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The phrase "work on a problem" is grammatically correct and can be used in written English.
It is commonly used when discussing ways to solve a difficult or complex issue. Example: "I have been working on this math problem for hours and I still can't figure it out." or "The team is working on a problem with the new software and hopes to have it resolved by the end of the week."
Exact(31)
And as more research teams around the world work on a problem, the odds shorten that at least one will fall prey to an honest confusion between the sweet signal of a genuine discovery and a freak of the statistical noise.
"Make a tool to work on a problem that is currently unknown".
I don't think I ever asked him to work on a problem.
But, she added, "It doesn't bother me" to work on a problem suggested by a machine.
The vendor for Cornell's e-list service (Lyris) continues to work on a problem affecting calendar invitations from Office 365.
They don't work on a problem long enough to uncover its root cause they just make a gut-feel diagnosis.
Similar(29)
When working on a problem, humans can have an "eureka" moment when they glimpse the problem solution.
Research has proven that the brain keeps working on a problem, even if we have moved onto another activity.
The classic work-on-a-plane problem?
As first mentioned in the introduction, Park et al. [6] recently have worked on a similar problem.
I enjoy that feeling of being completely lost as I work on a problem--my mind struggling to make sense of the few bits of information that I have been able to obtain.
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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