I have a player who multiclassed as a wizard and an investigator (a rogue/alchemist hybrid; for the purposes of this question, the investigator is functionally equivalent to an alchemist).
Some of the alchemist formulae are also wizard spells. The player wants to know if they can also learn the alchemist spells as wizard spells (so they can then scribe scrolls for these spells). Here's the RAW:
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. An alchemist does not need to decipher arcane writings before copying them.
RAW, it seems that a wizard/alchemist couldn't learn alchemist spells as wizard spells, even if the spells are on the wizard spell list. But a multiclass wizard/alchemist is an odd combination, and so I want to figure out what the RAI should be. And that hinges, I think, on the question of why wizards can't learn alchemist spells.
Is it that a wizard typically lacks training to read alchemical formulae? If so, I see a good argument for a multi-class character being able to derive a spell from a formula.
Is it that alchemical formulae are missing vital information? If so, then that's a good argument for why they can't.
This particular multi-class situation is fairly rare, so I haven't been able to find much discussion of this question anywhere else.
(From a balance and fairness perspective, multi-classing alchemist and wizard seems like a sub-optimal choice, and so in principle I'm not opposed to house-ruling that it does work; it doesn't seem like power-gaming to me.)
Best Answer
The arcane discovery alchemical affinity implies an alchemist/wizard can't normally copy from his formula book to his spellbook
Part of the benefit of the arcane discovery alchemical affinity says, "Additionally, you may copy spells from an alchemist's formula book into your spellbook just as you could with another wizard's spellbook." So Magical Marketplace's author, at least, believed it normally impossible for a wizard to copy into his spellbook a formula from an alchemist's formula book.
(Further, the alchemist's supernatural ability alchemy says, "A wizard, however, cannot learn spells from a formula book," and while Pathfinder isn't as clear as it should be when tossing around a very pregnant word like learn, Adding Spells to a Wizard's Spellbook nonetheless says, "If the [Spellcraft skill] check fails, the wizard cannot understand or copy the spell" (emphasis mine). The text continues immediately after, saying, "He cannot attempt to learn or copy that spell again until one week has passed" (emphasis mine). Parallelism makes understand and learn synonyms here, so a wizard, even after waiting a week, still won't be able to make that Spellcraft check to copy a formula because a wizard can't learn spells from a formula book in the first place. Note that I don't like this ruling as much as I like the anecdotal evidence from Marketplace because whenever the GM must make a ruling based on a rule's syntax there's usually more than one possible reading, making disagreements and hard feelings a possibility, so make of this what you will.)
A house rule could allow copying formulas into spellbooks anyway, despite the existence of alchemical affinity
A GM that makes a house rule that allows the PC to add his handful of appropriate alchemist's formulas to his wizard's spellbook (and still requires time and money to transcribe them) needn't worry that the PC is attempting some kind of crazy power-grab. Under such a house rule, a wizard who, late in his career, decides to take levels in alchemist trades versatility for power… and makes a completely uneven trade.