Dear NT:

You wrote:
> John is the first man to have won that prize.
>
> This means that no other man won that prize before John, but does it imply
> that no other man has won that prize since he won it? Can the sentence be
> used if other men won that prize after he did?
>
Yes. Indeed, that is what it is saying. If no other person has won the prize, you would say, “John is the only man to have won that prize.” If something is “first,” that generally means someone is second, unless you are describing a rare or recent feat–e.g., the first person to circumnavigate the world solo, but he is also the only person to do it.