Hello! Strange question incoming.

Is it possible for a character to be a sorcerer AND a wizard at the same time?

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Yup.

Just take both wizard and sorcerer levels.

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I play:

Yes mechanically it's possible but ... Weave-wise? Lore-wise?

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I don't see why possessing innate magical ability precludes someone from studying it 'formally'. You just kinda end up bad at it, since natural talent likely confuses the book learning. This is represented perfectly well by sorc/wizard builds being generally terrible.

Yup.

There is actually a prestige class that requires to have both Wizard and Sorcerer levels. PrC: Ultimate Magus.

And it is entirely of the perspective are "bad at it". Mechanically-wise sure.. you don't have high DC's or CL's nor potent spells.. But IC:ly your something most aren't, your both spontaneous caster and prepared caster, you understand the Weave whole lot differently than others. Perhaps that is your greatest advantage, after all.. In Amia the RP counts and not only the mechanics behind your build.

Any character can study magic, other thing is if they have what it takes to understand it or to utilize it via casting spells.
Not all casters can cast spontaneously, it requires a special bloodline usually.

EDIT:

Weave-wise?
Weave-wise your still using the same source of Magic, simply your character has more than one way to tap into the source. Plus potentially more casting times than most, not sure of the amount of spells you get with that combination.

Lore-wise?
It is not uncommon for mages who started as sorcerers to have some wizardly training as well, if you look at most known sorcerers in FR, they tend to have wizard levels in their builds. Or at least some. Perhaps it is simply due to the desire to understand where your power stems from and what makes your magic part of you. As mentioned, some of these combinations try to further their understanding and superiority through the PrC Ultimate Magus, an interesting class.

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http://www.d20srd.org/indexes/spells.htm

The first example that comes to mind, probably the most famous and powerful sorcerer in the Realms: the Simbul in the Unapproachable East is 20/10/2 Sorc/Wiz/Archmage.

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Good example and here's a follow up question; How would you portray the Arch mage prestige class?
30 Sorcerer? 30 Wizard? 25 / ???

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No particular build, as far as I can see. It seems to be about swapping spells for special abilities, so anything that meets the requirements and requests custom abilities should work. You can't really pull it off just with emulation, since that stuff doesn't have good NWN equivalents.

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I uh.. once took a break from amia and ended up deciding to prod about other servers most horrid of course.. but one was interesting as it added a massive amount of classes, such as Arch mage, invisible blade, etc... wouldn't mind seeing a few added here too. Would certainly add a few new things for people to prod and play with.

I would dare say that to become a PrC Arch Mage, it would require extensive roleplay with a mage toon. Plus I would say that to be recognized as an archmage requires that RP to back it up, not to have a mechanical class. Then again, if your request for it is accepted, I believe your golden enough.

For archmage PrC I would say that pure build either of Wizard or Sorcerer represents it the best - Dedication to your art to become supreme in your field.

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http://www.d20srd.org/indexes/spells.htm

Archmage is sort of arbitrary canon, as far as I have played with it, added with additional community observation. Aiseth was bold enough to declare who she considers to be archmages in the Amia/Ruathym region (including her self) perhaps for the benefit of onlooking Halruaans who are seeded research papers through red letters, in a way that encompasses the majority of known wizards at the time or for general interest readers. Consisting mainly of well known wizards and one known Beldor, (whatever he truly is).

How does she base the criteria for archwizardry? It's a record based on a regard for power and proof of knowledge, a unique spellcraft such as made-spells, a primary school focus and proof of mastery in such a field, released academic papers or articles of interest, actions taken to improve or alter their environment toward the benefit of magic's flourishing, or a cautious diplomatic role; a role that engages their local communities in some way. She intends to update this paper with new additions as other mages begin leaving a noticeable trail or mark. You may notice Colin Reyes is not regarded in said document or any of his cabal, which one might perceive as a political statement. Sorcerers as well are just exempt from such prestige regard.

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MuseReader: Aiseth Nosdivan- Master Enchantress

The Prestige Class archmage is misnamed, in my opinion. It is a status title that is rather arbitrary, as well-demonstrated by both Aiseth's post and IC writing.

There are archmages who would never boast themselves as such. And there are those who call themselves archmages, but are far from it.

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Playing:
Marcus Valis

A part of me wonders whether it is feasible for a sorcerer to develop a spellcasting methodology reminiscent of a wizard's study. After all, a sorcerer can bend their talents to cast any spell at all, if not have access to all the myriad options at once, and as such it stands to reason that a particularly studious one would research their options before devoting their energy to a specific pursuit. The problem is, I am unsure as to whether that is even possible. Wizards learn spells by study and practice, purely. But a sorcerer can innately shift magical energies to produce a desired effect, often as more a side effect of their desires and personality. This in mind, would their spell list still be dictated by their whims and emotions, or could they control it by use of a more logical perspective?

In short, could a sorcerer still be a sorcerer, but act like a wizard?

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Contents subject to change without warning, reason, necessity, or logical imperative.

Sorcerer is probably the most dynamic arcane class there is. The short answer to your question is yes. It is possible for a Sorcerer to learn how their gifts work, form a paradigm, or discover an internal paradigm. And once one of those things happen, they can go about modifying, enhancing, and possibly creating anew their manifestations. That could look very much like a wizard to an outside observer. Whether a Sorcerer's spells are completely determined by their blood or something they have some level of control over really depends on that particular sorc; there really isnt anything set beyond flavor and things like Pathfinder if you take it into account.

There is room for both the logical-minded sorc and the classical emotion-driven one. Or any mix in between. To make a grossly generalizing parable, Sorcerers are basically people who find themselves with superpowers one day, be it by blood or circumstance or fluke. If you give superpowers to a room full of 10 random people, they're each going to approach learning and living with those abilities in a unique way. If you're familiar with the television show Heroes, you understand.

To use my sorcerer as an example, he is probably the dead center of both archetypes. He understands deeply how traditional wizards practice and has studied spells and magic in controlled academic settings. Yet, he allows his own spellcasting to be mainly emotion- and want-driven, with both a knowledge and an empathy of how it happens. Sort of like someone studying classical forms of music, but then deciding to play free-form jazz for a living, producing music heavily through intuition but understanding why it sounds the way it does through technical knowledge.

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