Are professors not allowed to work on what they want to work on without a grant? In this video on mathematician Maria Chudnovsky, she says "with the MacArthur Fellowship, I'll be able to work exactly on the problems I want to work on."

Are professors not able to work on what they wish to work on without some sort of grant?

Do professors need a grant before starting research?
No, a professor doesn't strictly need grant funding to start work on an idea (and it's common to do some preliminary work on an idea to help get grant funding for that idea). However, grant funding helps professors to


support graduate students and/or postdocs,
pay his/her own summer salary, if the university only pays 9 months of salary a year,
be promoted/get tenure in departments where there is an expectation of bringing in funding,
sometimes buy out of teaching obligations


Thus a researcher who wants those things, needs grant funding.

Having no-strings-attached grant funding that comes with no obligation to research a particular area gives a professor freedom to do those things, and still spend their research time and effort on whatever they want.