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Can a wizard learn a spell, obviously arcane only, from an Alchemists formula?
It states in the Alchemist section of Advanced Players Guide that an Alchemist can work out the formula for his book from looking at a wizards spell book and making the appropriate skill checks. Could a Wizard reverse that process with the appropriate checks provided the spell is one that he could learn?
Without some houseruling, nope.
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.