British mathematician and logician Augustus De Morgan has De in his name. But the French physicist Louis de Broglie has de in his name.
Why so? Something to do with being French or British?
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This is a matter of style. In general, we capitalise the particles de, du, von, van, etc, if the owner of the name does so. The style guide of the (British) University of Sussex says:
Observe that certain surnames of foreign origin contain little words that are often not capitalized, such as de, du, da, von and van. Thus we write Leonardo da Vinci, Ludwig van Beethoven, General von Moltke and Simone de Beauvoir. On the other hand, we write Daphne Du Maurier and Dick Van Dyke, because those are the forms preferred by the owners of the names. When in doubt, check the spelling in a good reference book.