Maybe it's because I'm not a native speaker, but I would describe someone onle as a professor or the professor, depending on whether we're talking about a specific chair or about an academic appointment generally.
Since there is only one Chief Justice of the Supreme Court, describing him as "a chief justice" would be strange. That has nothing to do with formality.

Saying "Edward is Accountant of Payables" or "Sarah is Doctor of Radiology" may be. Perhaps the "of" clause has something to do with it?

My guesses:

(1) it harkens back to a time when there was just one professor per subject. All others were probably just "assistant" or "associates."

(2) it's considered more of a title than a profession. When something is a title, it's not unusual to have no article. John Doe is dean of Stanford. John Doe is shift supervisor at Starbucks.

This should be obvious. We say someone is Professor of Chemistry but not Doctor of Medicine or whatever because that is a job title. It is never Professor of Chemistry alone, by the way, but always Professor of Chemistry at X Y.

If you don't mention the affiliation, then you have to say a professor of chemistry and you can also say a priofesor of chemistry.
When you leave out teh word a the word professor must always be imagined as capitalized.

And I think this is actallya shortening. It might even be So and so Professior of Chemistry. The same as maybe Dean of Students.

No 'a" because there is only one of them. At least in theory.

Clarity. "Is professor" is decidedly unclear when there is more than one professor. Even limiting it somewhat: "John Doe is Professor of Chemistry at UCLA" is in error, unless there is only one such professor.

In general, "Is Professor" is not, from a meaning and clarity point of view, good usage at all.

No doubt this is why the usage has currency in our halls of higher learning.

I studied French in college and I do recall that when referring to one's occupation the construction was il est avocat (he is lawayer) rather than il est un avocat (he is a lawyer). If this is true of the other Romance languages, I wonder if there is some arcane grammatical distinction that we somehow ended up with and no one remembers why anymore. I certainly don't remember why the rule was that way in French and I'm certain there were probably times when "il est un avocat" was appropriate.

Surely the usage is that there is no article where a specific chair is referred to:

(i)Bloggs is Regius Professor of Roman Law in the University of Oxford(specific chair)

(ii)Bloggs is a law professor at Oxford (could be the holder of any one of many chairs).

We use the professional position without the definite article when providing title and location

Sometimes. It doesn't hurt my ears either to say "Tom Brady is the quarterback of the New England Patriots", "Sara is the Regius Professor of Roman Law in the University of Oxford", "George Bush is the President of the United States of America."

Uniqueness is (a?) part of it: "Joe Biden is Senator from Delaware" or "Randy Moss is Wide Receiver for the New England Patriots" doesn't work, except maybe as a footnote where clearly we are adding details about the person who is already known as an author or party guest, and not about the position.

Not being in academia, maybe I'm outside the loop, but "is professor of basketweaving" sounds patently wrong to me. As has been said earlier by other commenters, it must be a singular designation for that to seem right, such as "is Professor of Basketweaving."

It is endowed chair envy.

A well-endowed chair, no doubt.

From the British usage, where there is (by definition) only one Professor. It is the the equivalant of Chair of a Department in that sense...

One is referring to the individual's university rank and the other is referring to their occupation. Often, even lecturers and adjunct faculty are referred to as "a professor" but only someone who has reached the pinnacle of the promotion pyramid is referred to as "Professor of foo" (as opposed to "Assistant Professor of foo" or "Associate Professor of foo").

Also, to be used correctly 'foo' must be the full name of their department and not the general name for their field. So you would say someone is Professor of mathematical science and not that they are Professor of math.

I really don't find it common at all for people to say, "John is professor of English," rather than, "John is a professor of English." Who talks like that? Professors?

"John G. Roberts is Chief Justice of the United States."

No we wouldn't say that, even though theer is only one. But we would say "David Paterson is Governor of New York" or "george W. Bush is president of the United States."

Theer are two senators and if we want to say Senior or Junior we say something like "Joe Biden is the Senior Senator from Delaware." So and so is "a member of Congress" but maybe "Congressman from the xxth District"

I think we don't quite think of "Chief Justice" as an independently standing concept. Secretary of Agriculture maybe, but not Chief Justice. That would always be "the Chief Justice" We'd write so and so is Secretary of Agriculture at the bottom of an Op-ed piece buit otherwise probably not unless you were listing many diffeernt officeholders. Actuall if you were listing many then you could also say "John Roberts of Chief Justice of the Supreme Court of the United States, so and so is an Associate Justice, so and so is.."

William Howard Taft was Chief Justice of the Supreme Court as well as President.

We have to think over examples - and THEN we can try to deduce the rules.

In the case of college professors it probably does mostly stem from the usage in the case of an Endowed Chair (where there is only one of them and it is a job title) At must always be used.

Should be "Is Russian influence."

The growing influence of Borat, perhaps?

"John G. Roberts is Chief Justice of the United States."

No we wouldn't say that, even though theer is only one

We wouldn't? I would.

"It's good to be king." or "It's good to be the king." ?

Orin: my mistake indeed (but smaller margin)

416,000 for "is professor of" site:edu.

346,000 for "is a professor of" site:edu.

vassil petrov :
In Bulgarian there is no indefinite article, so we don't have that problem. I think this is true of all Slavic languages.

Right, not the "professor" problem. All the other Slavic languages have neither definite nor indefinite article (subject to whether you consider Macedonian a different language). That is why I was amused when the dispute of "Ukraine" vs. "the Ukraine" arose in the 90's. It was purely for the English-speaking world consumption.

I can't think of any time I've run across "is professor" except in a sentence of the form "John Q. Doe is professor of knowledge studies at Nowhere State University" that appears on a book jacket, in a prepared speaker introduction, or similar formal context. It is sui generis, in other words, and I don't see why you need to derive a rule.

That said, in similar contexts I think you would also encounter "Jane Q. Roe is general counsel and vice president of XYZ Corporation" and "Bob Z. Public is assistant undersecretary of the Federal Department of Bureaucracy." Titles don't require articles, but we only observe that rule in the context of this type of formal introduction.

I figured :-) Next one would say there is a (or there is no) Bosnian language, and where will it stop?

By the gates of Vienna, I guess.
Just kidding.
I wish you all the best.

By the gates of Vienna, I guess.

I did not get this reference and I am curious. Do you mean 1914 or maybe 1683?

I've only ever hear the "is professor" formation when referring to a named professorship, e.g. "Orin Kerr is Harlan Sanders Professor of Poultry Studies."

Sidney Wang: That what I said! "What meaning of this?"

And he right! Speakers of Russian and Hebrew would concur.

Yeah, but then there's them English folk who say "I went to university" and drop the "the," as though "university" were Heaven (which it certainly is not). They do the same thing with "hospital," as though hospital is a state of mind or something. What the hell? Thank god my ancestors fought and died for our right to have appropriate definite articles.

Hey, is that what the articles of confederation were about?

Yeah, but then there's them English folk who say "I went to university" and drop the "the," as though "university" were Heaven (which it certainly is not). They do the same thing with "hospital," as though hospital is a state of mind or something. What the hell?

As I said above, both countires do that same with "prison." In fact, that's how I know of that usage. I (an American) asked a Brit once about the lack of an article for "hospital" usage and she pointed out it's used the same way as Americans use "prison."

I would never say someone "is professor." I would use that only in the context where it's an official title, like "is Professor of Mathematics at State University." And I'd only use it for a generic full professor, not for an associate professor, assistant professor, or holder of an endowed chair (in which case I'd' say "is Rich Donor Professor of Mathematics at State University.")