K. Alex Müller was born on April 20, 1927, in Basle, Switzerland. His family was fairly wealthy (his grandfather founded a chocolate company) and could afford to entertain Müller's teen-aged interests in radio and electronics. The first years of his life were spent with his parents in Salzburg, Austria, where his father studied music. He and his mother later moved to Dornach, near his birthplace, to the home of his grandparents; and from there they moved to Lugano, the Italian-speaking part of Switzerland. Müller soon became bilingual. When his mother, Irma, died in 1938, Müller was only eleven. He and his father, Paul, lived in the eastern part of Switzerland, in Schiers, where he earned his secondary education at the Evangelical College. He arrived just before the start of World War II and left just after it ended. He assumed he would study electrical engineering after high school, but a high school physics teacher at Evangelical College recognized his talents and encouraged him to pursue physics instead. After completing his military service in the Swiss Army, he entered the Physics and Mathematics Department of the Swiss Federal Institute of Technology (ETH) in Zurich. He seriously considered changing to electrical engineering but was talked out of it. He received his doctorate in 1958.

From 1959 to 1963 Müller worked for the Battelle Memorial Institute in Geneva and was a lecturer at the University of Geneva where he was given the title of professor in 1970. In 1963 he became a research staff member at the IBM Zurich Research Laboratory, Ruschlikon. He spent the next 15 years investigating the properties of perovskites— compounds consisting of two different metal atoms and three oxygen atoms. His work enhanced his reputation and he took over as head of the laboratory's physics department in 1972. He was appointed an IBM fellow in 1982, allowing him the freedom to work on whatever projects he wished. During an 18-month sabbatical in the United States ending in 1980, Müller started working in the field in which he was to become famous, solid-state physics and superconductivity. He became particularly interested in a class of compounds known as ceramics: glass-like compounds of oxygen and at least one metallic element.

Some metals, as well as a fair number of compounds, show a dramatic change in the way they conduct electricity when they are cooled to very low temperatures. These materials in fact lose all resistance to the flow of electricity if they are cooled to a low enough temperature. Discovered in 1911, the phenomena of superconductivity had occupied the labors of physicists for decades. However, little progress was made in discovering a material that would superconduct at a temperature above 23 K (23 degrees above absolute zero, or 250 degrees below zero on the Centigrade scale). Such cold temperatures make practical applications of superconductivity difficult to implement.

Müller was convinced that higher temperature super-conductors could be discovered but the trick was to figure out which materials to test. Although the perovskites that he had been working with for years normally did not conduct electricity well, he reasoned that they could be induced to superconduct by varying the composition of the perovskites. In addition, a few other similar compounds had demonstrated superconductivity, but all these compounds began to superconduct at temperatures far below the record high of 23 K. Müller thought that perovskites containing the element nickel might superconduct at higher temperatures. In mid-summer 1983 he enlisted the aid of J. Georg Bednorz, a former student and now his colleague at IBM, in preparing samples of the compounds. The relationship Müller and Bednorz had was one of opposites attracting. Müller, called "a visionary theoretician, a bright, irascible Swiss physicist who liked to work alone at home," complemented his German counterpart, who was a skilled researcher and enjoyed spending long hours at the laboratory. Bednorz worked in his spare time and in the evenings making sample after sample, slightly altering the ratios of the elements in each sample. No sign of superconductivity was found in any of the samples. The project almost ended, partly because the equipment used for the measurements of conductivity was borrowed from another team, which meant that Bednorz could test for superconductivity only in the evening. The equipment was also out of date. In late 1985 colleagues at IBM agreed to let Bednorz use new automatic equipment during normal working hours.

At this time they switched from nickel-containing samples to ones that contained copper. Soon after, Bednorz read about the work of a team of French physicists who reported that a perovskite-type compound consisting of barium (Ba), lanthanum (La), copper (Cu), and Oxygen (O) showed metallic-like electrical conductivity at room temperature. In January 1986 Bednorz began preparing samples of the Ba-La-Cu oxide, altering the ratios of the various elements in each sample. The samples showed superconductivity occurring at 35 K, shattering the old record by contemporary standards.

Müller knew that there had been many unsupported claims for superconductivity at "high" temperatures (35 K is high in this context). Many more tests were done to make sure that the results were correct. By the spring of 1986 they were confident of their result, but they did not have the equipment necessary to test the magnetic properties of their sample, which would demonstrate beyond question that their compound was superconducting. They decided to publish their results anyway using the cautionary title "Possible High [Transition Temperature] Superconductivity in the Ba-La-Cu-O System." Their article appeared in September 1986, the same month they were able to confirm the sample's magnetic properties. By November two teams of physicists confirmed that their sample became superconducting at 35 K. After presenting these findings at the Materials Research Society meeting in Boston on December 5, 1986, the world was aware that the Müller-Bednorz 2-1-4 structure (so called due to the arrangement of the perovskite-like crystal arrangement) was the superconductor. Müller and Bednorz had also begun work on a 1-2-3 compound of yttrium, barium, and copper oxide, which also proved to be a superconductor.

Their discovery, while at first met with skepticism, ignited a flurry of research into similar compounds. Physicists realized that this new class of superconducting compounds brought them a step closer to large-scale practical applications, which had been their dream since 1911. With such impressive developments, a special session on the new superconductors took place in March of 1987 at the meeting of the American Physical Society in New York. The session became historic because of the unprecedented numbers of those attending. Therefore, it has often been referred to as the "Woodstock of physics." Their findings of superconductivity at higher temperatures were phenomenal and their achievement spread rapidly among physicists and the world. Other experiments continued to confirm their results. Müller and Bednorz were awarded the Nobel Prize in October 1987 for their discovery of new superconducting materials.

After his Nobel Prize, Müller continued to work on superconductivity ceramics at his IBM lab. In addition to his Nobel Prize, Müller was also awarded the Marcel-Benoist Prize (1986), the Thirteenth Fritz London Memorial Award, the Dannie Heineman Prize, the Robert Wichard Pohl Prize of the German Physical Society (1987), the Hewlett-Packard Europhysics Prize, the American Physical Society International Prize for New Materials Research, the Minnie Rosen Award (1988), and the Special Tsukuba Award (1989). He earned honorary degrees from the University of Geneva, Switzerland, the Technical University of Munich, Germany, and Universita degli Studi di Pavia, Italy (1987); University of Leuven, Belgium, Boston University, USA, Tel Aviv, University, Israel, and the Technical University of Darmstadt, Germany (1988); University of Nice, France, and Universida Politecnica, Madrid, Spain (1989); and the University of Bochum, Germany and Universita degli Studi di Roma, Italy (1990). He was elected as a Foreign Associate Member of the Academy of Sciences in the United States in 1989. Müller married Ingeborg Marie Louise Winkler in 1956. They have two children: Eric, a dentist, and Silvia, a kindergarten teacher.