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I have a question that comes up when writing mathematical problems.

Which of the following is correct:

The problem is well-posed

or

The problem is well posed.

I am sure the second is correct. However the first is used in all sorts of papers, books and Wikipedia.

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The hyphen means that the two words are acting as a unit. In other words, it is a choice between whether or not well is describing the word posed. If it is, then don't use a hyphen. Otherwise, put the hyphen.

There is no reason to use a hyphen because it is clear that well is describing posed--how is the problem posed? Well. Therefore, you should not use a hyphen.

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