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To make progress. After a months-long stalemate, we've finally made headway in the negotiations. I'm going to wait to take a break until I make some headway on my project.
Advance, make progress, as in We haven't made any headway with this project. This expression, first recorded in 1887, uses headway in the nautical sense of "a vessel's forward movement."
COMMON If you make headway, you make progress with something that you are trying to achieve. A spokesman said the two sides have made headway on some security issues. It appears that the police have made little headway in the investigation.
make ˈheadwaymake progress, especially when this is slow or difficult: We are making little headway with the negotiations. ♢ The boat was unable to make much headway against the tide.
make headway, to
To advance. This term transfers the original meaning of headway, the forward motion of a ship, to any kind of progress. Augustus Jessopp had it in Arcady for Better or Worse (1887), “Rarely, except in the open parishes, do the demagogues make headway.”
See also: make