Every piece of genre fiction from the last ten years has some variation of the Eccentric Intellectual Male Hero. Fewer pair these traits with a kind heart the way Doctor Who does with the Doctor, but this hyper-intelligent madman trope is everywhere, from superhero movies to action/adventure films to crime and detection television.
You never see this trope applied to women, though. If a woman is intelligent, she is either cold and calculating, or just witty enough to quip with the team of intelligent men on which she is the sole woman. Most importantly, though, she is never, ever eccentric. She is perfect in everything she does, not messy or unpredictable. She is often emotionless, because while emotion equals depth for male characters, it's seen as a weakness in women. She is always mature -- far more mature than her male co-star, for sure. And there is always a male co-star -- someone to ascend to True Hero in the end in a grand display of cleverness.
Now that the Doctor has fifty-five years of characterization as that eccentric intellectual man, though, that is what the Thirteenth Doctor must be. And this time, the Doctor is played by a woman.
A fear for a lot of people heading into this new series of Doctor Who was that the Doctor's oddities might be lessened -- that she might lose her immaturity and imperfections. Luckily, though, the new series currently airing has not abandoned the Doctor's personality. She is just as much the funny, whip-smart madwoman every man before her was. She talks fast in words no one else can understand, moves clumsily and stumbles over social cues, pulls absurd faces while pulling off clever plots and expounding on her love for science and discovery to no one in particular. And she is never doing this to support an all-important male character. Instead, she is the hero -- always the first to run into action, always steps in to protect the men and women on her team, always the most intelligent person in the room and is rarely challenged on that. It's something I've never seen a woman allowed to be onscreen before.
That isn't to say there aren't slips in the way the Doctor has been written in this current series, though. We're nearing the end of series 11 and we still have yet to get a true glimpse of the dark and angry parts of the Doctor's personality, a defining aspect of her previous incarnations' characterization. She has not yet had to make a decision that brought her morals into question, and those moments that should have brought them into question, like her walking away as a man is killed to ensure her companion would exist seventy years later (Demons of the Punjab) or her setting off a room full of bombs knowing the man who put them there would be in the center of the explosion (Kerblam!), were not addressed. She has been selfish and arrogant to a degree, but not nearly as much as the men who came before her were. Women are very rarely given tragic, nuanced pasts and the resulting boiling anger in fiction the way men are, and that is a part of the Doctor that would be thrilling to see played by a woman. The Doctor is an extremely flawed character, and while I'm clearly excited to see his eccentricities continue into the Thirteenth Doctor, I'm anxiously awaiting the moment when her character takes on the other layers past Doctors have been allowed.
However, even if we simply continue on the path the Doctor has been put on this season, I'm still hoping it will spark a shift in the way intelligent, heroic women are allowed to be portrayed in media. Women do not have to fit into this strange Intelligent Dream Woman ideal who looks perfect, speaks clearly and with maturity, and spends the majority of her screentime proving she can keep up with the guys. She can be as fast-talking, flawed, and eccentric as every man who came before her, just like the Doctor.