Pythia is the official nerd test for true Doctor Who deep lore.
A normal person who hears "Pythia" will say "What the fuck is that?", or possibly "You mean the Oracle of Delphi?" because that's what the Pythia was in real life and there are people who are nerds about real-life history instead of made-up shit like Doctor Who.
A Doctor Who super-nerd will immediately launch into an argument either for or against the canonicity of Looms. This means you are legally free to punch him in the balls.
But if you're online and therefore can't punch him, here's what you need to know.
The Curse of Pythia Edit
Ancient Gallifrey was a magical matriarchy, and even the official rulers were subservient to the chief seer and wise woman, known as the Pythia. Kind of like the utopian history many pseudo-scholars make up for pre-Christian Europe, because they can't imagine how we could ever overcome sexism in the present if it weren't true in the past (because it's not like we've overcome absolute monarchy or serfdom or the non-existence of the internet or smallpox or anything). But, unlike real-world fake-history, the Pythias were all evil and oppressive tyrants, because VNA-level dark. So Rassilon led a revolution to replace her evil and oppressive tyranny built on supernatural mysteries with an evil and oppressive tyranny built on scientific state secrets. (Also, blowing up a star, because fuck stars.)
Pythia saw the revolution coming, but she couldn't foresee the outcome, so she decided fuck it, cursed everyone so nobody on Gallifrey could have sex again, then killed herself. Which is why Rassilon won, and why she couldn't foresee it. Bravo Pythia. Her followers fucked off from Gallifrey out of embarrassment at her stupidity and became the Sisterhood of Karn. Rassilon invented Looms so his people wouldn't die out, because it took zillions of years before a few renegade Time Lords (like the Doctor's dad) figured out that they could just visit other planets, because Time Lords are as sad as their fans.
Then Leela decided if she's going to stay on Gallifrey for Andred, he's going to give her some timedick, over his protests. And she had a baby, so the Curse of Pythia was broken, and there was a giant Time Lord orgy.
All of this stuff only happened in two Virgin novels by Marc Platt. But a few other novel writers decided to fuck with his ideas. Rassilon restructuring all of history around rational causality immediately made the Curse stop working and there were never any Looms. And the Looms were a good way to breed a subclass of noncitizen soldiers for the Time Wars so they made up the whole Curse thing and allowed the rest of the universe to believe in it as disinformation. And the Curse never worked in the first place but Rassilon passed laws against fucking because that's how much of a dick he is, so everyone believed it worked. And the Curse did work but Leela's timedicking lifted the Curse retroactively so now it never happened. And the Curse worked just fine but everyone on Gallifrey knew the secret of going off-world to have sex. And the Curse always worked but that whole timeline ended when the Time Lords went through a bottle into another universe where it never happened. And lots of other contradictory retcons.
Besides, even in Platt's two novels, the Doctor probably had parents, because he's special. Maybe he's even half-human on his mother's side, or maybe not, but either way, timedick was involved. That's why everyone in Lungbarrow calls him Snail. Also, remember that The Other.
So, what kind of idiot cares whether the Pythia and the Looms are canon in the first place?
If you're asking that question, you don't understand fans.
RTD and Moffat do understand fans, so they like to write stuff to deliberately troll people who still want to argue about whether this shit is canon, which is why The End of Time and Hell Bent each gave us a woman who may or may not be the Doctor's mum but probably is. Some might argue that they should have instead spent their time writing satisfactory plot resolutions for those episodes, but watching people being stupid on the online forums has always been more entertaining than watching the show, hasn't it?
Today, the Doctor can dance with whoever he wants, but the Curse of Pythia means that fans who argue over the books can't have sex, except with fat chicks they meet on Tumblr who make them dress up as David Tennant and call them Rose.