We Do Not Know
I have tweeted Elio and Linda and they have said that ravenry and healing seem like they should be requirements though it is their speculation so I'd take it with a pinch of salt.
Hello! I'm currently looking into the maesters and was wondering if there are any mandatory links needed before forging their chain? Thanks!
Though never explicitly said, seems to me ravenry and healing must be absolute requirements.
However, given that we only have 14 known links and only 6, or 7, of these have their corresponding subjects known it seems likely that there are some common links even if they aren't mandatory. I'd assume the same as E&L here in that black iron (ravenry) and silver (medicine) are common and closely followed by yellow gold (maths and economics).
It would also seem that the acolytes/novices approach the Archmaesters when they believe themselves proficient in the subject to earn their link and this would then seem like they pick the links to study themselves which may indicate that there are no mandatory subjects.
He had been five years at the Citadel, arriving when he was no more than three-and-ten, yet his neck remained as pink as it had been on the day he first arrived from the westerlands. Twice had he believed himself ready. The first time he had gone before Archmaester Vaellyn to demonstrate his knowledge of the heavens. Instead he learned how Vinegar Vaellyn had earned that name. It took Pate two years to summon up the courage to try again. This time he submitted himself to kindly old Archmaester Ebrose, renowned for his soft voice and gentle hands, but Ebrose's sighs had somehow proved just as painful as Vaellyn's barbs.
A Feast for Crows, Prologue
Maesters also appear to have two main functions; staying at the Citadel performing research, teaching and forging new links and going to be the resident maester at a castle. It would seem likely for a maester to go to a castle they would need to have some common links to be useful there.
- Black iron (ravenry): The most common form of long distance messaging seems incredibly useful at a castle.
- Silver (medicine): Speaks for itself.
- Yellow gold (maths and economics): Maesters help run the castles so having a head for finances goes a long way.
There are some other subjects that probably help when going to a castle but don't seem needed.
- Iron (warcraft): Not necessarily important but I'm sure it'd look desirable to the castles occupants.
- Copper? (History): For teaching the children of the House
- Unknown (Literacy): Same as above
- Bronze (Astronomy): The maester can then advise on the changing of the seasons before the arrival of a white raven.
We also know that not all links are required to become a maester as Maester Luwin says only one in a hundred has the Valyrian steel link for higher mysteries.
Luwin slid a finger up under his collar and began to turn it, inch by inch. He had a thick neck for a small man, and the chain was tight, but a few pulls had it all the way around. "This is Valyrian steel," he said when the link of dark grey metal lay against the apple of his throat. "Only one maester in a hundred wears such a link. This signifies that I have studied what the Citadel calls the higher mysteries—magic, for want of a better word. A fascinating pursuit, but of small use, which is why so few maesters trouble themselves with it.
A Clash of Kings, Bran IV
As per whether or not there is a certain number of links needed to forge your chain well the above quote seems to say that Maester Luwin's chain is tight around his neck. This would than make it seem as if maesters wear a chain when they have enough links to wear it. Though as we saw with Pate the Archmaesters decide on when a novice/acolyte can earn a link so they might also decide on when they've earned their chain to become a maester.