1. Van Gogh devoted himself to painting pictures,

Question

2. van Gogh devoted himself to painting pictures,
3. Do you know about van Gogh.
4. Do you know about Van Gogh.
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Do we have to capitalize 'van'?
Which expressions are correct?

Answer 1

Capitalizing the “V” is standard in English, yes.

All are okay as long as you put question marks at the end of 3 and 4.

Answer 2

1. Van Gogh devoted himself to painting pictures,
2. van Gogh devoted himself to painting pictures,
3. Do you know about van Gogh?
4. Do you know about Van Gogh?

Answer 3

In the Netherlands, do they use #2 and #3?

Answer 4

I really don’t know.

In the US, when I see two-part names, both parts are usually capitalized. The only times I see lower case are in some Spanish names. Here are a few examples:

Van Buren
Di Carlo
Le Carre

But ~~> de la Fuente