How old is the alchemists' guild?

[HouseFossoway]

Pretty much the title. We are told in ACOK by Tyrion, (who I think we can say has a decent grasp of history) that:

" Once theirs had been a powerful guild, but in recent centuries the maesters of the Citadel had supplanted the alchemists almost everywhere." ACOK Tyrion V.

Which would imply that the alchemists' guild is very very old and used to be the main source of "wise" counsel that Kings and lords throughout Westeros received, but the newer order of the maesters who relied more on rational thought and not magic began to become more popular as magic started to disappear.

However, we are told that the maesters are also a very old order, dating back to the first Hightower King, way before the Andals (and thus even written language) arrived. So the alchemists are either even older than that, or the maesters were for the vast majority of their history not widespread or powerful at all.

It also seems weird that the alchemists who were very interested in Dragons and Fire suddenly grew less powerful once the Targaryens arrived in Westeros.

[Renly's Banana]

Being old =/= having widespread influence. 
It may be that the maesters are much older, but were perhaps just exclusive to the Oldtown area or the southern Reach. The alchemists were maybe a little bit more popular for a time, until the Citadel was created and started to become more powerful. 

GRRM never goes into detail about them, but it seems like the Alchemists' Guild follows the standard alchemist trope/lore, like transmuting random metals into gold. Tyrion makes some passing comment about them being famous for trying to do that. So if it's anything like our real life alchemists, they were nothing more than a passing fad. I'm assuming there were/are many different sorts of guilds in Westeros; I'm guessing the alchemists saw their heyday long before there was a unified kingdom, back when Westeros was less "enlightened." Then obviously saw another little surge in popularity during the height of Targaryen craziness.

[White Ravens]

1 hour ago, HouseFossoway said:

Pretty much the title. We are told in ACOK by Tyrion, (who I think we can say has a decent grasp of history) that:

" Once theirs had been a powerful guild, but in recent centuries the maesters of the Citadel had supplanted the alchemists almost everywhere." ACOK Tyrion V.

Which would imply that the alchemists' guild is very very old and used to be the main source of "wise" counsel that Kings and lords throughout Westeros received, but the newer order of the maesters who relied more on rational thought and not magic began to become more popular as magic started to disappear.

However, we are told that the maesters are also a very old order, dating back to the first Hightower King, way before the Andals (and thus even written language) arrived. So the alchemists are either even older than that, or the maesters were for the vast majority of their history not widespread or powerful at all.

It also seems weird that the alchemists who were very interested in Dragons and Fire suddenly grew less powerful once the Targaryens arrived in Westeros.

I see a parallel with Early Modern history in Europe.  Rational thought and knowledge based on observation of natural processes allowed the birth of science and critical thinking to replace alchemy and astrology.  We can look back on alchemists and astrologers as kooky fools but they simply didn't possess modern knowledge of the physical world so they based their ideas on things that they thought made sense at the time.  The seven planets influencing the seven known metals which both influence the seven organs in the human body, that sort of thing.  They didn't understand anything about the periodic table of elements or atomic structure so they came up with the notion that gold is an expression of metal in it's purest form and this lead to the belief that lesser metals contained impurities that that could be removed leaving gold as the pure result of their efforts.  It makes sense in the context of their world view.
Alchemists working in their laboratories eventually amassed enough information for the birth of chemistry in its modern form.  Astrology lead to closer scrutiny of the stars and planets and orbital paths and this knowledge lead to the development of astronomy as a true science.  Science eventually proved the alchemists and astrologers wrong and I think a similar thing is happening with the Maesters and the Alchemists Guild.  For me this implies that the Alchemists Guild is older than the Maesters.