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What does resident mean in title like resident mathematician?

And what are the main subjects where resident is attached to a title? For example, does a resident statistician exist? Or a resident medieval historian?

What are the place where the mathematician resides? I think they are not universities but maybe hospitals or museums, am I correct?

For example, from Writing a successful thesis or dissertation: Tips and strategies for students in the social and behavioral sciences by Fred C. Lunenburg and Beverly J. Irby:

Ideally, commitee members should supplement your chair's expertise. If your study requires complex statistical procedures and your chair is not a statistician, you may want to add to your commitee a faculty member who teaches your department's statistics courses. We call this person a resident statistician.

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To pick up your example, a resident statistician is somebody who holds a position:

  • at a research institute (or similar) that does not focus on statistics,
  • that entails to consult other researchers at the institute on statistical questions.

I have never seen this as an official title or job description; rather the resident statistician is hired as a regular researcher or professor. Some resident statisticians perform their own research, while for others consulting is a full-time job. It may also happen that somebody is hired for other reasons and then morphs into a resident statistician because they turn out to be good at it, nobody else would do it, etc.

I use to describe myself as the resident data analyst of my current life-science research group, because it is good way to characterise (part of) my role in a few words.

Do not confuse this with artists in residence.

And what are the main subjects where resident is attached to a title? For example, does a resident statistician exist? Or a resident medieval historian?

In my experience, resident statisticians, mathematicians, and similar are the most common, but I also know cases of resident biologists (in a biomathematics group) and physicists (in a quantum-philosophy group). I can imagine that a group investigating historical climate would have a resident medieval historian to investigate historical weather records.

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I think there is no formal/official sense of this, at all.

"Consult your resident expert-on-X" is a traditional (in the U.S.?) way to say "talk to the person in your closest circle who knows about this". That person may already be known to you, as "the person we can go to, to clarify issues about X"... for example.

(The modifier "resident" just means "physically present in your department or building or ...")

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Resident means:

Located here a long time

It is the same as the non-academic meaning, but different from the medical meaning. Any employer could choose to give this title, but few do.

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