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Free sign up"open problem" is correct and usable in written English.
You can use this phrase when you are referring to a problem or issue that has yet to be solved or resolved. For example, "The development of a new vaccine to fight the virus is proving to be an open problem."
Dictionary
open problem
noun
A problem that has been posed in a field of study such as mathematics or theoretical computer science, but whose answer is not yet known.
Exact(60)
This settles a long-standing open problem.
It remains a major open problem if better bounds hold.
Giving a complete analysis remains an open problem.
Robust mobile robot navigation is an open problem.
The criterion also allows an open problem by K.-H.
However, the general flexible case is still an open problem.
In the present paper, we resolve this open problem.
Silvey identified finding such an inverse as an open problem.
Whether this hierarchy is strict, is an open problem.
Replica placement in these networks is still an open problem.
However, he left public key cryptography as an open problem.
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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