Michael Hofstadter is the younger brother of Leonard Hofstadter and their sister. 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.
In "The Pants Alternative", it is revealed that 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.
He was mentioned by Beverly in "The Explosion Implosion" that of all of her children's spouses, Penny was her favorite. This implies that Michael is now married, obviously to the New Jersey judge.
In "The Celebration Reverberation", he sends Leonard his Christmas letter and telling about all his accomplishments, including building a hospital in Rwanda. This causes Leonard to spiral about his own lack of accomplishments.