This is a question bugging me for a long long time, especially for a non-native speaker like myself.
We have physicist standing for the people doing physics research, as is linguist, chemist, etc.
But for math, the counterpart of "-ist" suddenly becomes "-ian": I call myself a mathematician.
What bugs even more is that we have physician as well, yet representing a totally different occupation with physicist.
This is not the end, in mathematics, we have so many adjectives derived from the names of mathematicians. Through some wikipedia-fu I learned they are called eponymous adjectives, most of which I used often end with "-ian": Newtonian potential, Cartesian coordinate system, Lorentzian transformation etc. These words often indicate somewhat the relationship of possession.
Yet again, not all possessive relations are represented using "-ian", there are: Maxwell's equations, not Maxwellian equations; Gauss's divergence law, not Gaussian law (even though there are tons of things with Gaussian in it).
What confuses me even more, is that "-ian" after people's name can not only represent "of someone", it also can stand for "a believer or supporter of someone's theory". For example, I call myself a Kantian. There is Leibnizian as well, the supporter of Leibniz's philosophy.
Now my questions are:
Is there a standard rule to decide which one to use, "-ian" or "-ist", when describing an occupation?
For eponymous adjectives, my vague impression is that: when something is derived not by that specific person, but rather whose derivation bears the spirit of that someone's theory, then we use "-ian". For example, Newtonian potential is not invented by Newton, yet Maxwell's equations are unified by Maxwell. But another example is that Descartes invented Cartesian coordinate system, but the system is not called Descartes' coordinate system...How to tell if we want to invent some new terms? For example, if I proved a new theorem using some idea from Newton, do I call the proof Newton's argument or Newtonian argument?
Can "-ian" be used interchangeably in "I am a Kantian" and "This is a Kantian style argument."? or there is some tradition for each word ending with "-ian"? i.e., Some words ending with "-ian" can be only used as noun or adj.