Dr. Alfred Hofstadter, Ph.D., is the father of Leonard Hofstadter.
Alfred is an anthropologist, living in New Jersey. He has worked with Dr. Louis Leakey whose surname ends up being his son Leonard's middle name ("The Middle-Earth Paradigm").
Marriage and Parenthood
At some point, Alfred married a woman named Beverly, but it's unknown how they got together. They had three children: Leonard, Michael and an unnamed daughter. The marriage was a loveless one, with Beverly being nothing but cold, emasculating, unaffectionate and distant towards Alfred and unmotherly towards their children. Beverly also ran an unbearably tight ship and seems to have cowed Alfred into following into her footsteps during their marriage. Leonard's relationship with Alfred was obviously a good one, given the latter's friendliness, but it also seemed to have been distant as Alfred would've likely spent a lot of time away from home, working in the field, unless he never worked away from home.
Although much of Leonard's childhood resentment stems from Beverly, Leonard has described how the only father-son time Alfred spent with him was with a 2,000-year-old skeleton of an Etruscan child ("The Fish Guts Displacement"). Leonard's lack of love from his parents as a child, particularly his mother, led him to build a hugging machine at the age of 10, which Alfred used to borrow ("The Maternal Capacitance").
Alfred's marriage to Beverly ended after he had an affair with a waitress from the university cafeteria. Beverly claims that Alfred's reasoning for cheating was that Beverly was "cold, emasculating and hadn't shown him affection for years". There's no love lost between them with Alfred describing Beverly as his "hateful shrew." and her calling him a "wrinkled old bastard." According to Beverly, she and Alfred only had intercourse for the purposes of reproduction, except for a pro forma consummation of their marriage. In 2009, Beverly told Penny that she hadn't had intercourse with Alfred in eight years and had been responsible for her own orgasms since 1982. From Leonard's comments, his father's physical health has improved since his divorce from Beverly.
Alfred first appears when he and Leonard arrive at the apartment building and head up to Apartment 4A. He was curious to when the elevator would be fixed and Leonard said 'Any day, now' and so they took the stairs as everyone had to, which was okay with Alfred since he would prefer to have a heart attack rather than see Beverly. On the way up, he referred to Penny as a sweetie, showing that he seems to have been more supportive and respectful of her relationship with Leonard than Beverly has ever been.
Alfred arrives with Mary at 4A and later attends his son's wedding redo ceremony. They spend the evening talking, but do not have an affair. They do announce that they plan on visiting each other at their homes in the future.
Despite divorcing his ex-wife, Beverly, because of an affair he had, and has his flaws, Alfred is not an awful person, he just had a difficult relationship with her. He is actually a charming, nice, gentle, caring, and intelligent man who cares and is proud of his son Leonard much more than Beverly is. He is a respectful person, referring to Sheldon as 'Dr. Cooper' out of respect for the latter's status.
His kind, friendly, loving and caring nature was also displayed as he and Leonard climb the stairs. Alfred says that Leonard's got a good one there (a good gal) and he asks "How the hell did you do that" which came across as gentle ribbing from Alfred as opposed to dismissiveness when Beverly says the same sort of thing.
Alfred could be sharp-tongued and extremely cynical at times, especially where his ex-wife is concerned: after kindly and politely greeting his companions before Leonard and Penny's wedding, Alfred (without missing a beat) referred to Beverly as 'my hateful shrew', and stating later on that the thought of not having to see her sour face in the morning was enthralling to him. In drastic contrast, he immediately hit it off with Mary Cooper, with whom he bonded over their contempt for Beverly. He showed himself to be rather gentlemanly, stating that despite his own agnosticism he genuinely respected Mary's own, whereas Beverly mirthlessly scorned Christianity to Mary's face.