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
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.
I am not merely allowed, but encouraged to work on whatever research I fancy. It's just that the school won't throw resources at me willy-nilly to do it.
Worse, I have to deal with my contracted teaching load first and do the research on the side. If I was at a prestigious, research institution that teaching load might be half-time or so, but I'm at a small, state university and the teaching load is 12 credit hours per semester.
So I am encouraged to do all the research I can with no money, no space1, no equipment2, no assistants3 and no release time. Thus the need for grant money.4
What the fellowship in question gives the recipient is not permission, but the resources to spend their time working on their project
1 Actually, with the remodel the state has recently funded this will soon be "very little space", yahoo!
2 Well, IT has been willing to give me an obsolete computer to use as a platform for the programming task that is stage one of a student project. But when a single-core, 4GB RAM, 500 GB storage computer with keyboard, mouse and monitor is a big step in equipping your corner of a shared lab you know things are tight.
3 I do have a number of in-major students who are interested in working with me, but that is more of a teaching obligation than a load off my shoulders because they still have so much to learn. But they can do a little bit of tedious stuff without close supervisions. And of course, they get more independent the longer we work together. And then they get a industry job or into grad school and I send them on their way and start looking for a new prospect.
4 So far this has really meant guiding the students through applying for the school's student research grant process and turned up a few hundred dollars a couple of times.
No, but subject to other time constraints. She can probably use the grant money to pay off the need for teaching any classes for a few semesters, and focus on nothing but her chosen research area. Perhaps the comment would be clearer replacing "exactly" with "exclusively".
The other answers here are covering most of the details, but bullet point version of the answer is:
This is why all the professors I know work 80 hours weeks!
A professor of philosophy can work on his research without a grant. (If necessary, he can buy his own paper and pencils...)
But to do her research, a high-energy physicist requires a multi-million dollar lab, that costs a lot to keep it running. So unless she is really rich, she does require funding.
There was in the news a few years ago a story whose details I vaguely remember. A microbiologist had retired from the university, and then set up in his basement a lab to continue his research. But when the authorities found out, he was in big trouble. Apparently his premises did not have the licensing to house work with pathogens, or something.
A professor can always choose to work on a project without funding. Economically it may not be ideal, and their University may not thank them for it; it's also hard to do anything that requires much expenditure (obviously), but it can be done, and it is done very often. Furthermore, a lot of significant work is done pro bono; IPCC lead authors, for example, are not paid for their work specifically on IPCC tasks, and at least one funding agency (National Science Foundation) expressly forbids the expenditure of NSF funds directly on IPCC activities. Note that this is different than NSF funds being used to fund the science that goes into the IPCC reports: this clearly happens all the time. An IPCC lead author cannot, however, write an NSF grant (or claim a month's summer salary) for the purpose of supporting their time and effort as an IPCC author.
Doing any extended research without funding is very difficult simply for practical reasons (unless the professor has an independent income!). When Maria Chudnovsky says that the MacArthur will let her work on exactly what she wants to work on, she's referring to the very valuable freedom the MacArthur Prize affords of independence from grant writing and reporting, and from the unfortunate fact that funding agencies cannot and do not fund every excellent idea that comes in over the transom - there are too many good ideas and not enough money for that. Agency programs also develop priorities, some explicit, some unspoken, that steer their funding decisions. All of these complications fall away - for a few years, anyway - with an award like the MacArthur Prize.
Other answers here are useful but incomplete and I believe actually miss the main thrust of what the original quote is referring to.
Despite wide support to pursue research as an academic, there are limitations on the amount of time most academics can commit to their research. A primary way to expand the proportion of your time that you can devote to research, as well as to resource projects that could not otherwise be undertaken at all, is to apply for research grants, primarily research grants external to your employing institution.
However, the vast majority of such grants are awarded for specific research projects or fairly defined research programs. Funding agencies virtually all require these to be defined to a fairly specific degree of detail in the competitive application process. When funding is awarded, it is an expectation of the funding agency that the research that is undertaken will be the work that is funded, and there are typically also reporting mechanisms that can be used to monitor this. While the specifics will vary between disciplines, such an approach by definition leads to relatively 'monolithic' research projects, where the entire edifice must be at least sketched out in advance in some detail, thus tending to direct funding to more clearly defined work and to methodologies where such an approach is possible. Applicants further may feel constrained to propose the focus of the research work to a topic they feel is more likely to be funded, and to using methodologies that they feel are more likely to lead to a successful outcome in the competitive application review process. Moving away from your mathematics example to health research, for instance, applicants may feel compelled to propose a randomized controlled trial to investigate an intervention, rather than using other approaches (e.g., a single case experimental design series) as randomized controlled trials are still perceived as the 'gold standard' even if other approaches may also have merit.
When funding such as the MacArthur Fellowship is awarded to a person, rather than a project, the person is free to pursue research in whatever way they deem best—rather than being constrained by having to pre-define their approach and filter this to maximise likelihood of being funded.
