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The phrase "are the important problems" is correct and usable in written English.
It can be used when discussing or identifying significant issues or challenges in a particular context.
Example: "In our meeting, we need to address what are the important problems facing our project this quarter."
Alternatives: "are the key issues" or "are the critical challenges".
Exact(2)
"I look at what are the important problems: energy, healthcare, water".
Dynamic responses of structures due to earthquake excitation are the important problems in engineering, thus, the information concerned is plenty.
Similar(58)
"But right now those are not the important problems," he said.
It's about the important problems that have to be solved for humanity to have a bright future, Musk said.
Often the problem we are focused on isn't the important problem.
Road and traffic accidents (RTA) are one of the important problems in India.
Dynamics are the most important problems in the microgrid operation.
1. "Honest people have differences of opinion as to what they believe are the most important problems facing this country.
Prediction of plate behavior in large deformation is one of the important problems in plate theories.
A recent CBS News poll found that 54% of adults think the economy and jobs are the most important problem the U.S. is facing today.
Many evolutionists suggest that epistatic interactions are the most important problem of adaptive evolution.
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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