The term "greatest" is ambiguous and ill-defined. It can mean most popular, most financially successful, or most critically approved.
Any information gathered about this question is subjective
To answer this we need to know who "he" is in your question.
"The Metamorphosis" is one of the best known works by Franz Kafka. The novella was originally published in 1915 and is often considered one of the greatest works of fiction of the 20th century.
Different people would interpret this differently, and there is no generally accepted rule (as the fact that you have asked the question indicates). Of the two suggestions you offer, I would prefer the former. However, to avoid ambiguity I would reword it altogether and say something like 'around the year 1900'. Sometimes the context makes it clear - if you have been talking about the 1890s then say 'at the turn of the 19th century' it will be obvious that you mean 19th to 20th. (You could drop the '19th' altogether in that case.) Other constructions may be clear but they read a bit clumsily: 'the turn of the 19th/20th century'; 'the turn of the 19th/20th centuries'; 'the turn of the 19th to 20th century'. Better to reword, I think.
The origin of plagiarism is early 17th century, from Latin plagiarius 'kidnapper' (from plagium 'a kidnapping,' from Greek plagion) + ism.
The plural form of the noun century is centuries.
Leibniz was one of the two greatest mathematicians of the 18th century.
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SportsCentury The Century's Greatest Athletes - 2000 was released on: USA: 1 January 2000
the 19th century
WWE The Greatest Superstars of the 21st Century - 2011 was released on: USA: July 2011
Traditional African art had had the greatest influence on 20th century sculpture and painting.
It would depend on what research you were involved in and during which century.
Edward Burger
James Joyce
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Albert Einstein.