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I remember a video, perhaps a Numberphile episode where a mathematician was described who would simply move in to the home of a collaborator with which they were engaged to so that they could work more closely together, essentially sleeping on their sofa and going to work with them and keeping a temporary office nearby.

They would travel from one city to another basically following the math, in order to maximize focus on the problem.

Is it possible to identify this mathematician and the general field(s) in which they worked?

"bonus points" for help finding the video (Numberphile?) in which they were mentioned and these stories described.

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The man is Paul Erdős. As pointed out by the OP in the comments, his "nomadic" lifestyle is briefly mentioned in the Brown Numbers - Numberphile video, 3.05-3.30. It is also concisely described in Currey's book Daily Rituals read in this YouTube video that refers to Hoffman's popular biography The Man Who Loved Only Numbers, which is featured in Hoffman's own video.

Despite Hoffman's title, Erdős's interests were not confined to number theory but covered also combinatorics and graph theory (where he pioneered probabilistic methods), and analysis (approximation of functions), and he made sporadic contributions to other areas, such as general topology (an example of a totally disconnected space that is not zero-dimensional). AMS Notices surveyed Erdős's mathematics in some detail in 1998, 2 years after his death.

Here is Currey's excerpt:

"He was also, as Paul Hoffman documents in his book The Man Who Loved Only Numbers, a true eccentric — a “mathematical monk” who lived out of a pair of suitcases, dressed in tattered suits, and gave away almost all the money he earned, keeping just enough to sustain his meager lifestyle... Erdős liked to work in short, intense collaborations with other mathematicians, and he crisscrossed the globe seeking fresh talent, often camping out in colleagues’ homes while they worked on a problem together. One such colleague remembered an Erdős visit from the 1970s:

"…he only needed three hours of sleep. He’d get up early and write letters, mathematical letters. He’d sleep downstairs. The first time he stayed, the clock was set wrong. It said 7:00, but it was really 4:30 A.M. He thought we should be up working, so he turned on the TV full blast. Later, when he knew me better, he’d come up at some early hour and tap on the bedroom door. “Ralph, do you exist?” The pace was grueling. He’d want to work from 8:00 A.M. until 1:30 A.M. Sure we’d break for short meals but we’d write on napkins and talk math the whole time. He’d stay a week or two and you’d collapse at the end."

The colleague is Ralph Faudree, and the quote is taken from Hoffman's book, p.256.

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  • $\begingroup$ Okay this must be therm! This certainly all sounds like what I remember. What surprises me is that I didn't recognize the guy with the number's name when I heard it. I'll keep hunting for the Numberphile video on my own, butI can't imagine that this isn't the answer. $\endgroup$
    – uhoh
    Commented Oct 18, 2020 at 9:53
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    $\begingroup$ Found it! Brown Numbers - Numberphile Erdős conjectured that there are only three Brown Numbers. Brown Numbers, Brocard's problem $\endgroup$
    – uhoh
    Commented Oct 18, 2020 at 10:21
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    $\begingroup$ @uhoh Hoffman's book is well worth a read. It also contains many humorous anecdotes including one about Erdos' trip to a hospital for corrective eye surgery. $\endgroup$
    – nwr
    Commented Oct 18, 2020 at 16:31
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    $\begingroup$ @uhoh Thank you, I edited the link into the post. $\endgroup$
    – Conifold
    Commented Oct 18, 2020 at 17:30
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    $\begingroup$ xkcd.com/599 $\endgroup$
    – user3067860
    Commented Oct 19, 2020 at 15:30

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