Suppose you can't ask for anyone's help with anything at all in your research, but you'll be able to get any online/offline book/material and funds you want to study.You have been given a topic to research, is it possible to complete your research producing some acknowledgable result?
The gist of the question is "Is Phd something managable by individual efforts?"
Someone else has to give the PhD. If you could give it to yourself, it would not be worth much. This is organized such that university award PhDs. So without a university you cannot get a PhD. This typically involves getting an advisor from that university.
This makes sense: the process of doing your dissertation research and writing it down with the help of your advisor is the learning experience. We don't expect a student to know everything before they start and all we need to do is test that student. It would be an extremely inefficient test if it takes 3, 4, or more years. Instead we expect them to need to learn a lot.
So in short, no this cannot be done alone. At the very least you need an advisor.
To be clear: at least in modern mathematics, whether or not such a thing is "possible", it's not advisable. It wouldn't set you up for anything good subsequently, unless you are ... ahem ... "the chosen one". Etc. That is, even very clever young people can benefit (woof, to say the least...) from guidance...
Anti-ironically, if you think you cannot benefit from any inputs from more senior mathematicians... ah, well, "there's your problem".
There is such a thing as a PhD by publication. This means that instead of the traditional model where a PhD candidate works with an advisor from the beginning of their PhD project, the candidate instead applies to a university to be examined on the basis of research they have already published. In principle, the already-published research could have been done "on your own" without an advisor; whether that is "manageable by individual efforts" depends on how literally you take that, since it would at least be very unlikely to complete enough research without ever writing an "Acknowledgements" section.
For example, at the University of Portsmouth you can apply for a PhD by publication by submitting "peer reviewed academic papers, complete books, chapters in anthologies, or equivalent materials accepted for publication, exhibited or performed" plus a 5,000 to 10,000-word commentary tying it all together. You still have to pass a viva voce examination, and I would guess (or hope) that the university assigns a supervisor who can help you with the commentary and to prepare for the viva. Nonetheless, the actual research of the PhD project would have been done "on your own".
One of my former colleagues took this route as an already established academic, earning his PhD on the basis of 10 years of research which he had completed while employed as a senior lecturer. As far as I know, he did not have a PhD supervisor while conducting that research, though I'm sure he benefited from working in an environment where he could learn from other researchers.
There is also such a thing as an honourary PhD, but this isn't a thing you can plan to earn.
In addition to Maarten's answer: Whether you would be able to produce quality research worthy of PhD entirely on your own depends heavily on your research area. For instance, it is possible in math, theoretical physics, theoretical computer science, philosophy. (By the time I got to graduate school, I was working on research entirely on my own, without any input from my PhD advisor. But I needed help and direction when I was an undergraduate student. I know many professional mathematicians who had similar experience.) It is impossible in lab sciences, for instance, in experimental physics, chemistry, biology, medical sciences.
Edit: One of the most remarkable modern examples of working in isolation that I know is somebody writing a PhD thesis in Complex Analysis while serving 2 years in the military after graduating from college. (The person was lucky to work in the logistics branch of the army.) The person defended his thesis, of course, only after finishing his army service.
My brother-in-law did that. He worked for years as an independent engineer/consultant in industry and ultimately created theoretical models, calculations and did measurements which were published, and then combined into a PhD.
This is very dependent on the area your PhD is in. You cannot do experimental high-energy physics on your own but anything industry-related or theoretical is conceivable.
Obviously, someone needs to be your thesis director (the "sponsor" of your PhD at an institution) and the institution must be willing to accept your PhD project and manage its lifecycle (submission, defense, ...)
Proving you can do research autonomously is only one part of a PhD, i.e. theses are submitted in partial fulfilment of the requirements for a degree. In addition, many PhD candidates are ipso facto working on their own, rarely seeing their advisor/thesis director.
An academic degree is a form of recognition granted by an institution, and I know of none where you can get a degree without being first registered in a program. In the case of a PhD, the program requirements, in addition to the thesis, will often include courses and seminars so the candidate is exposed to the current trends and ideas in the field, either as background material or as state-of-the art concepts. Part of the requirements is that a candidate should have a sufficiently broad knowledge and demonstrated sufficient mastery of their research area so the contents of the thesis are relevant to others and actually advance knowledge in the field. After all, if you don’t know the field how can you move it forward?
I feel what you are asking is a bit like: can I become a commercial pilot on my own? You can learn to fly on your own, but no serious airline will certify you as a company pilot unless you learn a lot more than just operate the aircraft.
