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"The Maternal Capacitance" (mentioned)
Michael Hofstadter is the younger brother of Leonard and Hayley Hofstadter. He is a tenured law professor at Harvard University. His mother, Beverly, mentioned him to Howard Wolowitz when she visited ("The Maternal Capacitance"). She describes him as being more successful than Leonard.
Leonard has said that Michael is eight inches taller than him because of the nurturing and attention he received from their mother.
When Leonard was young he had to give back a ribbon he won for an experiment seeing if Lima beans grew better with classical music. His mother pointed out his younger brother Michael did a Lima beans growing worse with rock ‘n’ roll music experiment already.
In "The Spock Resonance", Leonard reveals that Michael was mean to him.