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The phrase "breakthrough by" is correct and usable in written English.
You can use it when you want to discuss the accomplishment of a goal or achievement. For example: Scientists have recently made a major breakthrough by developing a vaccine for the coronavirus.
Exact(60)
Breakthrough by Hayes There was another rookie breakout today.
His rhetoric was a breakthrough by way of synthesis.
South Africa might have wanted/expected a breakthrough by now.
You once mentioned that you had a stylistic breakthrough by writing Dr. Seussian-type poems.
Last week, astronomers announced that they had made a giant breakthrough by finding something small.
That show was seen as a breakthrough by many of the music's followers.
The breakthrough by the French film comedies this year comes despite strong competition from American blockbusters.
Her music hasn't changed since she made her international breakthrough by accompanying mornas with acoustic instruments.
The breakthrough by women is significant because engineering is such an important profession.
Then it was the great leap forward, which aimed at making an economic breakthrough by means of mass mobilisation.
Shakib al Hasan provided the breakthrough by trapping Barresi lbw and Razzak soon saw off the pinch-hitter Mudassar Bukhari.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com