Kenneth Wilson, the Nobel Prize-winning physicist who pointed the way to a detailed understanding of some of the most familiar phenomena in nature, such as the transformation of water into ice, died June 15 at a nursing home in Saco, Maine. He was 77.

The cause was complications from lymphoma, according to Cornell University, where Wilson taught for most of his career. He was a resident of Gray, Maine.

The 1982 physics Nobel recognized Wilson’s sophisticated explanations for the sudden, significant and widely observed shifts from one state of matter to another. Such changeovers include those between liquid and solid and between vapor and liquid.

In effect, he created a powerful general theory that could be applied to such specific and age-old questions as why ice melts and why water boils. The work also explained lesser-known occurrences such as abrupt changes in matter’s magnetic properties and its ability to conduct electricity.

His areas of research required new mathematical tools that could cope with the moment-by-moment goings-on in an unruly and unseen world of darting, swirling atoms and molecules, all simultaneously pulling and pushing at each other.

Phase transitions occur at the intersection of precise levels of temperature, pressure and volume, known as the critical point. The critical point is a place where different states might coexist in precarious equilibrium, each on the verge of becoming the other.

Wilson’s theories explained in the most minute detail what happened at that point.

Even beyond that success, Wilson was admired for the qualities of mind he showed in achieving it. He was praised for his work in elementary particle physics and for his ability to adapt to phase-transitions research a concept known as the renormalization group. This was a way of eliminating troublesome divergences that showed up in quantum field theory, a major scientific effort to account for the most basic phenomena in the universe.

From 1988 until retiring in 2006, he was a professor at Ohio State University and helped start its Physics Education Research Group. The way he thought about physics — and about how to think about physics — made him influential among colleagues, but he also relished being a bit of a provocateur.

“If your aim is to have an impact on science literacy — in fact, on literacy in all its forms — you need to rivet your attention on the 46 million students in our public schools, not on graduate students in our universities,” Wilson once said. “And you need to understand the challenges confronting K-12 teachers.”

“My view,” he added, “is that in light of the extraordinary demands we make on teachers today, the timeline for teacher preparation ought to be 10 to 20 years.”

Kenneth Geddes Wilson was born Jan. 8, 1936, in Waltham, Mass., and was the oldest of six children. His father, E. Bright Wilson Jr., was a Harvard University chemist who did leading work on the study of molecules through their microwave emissions. His mother, the former Emily Buckingham, did graduate work in physics before her marriage.

Kenneth Wilson once said he spent his time waiting for the school bus figuring out cube roots. His father brought him books on mathematics and physics; he skipped several grades and said he found high school “dull.”

At Harvard, he was twice among the top five in the country in the annual Putnam Prize mathematical competition. He was a track star as well, and a champion college miler.

He completed his undergraduate studies in 1956, then did graduate work at the California Institute of Technology. Despite his demonstrated mathematical prowess, he chose physics as the subject of his studies. “It was connected to the real world,” he explained.

At Caltech, he worked with Nobel laureates including Murray Gell-Mann and began an involvement with the study of elementary particles and with quantum field theory that led to his interest in renormalization and to his Nobel work.

He received his doctorate in 1961 and began working at the Swiss-based CERN, the European nuclear research center. Two years later, was recruited to the physics faculty at Cornell University in Ithaca, N.Y.

“I accepted the offer because Cornell was a good university, was out in the country and was reputed to have a good folk dancing group, folk-dancing being a hobby I had taken up as a graduate student,” he wrote in a biographical statement when he received the Nobel.

He was an early user of computers, which attracted him by their promise of coping quickly with the vast number of equations generated by many molecules influencing each other during phase transitions.

Wilson is survived by wife Alison A. Brown; brother David Wilson, a professor of molecular biology at Cornell; sister Nina Cornell; half-sister Anne Goldizen; half-brothers Steven and Paul Wilson; and stepmother Thérèse Wilson.

Wilson was known for his eagerness to avail himself of the power of computers, and he was an advocate for creation of supercomputer centers in the United States. In the 1980s, he also pushed the National Science Foundation to get the supercomputers connected by innovative technologies that became the Internet.

In an interview once, he was asked where the inspiration came from for a key research step.

“From my utter astonishment at the capabilities of the Hewlett-Packard pocket calculator,” he said.

He continued: “I buy this thing and I can’t take my eyes off it, and I have to figure out something that I can actually do that would somehow enable me to have fun with this calculator.”