicists to predict the behavior of matter when it reaches "critical points" of temperature or pressure, such as the point at which a liquid turns to a gas, or a magnetic bar loses its magnetism.

Wilson built a simplified mathematical theory to describe what happens to matter when it reaches the point of changing into a new state, solid to liquid, liquid to gas, and so on.

He discovered that it is not necessary to calculate the behavior of matter in great detail to predict its behavior when it approaches the critical transition point.

Using only two critical numbers about the shape and the one-, two-, or three-dimensional nature of the matter, Wilson was able to calculate curves that describe, for example, how the density of a hot liquid will fluctuate as its temperature rises toward the critical temperature at which it becomes vapor.

"Wilson succeeded in an ingenious way to solve the problem. Instead of a frontal attack, he developed a method to divide the problem into a sequence of simpler problems in which each part could be solved," the Swedish science academy said in its announcement.

Wilson's mathematical method is so broad and powerful that it may be possible to apply it to things as different as the behavior of infinitesimal particles like the quark, the level of air turbulence around an airplane, and the way metals mix.

Wilson published his theory in two papers in 1971 and 1972, the second coauthored with Michael Fisher of Cornell.

Eight or more physicists contributed background work to the development of the theory, including Fisher of Cornell and Leo Kadanoff of the University of Chicago, but as the Swedish science academy said when it announced the award, Wilson took a different approach and solved the 100-year-old problem "in a definite and profound way."

The other workers had only bits of a theory that did not allow specific predictions to be made, but Wilson came up with a complete theory that allowed prediction and simplified the whole subject.

Wilson said he was "very surprised" to get the award, "and especially so that I'm getting the prize alone." He said he would have expected to share the award with Fisher and Kadanoff at the University of Chicago. The three shared Israel's Wolf Prize in Physics several years ago, he said.

In Chicago, Kadanoff said, "He did magnificent work. He's very, very deserving of it. I couldn't be more pleased."

At Cornell, Fisher said, "That was a very nice thing for him to say. I'm delighted he got the prize. His contribution to theoretical physics has been outstanding."

The announcement that Wilson had won the Nobel was almost expected by his family and friends, according to his father, E. Bright Wilson, a retired professor of physical chemistry at Harvard University.

Wilson is the oldest of six children. All went on to careers in academics or science. His younger brother, David, is a biochemist on the Cornell faculty. A sister grew up to be an economist, while another brother runs his own electronics firm.

In chemistry, Aaron Klug discovered a method of figuring out the shape of molecules important to life. The shape of molecules determines what they do and how they do it; for example, the hemoglobin molecule has a "pocket" in which it can capture an oxygen atom to be carried through the bloodstream.

When trying to discover the shape of important molecules, researchers often crystallize them and pass X-rays through them to study the scatter pattern of the X-rays. The pattern gave a clue to the three-dimensional shape of the molecules.

But many molecules resist being crystallized, and so their shape could not be determined.

Klug opened up a new branch in the study of molecule shapes by using an electron microscope to take pictures of the molecules as they lay in a thin, two-dimensional crystal film, and then extracting three-dimensional images from that.

A picture of a molecule taken by an electron microscope is fuzzy and blurred. But Klug managed through mathematical methods to extract three-dimensional pictures of the molecules from the two-dimensional image.

"It is like taking a thousand blurred pictures of a face, and extracting from them enough information to make one clear image," said Carl Pabo of Johns Hopkins University.

In addition to developing this method, Klug has been a key researcher in determining the structures of a number of important biological molecules, including the structures that hold in place a cell's DNA, or deoxyribonucleic acid, which is the basic material in the chromosomes of the cell nucleus.

Knowledge of these structures is important in controlling the normal functions of the cell, and also in understanding what goes wrong when a disease like cancer strikes a cell.

Klug has worked 20 years for the Medical Research Council at Cambridge University's molecular laboratory and has headed its division of structural studies since 1978.

Each prize brings its recipient the equivalent of $157,000.

Klug is a naturalized Briton who was born in Johannesburg, South Africa, but has been working for the past 20 years in Cambridge.

News services reached him at his laboratory yesterday, and Klug told them he was surprised by suggestions a Nobel Prize might affect his future work. "My future work?" he said. "I shall continue, of course. These problems are never ended."

Klug said he "was delighted" by the award, "and somewhat surprised because the kind of work I do is not spectacular. It's by no means glamorous work but it has to be done and I'm very pleased it has been recognized in this way."