Voevodsky was too lazy to search for an apartment, so he lived in his office (at Harvard each graduate student gets a personal office) and slept on the roof. Unfortunately, the windows of dean office (Willy Schmid) had direct view at that roof. Volodya didn't adhere to the usual day routine (and didn't adhere to anything at all), sometimes he slept during the dean office hours. Some day Schmid looked through the window and saw a roof and Voevodsky was sleeping at the roof. It has to be said, that living and sleeping in the office is a terrible taboo and social stigma in America, so Schmid was outraged. Voevodsky was almost expelled, but everything turned out well, though he was forced to rent an apartment and he has lived there from then on.
I was a grad student at Harvard... let me correct a few things. First, Wilfred Schmid would probably never be called Willy. It's a funny idea though. Like calling the Queen of England Lizzy. He wasn't the dean... he might have been the dept chair at the time. As for living/sleeping at the office -- it's not a "terrible taboo and social stigma in America". (I'm American). But it's not allowed due to problems with hygiene (no showers in most bathrooms), smell, clutter, disruption at odd hours, etc.. So it's not allowed in any workplace. When it happens, the response of most departments is sympathy and an effort to find the cause and find the person a place to live. And grad students at Harvard are financially supported well enough to afford a decent room in the area. I mean... I wasn't rich, but lived comfortably in apartments shared with a few other grad students.
I was a grad student at Harvard in the math department too. In my time there was a student who decided he was going to sleep in his office (I don't think sleeping outside is such a great option in the New England winter). These offices are small - there's a desk, then room for a chair, and shelves for books above the desk. They are essentially for solo work. Anyway, this student was handling it fine - showering in the university gym and doing laundry in the basement of the nearby graduate residence halls, and rolling his bed up in the morning so as not to be reported by the cleaning staff. Then his girlfriend visited from abroad and she was so appalled with the suggestion that they bed down together essentially under his desk, that he ended up having to pay for them to stay for a week in a decent hotel. After that he found himself an apartment-share pretty quick.
> As for living/sleeping at the office -- it's not a "terrible taboo and social stigma in America". (I'm American). But it's not allowed due to problems with hygiene (no showers in most bathrooms), smell, clutter, disruption at odd hours, etc.. So it's not allowed in any workplace.
And as a Russian, my impression is somewhat similar to the original - in order to avoid all the problems that you mentioned it was made into that "terrible taboo". I mean many (if not pretty much any) taboo had pretty reasonable rationale at the time and place of its creation.
Not having a home in general is looked down upon here. Everyone is expected to have their place of work/study to be separate from the place where they bathe, sleep, etc.
My guess is that the US is a very individualistic, achievement, money-is-good, capitalistic place. Not owning a place to rest your head, being homeless, etc is associated with moral failure: laziness, lack of drive, addiction to drugs...
When I see the description that monort gave, I would think that in Germany this would be seen as somewhat bizarre (as in mathematician ;-) ), but not as "terrible taboo and social stigma" or something to be outraged about (as dean Schmid was in monort's description).
Quite the opposite: If you keep in mind that in many large German cities (such as Munich, Stuttgart and Berlin) it is hard to find an apartment, in particular if it is supposed to be affordable, I can imagine quite well that "living to the logical consequences that it is not worth the time to look for an apartment" could easily give him lots of sympathizers in Germany.
On the other hand Voevodsky would probably get in trouble with German law (Meldegesetz (https://de.wikipedia.org/wiki/Meldegesetz) - I don't know an "official" English translation of this word, but perhaps "registration law" might fit). But always keep in mind when talking about Germany, what Germans think and what the German laws say are two very different animals.
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Concerning your point
> There is no stigma against homeless people in your country?
monort's description of Voevodsky's lifestyle does not sound like the lifestyle of a homeless person. So the argument void. But to give nevertheless a point: I don't think there is a lot of a stigma against homeless people in Germany. The stigma is rather against things that accompany being homeless like drinking, rarely showering etc.
EDIT: To elaborate on the point that I don't think there is a lot of a stigma against homeless people in Germany: I (as an academic) actually know someone who was homeless for a longer time in life (at least 6 months, probably much more) and also had an interesting discussion about homeless people face in Germany with a homeless person who was begging for money when I was waiting for a train that was massively delayed.
I (American) have the same reaction you do. I think this is an incident where something is not properly explained so non-Americans think this is just some weird American thing.
The text " living and sleeping in the office is a terrible taboo and social stigma" is not phrased well. The issue with living at your office is much more due to liability reasons. If someone is allowed to live at their office, then the organization might be liable for anything that person does, or anything that happens to that person, even when not working. Also, as an organization it looks bad to have your graduate students / researchers be homeless, not to other grad students or researchers on an individual level, but in the sense that outsiders will react "I do not want to work at Harvard because they work their researchers so hard / pay their researchers so little that they have to live at their office."
This also happened about 25 years ago, when there was more of a stigma in the US for living an untraditional lifestyle. It's much, much more common these days for people in their 20s to live semi-homeless (e.g. in a car) and housing usually costs a lot more know, adjusted for inflation.
Voevodsky was too lazy to search for an apartment, so he lived in his office (at Harvard each graduate student gets a personal office) and slept on the roof. Unfortunately, the windows of dean office (Willy Schmid) had direct view at that roof. Volodya didn't adhere to the usual day routine (and didn't adhere to anything at all), sometimes he slept during the dean office hours. Some day Schmid looked through the window and saw a roof and Voevodsky was sleeping at the roof. It has to be said, that living and sleeping in the office is a terrible taboo and social stigma in America, so Schmid was outraged. Voevodsky was almost expelled, but everything turned out well, though he was forced to rent an apartment and he has lived there from then on.