I faced this problem when interpreting the transcript of records today. The subject is: "European History of the second half/part of the XX century till today" So is it better to say "part" or "half"?
P.S. does "till today" sound all right?
Suppose that we believed that an important event divided a century into two parts and those two parts were not of equal length. Examples might be the Stock Market Crash in 1929, Yuri Gagarin being the first man in space in 1961, or Margaret Thatcher becoming Prime Minister in 1979. We then have the century divided into two parts, that are not halves.
If we literally mean the second 50 years (or some approximation thereof), then second half is surely preferable.
Both are correct, but second half is the more common expression:
- Ngram second half vs second part of the century.
A more appropriate sentence could be :
Echoing the comment from @WS2:
The sentence you've presented is confusing two ways of expressing time. The phrase, "second half of the XX century" (likewise, "second part of the XX century") is describing a duration of time, while "till today" is describing a discrete instance of time--so it doesn't make sense semantically to say "second half of the XX century till today", regardless of your word choice.
If you're trying to convey the time period from XX50-present day, just say so: e.g. "European History from 1850 to present day".
Let's not over think this. All the proposed phrasings are correct. Some are clumsy, but all are correct.
We've entered the realm of subjective preference. I would vote for "Second half" because using "fuzzy" terms when speaking about a broad swath of time is more convenient. (It's the same reason historians use "circa".) Using "half" over "part" is a bit more clear and requires fewer details to make your point.
Go with "Second half".
RE: Your p.s...
When I was teaching history at a local uni., I read pounds and pounds of papers that would all say "until present day", "up until now", or some other such end-of-time-period phrasing. I hated them all.
Let me ask you this... do you have to close the time period to which you're referring? Do you specifically have to exclude the 14 years since the turn of the century? Will your readers really be puzzled if you don't close your reference? If we're talking half-centuries, you're already generalizing. Your point will almost always be made better if you just exclude closing your time-period. E.g.: "In the second half of the 20th century, we discovered that littering jungles with non-reclaimed land-mines is a bad thing." It's highly unlikely anyone would be upset with a soft definition of your time period. Focus on the point you're making, don't worry about the nit-pickers and date-watches.