Learn English – When can/can’t you add “-less” at the end of a word

Is there a standard rule to decide which one to use, "-ian" or "-ist", when describing an occupation?

The suffix in mathematician and physician (and other words such as politician, magician) is actually -ician (from the French -icien) which is constructed by taking the suffix -ica (names of arts or sciences in Latin such as: magica, mathematica, politica etc) and "adding" -ian to the -ica suffix (I write "adding" because the "a" is dropped from -ica):

magica -> mag-ica -> mag-ic(a)-ian.

So, the suffix -ician means someone who is a specialist or practitioner.

(Also the -ician rule also sometimes - confusingly though, not always - applies to such words which don't end in -ica but instead just -ic, such as: academic becomes academ-ic -> academ-ician and the same for geometr-ic: geometr-ician.)

As for the specialist words ending with -ist (linguist, chemist), I am not sure, but I think the Latin word stems for these words end in just -a rather than -ica: chemista (chimista?) and lingua. I think these -a word stems get the -ist suffix, from the French -iste or Latin -ista. (agential suffix)

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.

Here I am not as sure. The suffix -an means "pertaining to," from Latin -anus, in some cases via French -ain, -en. I cannot explain the added "i" in Newton-i-an. Maybe it is added to make the word sound better than just "Newtonan".

First of all, expirable is a word. It's been hanging around since at least 1913.

expirable

Adjective

That may expire; capable of being brought to an end.

Part or all of this entry has been imported from the 1913 edition of Webster’s Dictionary, which is now free of copyright and hence in the public domain. The imported definitions may be significantly out of date, and any more recent senses may be completely missing

wiktionary

That said, expirable makes me think it has an expiration date. If that's the impression you want then I think you're fine.

Wish more programmers took this much care when naming things.

Expiring URL vs Expirable URL

The semantic difference here is an Expiring URL had better always have an expiration date. Where an Expirable URL might have it's expiration date set, it might not. So pick the name that goes with how you intend to implement.