Magic is music, it is the foundation upon which all of Creation was built. There are many ways a spellcasters have engaged with the music of creation but one of the oldest methods was that of mathemagic.
This turning of musical notes into formulae and calculations is the only method that continues to evolve and develop by the ingenuity of mortal folk, without the influence or intervention of supernatural forces. It is this art that arcanists of old developed, forming the Schools of Magic, and leading to many of the magical institutions that can be found amongst the worlds of the Material Realm.
However, this path does require time, effort, and dedication. It requires years of continual study. This need has led to many worlds, where magical use is permitted or accepted, containing institutions dedicated to the training of arcanists. These could be guilds, schools, universities, or more unique organisations. But be they part of an organisation or operating on their own, all arcanists are scholars constantly seeking to expanding the knowledge of what magic is and how it can be channelled to more and more incredible feats.
How arcanists relate to the world very much tends to reflect that world’s relationship with magic.
Worlds where magic is accepted will have large multinational institutions to teach prospective students, acceptance into these institutions will be lauded by the common people, and magic is often viewed more with wonder than mistrust.
However, in worlds where magic especially Cosmic Magic is scorned or feared, institutions may not exist or be small hidden groups. An arcanist is more likely to be taken in as an apprentice to someone more experienced, constantly on the move trying to keep their skills secret.
Others may find themselves forcibly recruited to serve a nation’s government, as their destructive potential is manipulated for the sake of another.
These are merely examples of how each arcanist can relate to the world they come from. So, when either making a world or a character, consider how magic is treated and relates to the world’s themes, and from there you can see threads to pull upon to make something in keeping with the themes or that is an exception running in opposition to them.
Arcanists tend to have at least a simple understanding of the cosmology of creation and the many realms that form it. It is from these realms that entities are summoned by conjuration spells to perform an arcanists bidding, or whose raw energies fuel evocation magics.
As such it is advised that an Arcanist speak with their GG about what they may know about the cosmology of the setting, if you are both in doubt consult Appendix D: Cosmology for ideas about the different Realms and agree between you both what is true for your Campaign’s setting and what your Character may know.