Dr. Alfred Hofstadter, Ph.D., is the the father of Leonard Hofstadter, Michael Hofstadter and a daughter and ex-husband of Beverly Hofstadter. He is an anthropologist who once worked with Dr. Louis Leakey.
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.
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.
Not much is known about their relationship, but it is known that they had a troubled marriage and Beverly does mention that they were getting divorced in "The Maternal Congruence" after he cheated on her with a waitress from the Princeton cafeteria. In that same episode she tells Penny that her divorce doesn't affect her too much because she and Alfred haven't had intercourse in 8 years and that she's been responsible for her own orgasm since 1982.
It is revealed in "The Raiders Minimization" that when Leonard was six, he walked in on his parents naked and Beverly was swatting Alfred's bottom with Leonard's brand new ping-pong paddle, and Leonard thought it was a dream until that episode. In her first appearance, she claimed to use sex only for procreation.
In "The Expedition Approximation" when Leonard and Penny go to Howard and Bernadette for advice on how to handle money while being married, Leonard tells Penny that while he grew up, his mother emasculated his father financially, and in every other aspect of his life.
In "The Convergence-Convergence", Beverly is appalled that Leonard invited his father without consulting her, but Leonard retaliates by saying that Leonard doesn't need his mother's permission for his father to be at his wedding. Beverly mentions that Alfred claimed she was cold, emasculating and hadn't showed him any physical affection for years. The two exes come into each other's presence once again in order to attend their son's re-wedding and snipe at each other, including at dinner where Beverly ends up interrupting Alfred's toast to Leonard followed by arguing with each other. Leonard noted that after the divorce his father stopped twitching and seemed to grow an inch and a half.
In "The Conjugal Conjecture", Alfred snapped at his ex-wife until at the wedding ceremony where he said that even though they brought the worse out of each other, the best thing to come out of their relationship was Leonard. Surprisingly Beverly agrees. On the way to the airport the next day, they seemed to be civil to each other for about one minute until they started bickering over Leonard's driving.
Perhaps the most prominent example of Beverly's extreme ignorance is represented by her own husband, Alfred. Though they were both brilliant and accomplished, she showed just as little emotion to him as she did Leonard. Though not seen on screen, it is heavily said that Beverly was cold and unloving towards him and this eventually provoked Alfred into having an affair with another woman, possibly on account of the fact that someone else would give more affection to him than Beverly. What is most noteworthy about this situation is that Beverly was completely incredulous to this and didn't seem to reflect on her own actions after the divorce, believing that their relationship crashed and burned for the sole reason that Alfred had an affair - she verbally stated that Alfred called her cold, emasculating and hadn't shown him any physical affection for years, completely ignorant to the fact that this was a faultless description of herself. In saying this, Beverly showed true emotional rage for the first time in the series, and this rage is purely self-righteous and shows she is unapologetic about how she treated him, not considering that her emasculating and misanthropic behaviour was the reason he'd discarded their relationship.
Not much is known about their relationship, although it is likely that Leonard likes his father more than his mother. Leonard has once referred to him as "Father", but called him "Dad" in the latter's first appearance. In "The Fish Guts Displacement", it appears that he wasn't very affectionate with Leonard since Leonard said that the only father-son time he spent was with a 2000 year-old skeleton of an Etruscan boy who Leonard hated which he had to compete against for his father's favor. He also borrowed Leonard's hugging machine to compensate for the lack of intimacy in his marriage with Beverly. His father worked with noted anthropologist Dr. Louis Leakey which was the source of Leonard's middle name. He does attend the redo of Leonard and Penny's wedding where he fights with his ex-wife and takes an interest in Mary Cooper. During Alfred's first appearance, he and Leonard are seen to get along fine, which shows that Alfred has total love for his son, even when at the restaurant he smiles at Leonard's toast to Penny and at him kissing her and then attempting to give his toast, tells Leonard that he is happy that he found a woman who loves and cares for him.
In "The Conjugal Conjecture", Alfred stood up at the wedding ceremony where he said that even though he and Beverly brought the worse out of each other, the best thing to come out of their relationship was Leonard. He was very proud of his son and daughter-in-law.
In "The Birthday Synchronicity", Leonard says that he has come to peace with his relationship with his parents, likely suggesting that Alfred and Leonard have had a better relationship.
Nothing is currently known about Alfred's relationship with his other two children, but it's likely that he is proud of them the same way he is of Leonard and holds all three of them in high regard.
Alfred is very fond of Penny. He refers to her as a "sweetie" and toasts Leonard by saying that he is happy that Leonard found a woman who loves and cares for him. Penny had not seen him since the divorce before inviting him to their redo ceremony.
It is revealed that before Alfred's first appearance, he had met Sheldon at some point and they meet up again by addressing each other as "Dr. Hofstadter" and "Dr. Cooper", respectively. The relationship between them wasn't seen very further, but it's presumed that they are on very good terms. While Sheldon was still oblivious about the flirting going on between his mother and Alfred, Sheldon says that if he had known that Alfred was broke, he wouldn't have made a big deal about the bread and passes the bread to him, to Alfred's confusion. It's likely that the two could end up becoming stepfather and stepson after it appeared that Sheldon's mother had hooked up with Alfred. In "The Conjugal Conjecture", Sheldon shocked Alfred over his comments about his relationship with Sheldon's mother even asking if they had discussed Alfred's genitals. Sheldon also called him a mediocre academic with the sexual prowess that was subpar (according to Beverly). He compares him to Leonard with a bigger prostate.
Alfred's relationship with Amy hasn't gone so far yet since during their only moment of talking was when Leonard introduced the two to each other, but they are presumably going to be on very good terms. In "The Conjugal Conjecture", sitting with Amy and hearing about her long courtship with Sheldon, he calls her a very patient woman. He pats her on the leg and Sheldon tells him to stop because she was his girlfriend.
The other guys
It is unknown whether Alfred has already met Howard, Raj and Bernadette since they had no chance of sharing scenes with him in his first appearance since the three were unable to make it to Leonard and Penny’s pre-wedding ceremony dinner because Howard was pulled over and being given a sobriety test by a police officer. Alfred has also presumably still not met Emily, Claire or Leslie.
Alfred eventually met Stuart at the 2nd wedding ceremony, who was touched when Alfred and Beverly agreed that having Leonard was one of the best things from their marriage.
Alfred meets Mary Cooper, Sheldon's mother in "The Convergence-Convergence". The two appear to get along really well, as seen in Amy's car where they bond over their mutual dislike of Beverly and express admiration in each other's beliefs and later at the restaurant they clink glasses and later, leave the restaurant for the hotel where their rooms are booked, implying the two could be hooking up. Neither their respective sons nor anyone else can reach either of the two on their phones later that night. In the next episode, they admit to having not slept together, but plan on still see each other. In "The Conjugal Conjecture", it is learned that they only enjoyed each other's company and did not spend the night together, though they do plan on visiting each other in the future.
- Despite being an agnostic, Alfred prayed to God many times to turn Beverly into a pillar of salt. Mary Cooper says that it came close and God had turned Beverly into a giant block of ice.
- While it's said that Alfred was not very affectionate with Leonard during the latter's childhood, the two men get along fine together during Alfred's first appearance. It is therefore unknown how he could be biased and withholding affection from Leonard and his siblings and denying birthdays and Christmas for them if he is a nice, gentle, charming, intelligent and caring man and in the episode "The Cooper-Hofstadter Polarization", Leonard said he could never please his parents. But there are possibilities:
- Beverly likely turned him into someone a bit awful, controlled him and pushed him into doing what she did, but Alfred kept his true nature inside him and secretly had affection for his children, despite the fact that it is currently unknown what Alfred's relationship with Leonard's brother and sister is like, although it's possible he holds them, as well as Leonard, in high regard.
- Because of him being an anthropologist, he may have been working very much that he wasn't able to leave the office to get to know his own children
- Beverly forbade Alfred from showing affection to the kids
- In "The Contractual Obligation Implementation", Leonard says that he supposes he's always been into science since his mother and father are scientists and was kind of led in that direction, or a better word "pushed". But while it seems that Beverly pushed Leonard into science, Alfred would've obviously/likely let Leonard become whatever he would've wanted to be (even if it wasn't a science career or a career related to science), given his charming personality.
- Before his first appearance, Alfred had last met Penny during his divorce which was in Season 3 or later and he had also met Sheldon likely at this point too, while it is unknown whether he had met Howard, Raj and Bernadette, and in his first appearance, he meets Amy for the first time. But it's possible he had already met Howard and Raj back then, given their much-spent time with Leonard, Sheldon and Penny and he meets Stuart and Bernadette for the first time at Leonard and Penny's re-wedding.
- He is one of four fathers of every main character who has physically appeared on the show: the others being Raj's father V. M. Koothrappali, Penny's father Wyatt and Bernadette's father Mike Rostenkowski (Sheldon's father is dead, Howard's left him at 11, Amy's hasn't been seen or mentioned yet, Stuart's is only mentioned, Leslie's hasn't been seen or mentioned and Emily's is only mentioned and possibly dead).
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Green = Appeared, V = Voiced, F = Flashback C = Cameo, M = Mentioned, P = Pictured, Dark Grey = Did not appear, Black = Not aired/Not available