
Mummy Holmes
One of the biggest areas of contention in the Sherlock fandom is the character of Mummy Holmes. Who is this woman who raised not one, but two genius sons? The oddness of their personalities, and the uniqueness of their separate forms of genius imply that they came from a very strange, severe, and possibly even an abusive family background, yet when we see Mummy Holmes she is unremarkable, ordinary even.
Up until season three, she was only alluded to as in this exchange between Sherlock and Mycroft in A Study in Pink.
Mycroft: "This petty feud between us is simply childish. People will suffer. And you know how it always upset Mummy"
Sherlock: "I upset her? Me? It wasn't me that upset her, Mycroft."
It isn't until season three that we see her. She is sitting in Sherlock's sitting room rattling on about his father losing his glasses down the back of the couch. Mummy Holmes is introduced as a chatty character, almost silly. When John mentions how ordinary Sherlock's parents are, he replies that it is a cross that he has to bear.
Sherlock obediently listens to her, but finds a way to get rid of her as soon as possible. He kicks her out when John arrives, but then she places a foot in the door and refuses to leave until she gets him to promise that he will call. This suggest that she is not a complete pushover. Mummy is clearly shown as the dominant parent in the family. Their father mostly smiles and echoes back the words that she says.

Sherlock and Mycroft clearly have issues with their parents ordinariness, as evidenced by their dislike for spending time with them. See the phone call about Les Miserables (a telling name) being like torture when spent with their parents, as well as Mycroft's mocking comments about Sherlock's drug problems disturbing his parent's line dancing.
In The sign of three, Sherlock states that his mother "Understands very little." And that he and Mycroft have enough issues with her to elicit separate lists of her problems.
"I have a list. Mycroft has a file."
Many in the fandom felt that the sheer ordinariness of Mummy Holmes was offensive. It was as if they were using Sherlock and Mycroft's parents as a joke. There were references to the show Frasier where, as I understand it, the children had aspirations above their parents. These parents couldn't possibly raise these children, they say, and point instead to a host of fanfics which explain away Sherlock's asexuality and Mycroft's overprotectiveness with absentee parents. Mummy Holmes as portrayed is said to be just too weak to raise Sherlock, much less Mycroft.
In The Last Vow, the Holmes are shown having a typical Christmas Dinner with the Watsons, as any normal family might do. There are facts which suggest that this is not at all typical, however. For one thing, Mycroft disrupts this cosy domestic scene exclaiming "Why are we doing this? We never do this." Which is supported by our previous view of a Holmes Christmas night when Mycroft and Sherlock meet at the morgue to view Irene Adler's body. They imply that other than a phone call, they typically had no family celebrations on that date. At least not as adults. 1
We learn, in this episode, that Sherlock's mother left a career in Mathematics to raise her sons. We also learn that she is a genius. All of these facts combine make for a contradiction of a person. How can Mummy Holmes be both a loving mother of two genius sons, someone that they compete to please, and yet someone they both greatly resent? The most likely explanation is that the writers changed her character as they went along, but assuming that the character makes sense. What is Mummy Holmes really like?
No Shy Violet
Evidence is that Mummy Holmes is no shrinking violet. When Sherlock tried to push his parents out of the flat, she stopped him with a foot in the door. This is not the act of a passive person. Mummy Holmes is no Mrs Hudson. She is clearly mistress of her own household, and her boys tow the line around her, as evidenced by the time when she finds them smoking and gives them a stern look.

Despite all of their talk, she is still their Mummy and they do try to please her. So how do we reconcile these vastly disparate images of the woman who raised the two most brilliant men of their generation? Here is my theory.
Mummy Holmes' Guide to Childrearing
I was listening to the Philosophize This podcast on Plato, when Steven West described Plato's views on government. Here is my summary of what he said.
Plato's Utopia of the Aristocracy:
A just city and a well working human being have three parts.
1. The appetite (desire for sex or money) - represented by the producers or workers
2. The spirit (wants honor or notoriety) - comparable to the guardians - The police and the nobles
3. The rational (desires knowledge) - e.g. The ruling classes
A good ruler must be raised perfectly. He must be taught not to value appetite or notoriety above knowledge. He should not let his desire for food, sex, fame, or glory overtake him, but he should make decisions based on reason. He would be trained to see the world the way it is. To value truth. He would be exposed only to stories that would teach him the correct values. According to Plato, this is the way to make the best rulers.
Sherlock's mother was a mathematician. In academia, mathematicians are believed to be the most abstract thinkers. If anyone would look to Plato for guidance in raising her sons, it would be a mathematician like Mummy Holmes. Imagine that she decided to raise her sons as philosopher kings. Mycroft himself described Sherlock this way.
"He has the mind of a philosopher or a scientist. What does that say about his heart?"
Evidence in support of Platonic Childrearing:
1. Mycroft says, "We both thought you were an idiot, that is until we met other children."
Children in Britain go to school at four or five. In canon, Mycroft Holmes is seven years older than his brother. How could he not have met other children?
Perhaps Mummy Holmes found a way to keep him home when he was young to make sure that he was not unduly influenced by others. This suggests that rather than an absentee parent, she was perhaps a bit overprotective of both her sons. This is supported by the heavy-handed way that Mycroft looks after his brother. Perhaps he learned such techniques at his mother's knee, so to speak.
2. Sherlock knows nothing about popular culture, movies, or TV.
This suggests his exposure to popular culture was severely restricted in youth. John is the one who introduced him to trash TV.
3. Sherlock and Mycroft greatly value rational thought.
This is obvious. Even their childhood game of deduction is a competition to see who can be the most clever.
4. Both Sherlock and Mycroft deny their appetites.
Sherlock lives the life of the ascetic. He rarely eats. He does not engage in sex or desire power or luxury, yet he has money to buy very expensive clothes. He wears the best, but his cuts are modest and conservative. Other than his coat, he is not proud or showy in his dress like Moriarty.
When Sherlock chides Mycroft, what does he chide him on? His appetite,and later we see Mycroft exercising even though his weight is not extreme.
What does Mycroft chide Sherlock on? His compassion and desire for affection. (Caring is not an advantage). Neither if them are married. Neither of them even date. And when their mother visits, she does not mention that fact. (A bit strange for someone who is the right age to be a grandmother.)
5. A respect for order and government
This is most obvious in Mycroft who is described by the phrase, "He is the British government."
Sherlock is less respectful of the laws of society, but he works inside the system with the police, unlike Moriarty who is a law unto himself, and an agent of chaos and anarcy.
6. They share a belief in truth.
If there is anything that defines Sherlock Holmes, it is his unearing belief in the power of the rational mind to explain the world. Sherlock's job as a detective is all about finding out the truth about a crime. Mycroft's back room dealings imply an understanding of the real avenues of power, as opposed to the appearances. Neither of them is afraid to call out the other if they attempt to lie.
What better legacy could a mathematician give her children than the power to see past the lies of society and find the truth.In my opinion, Mummy Holmes will always be a woman who believed in great ideals and enforced them on her children to create the exceptional adults that they have become.
1. Christmas as a family get together is both refuted and supported by the story. Mycroft did say, "You can imagine the Christmas dinners." And Sherlock says twice, "Oh, It's Christmas!" implying that Sherlock associates Christmas with having fun, although fun for Sherlock may not be the same as it is for most people.