From the SRD (emphasis mine):
Although the alchemist doesn’t actually cast spells, he does have a
formulae list that determines what extracts he can create
...
An extract is “cast” by drinking it, as if imbibing a potion—the effects
of an extract exactly duplicate the spell upon which its formula is
based
...
An alchemist can also add formulae to his book just like a wizard adds
spells to his spellbook, using the same costs and time requirements.
An alchemist can study a wizard’s spellbook to learn any formula that
is equivalent to a spell the spellbook contains. A wizard, however,
cannot learn spells from a formula book.
Alchemists cannot learn spells, they learn formulae, that are based on actual spells, but are not spells. Thus, if a wizard’s spellbook contains a spell that is the equivalent of a existing formula, you can study the spellbook to add that formula to your own formula book (essentially recreating the formula from the spell). However, the wizard cannot do the opposite.
Also, as a side comment, since alchemist extracts work like potions that must be ingested, makes sense that most formulae mimic spells that are either of personal range, buffs or healing, due that method of application. Attack and debuff spells could not be properly applied with that method (just imagine the consecuences of pouring a fireball down your throat), so it would not make sense that the alchemist could learn any wizard spell.
- If a level 1 alchemist has Int 11, he can create 1 1st-level Extract Per Day.
- If a level 1 alchemist has Int 12-19, he can create 2 1st-level Extracts Per Day.
- If a level 1 alchemist has Int 20-29, he can create 3 1st-level Extracts Per Day.
But, barring other influences (e.g. archetypes, feats, magic items, special abilities, traits), that's all he can create. He can't create 2nd-level or higher extracts, and he can't use the higher-level bonus Extracts Per Day to create lower-level extracts.
Although a high Intelligence score lets an alchemist create more higher-level Extracts Per Day, an alchemist can't create additional higher-level Extracts Per Day those until he has a number instead of a dash of Extracts Per Day of that extract level according to Table: Alchemist.
So while a high Intelligence remains extremely valuable for an alchemist, that high Intelligence doesn't let him create Extracts Per Day of an extract level beyond what his alchemist class level dictates he can create.
The alchemist's Extracts Per Day follow the same rules as Bonus Spells Per Day for spellcasters.
What would happen if an alchemist could
I'm mainly guessing, but I think you were thinking that because of an Intelligence score of 18, a 1st-level alchemist would be able to create 1 additional 1st-level, 2nd-level, 3rd-level, and 4th-level Extracts Per Day if he could gain access to those formulae. The game expects, however, according to Table: Alchemist, a 10th-level alchemist to be able to create 1 4th-level Extract Per Day. In other words, an ability most characters would wait to use until halfway through their careers (i.e. creating 4th-level extracts) would be available to a 1st-level alchemist with Intelligence 18.
The game doesn't expect a level 1 alchemist to use 4th-level extracts like freedom of movement and greater invisibility even once per day, and you'd likely find such a character overcoming challenges far beyond his expected abilities, leading to DM frustration at the DM's inability to challenge such a character without killing him outright and, perhaps, boredom (or terror!) while playing a character who can casually overcome challenges far beyond his ability in an extremely limited manner. You can play that way, but you should be aware you're choosing to change the rules, and your experiences with the game will be vastly different than those who are otherwise playing the same game.
A minor rules quirk
The supernatural ability alchemy says, "An alchemist begins play with two 1st level formulae of his choice, plus a number of additional forumlae equal to his Intelligence modifier." That last part means that an alchemist always begins play with 2 1st-level formulae but that his Intelligence modifier lets him select additional formulae of any level. He can't use those higher-than-1st-level formulae when he's a level 1 alchemist, but he could totally have in his formula book as many 2nd-level-through-6th-level formulae as his Intelligence modifier allows.
Again, the level 1 alchemist can't yet create extracts with such formulae, but he could—if he encounters appropriate folks during the campaign—trade that formula knowledge for other goods or services from a higher-level alchemist that desires such formula knowledge. Of course, such a higher-level alchemist may, instead, opt to simply disappear the low-level alchemist and abscond with his formula book, but a low-level alchemist choosing to have high-level formulae in his formula book is an option, albeit an unusual and potentially dangerous one.
Best Answer
You add it to the formulae you “know,” but alchemists don’t really “know” formulae (and wizards don’t “know” spells) the way a sorcerer for example does.
The so-called “spontaneous” spellcasters, like sorcerer, gain a very limited number of spells known as they level up. Those spellcasters cannot (easily) add to this number. They know these spells innately, and require no external aid for them.
Other spellcasters, like wizards, are known as “prepared” spellcasters, and do not learn spells innately. Instead they require a spellbook (or a god/faith, in the case of divine prepared spellcasters), and even though they “know” every spell in their spellbook, they still need the spellbook to prepare those spells, and can only prepare a selection of those spells each day. On the other hand, however, they can easily add as many spells as they like to the spellbook(s). Thus, unlike spontaneous spellcasters, prepared spellcasters do not have a specific number of spells known. It’s just however many spells they have put in their spellbook.
Alchemists work much like a prepared spellcaster; instead of “spells” they have “extracts” and so instead of a spellbook they have a formula book. Aside from that, they work about the same: they can add as many extract formulae to their formula book(s) as they like. They “know” all of these formulae, but require the formula book to prepared them.
Correct, the number of spells you know is completely independent from the number of spells you can cast per day. Alchemists and wizards must “prepare” their extracts/spells ahead of time, and because they can add as many formulae/spells to their books as they like, in any given day they won’t be able to prepare all of the extracts/spells they “know.”
You can only copy spells that are found on your formula list. Wizard spells that aren’t on this list cannot be made into formulae and cannot be copied by an alchemist.