His grandfather Alvarez was born in Spain but ran away to Cuba, and later made a fortune in Los Angeles real estate before moving to Hawaii and then to San Francisco. Luis' mother's family, originally from Ireland, established a missionary school in Foochow, China. Alvarez's parents met while studying at the University of California at Berkeley.
Alvarez attended grammar school in San Francisco and enrolled in the city's Polytechnic High School, where he avidly studied science. When his father accepted a position at the prestigious Mayo Clinic, the family moved to Rochester, Minnesota. Alvarez reported in his autobiography Alvarez: Adventures of a Physicist, that his science classes at Rochester High School were "adequately taught [but] not very interesting." Dr. Alvarez noticed his son's growing interest in physics and hired one of the Mayo Clinic's machinists to give Luis private lessons on weekends. Alvarez enrolled at the University of Chicago in 1928 and planned to major in chemistry. He was especially interested in chemistry, but soon came to despise the mandatory chemistry laboratories. Alvarez "discovered" physics in his junior year and enrolled in a laboratory course, "Advanced Experimental Physics: Light" about which he later wrote in his autobiography: "It was love at first sight." He changed his major to physics and received his B.S.
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