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Is it possible to become a researcher on my own? How do I replicate the grad school experience through self study or being an autodidact?

I came across these two sites: How to Become a Pure Mathematician (or Statistician) and How to become a GOOD Theoretical Physicist.

I came across such a thing on CS Theory Stack Exchange too.

Is it true that if I follow actively what has been given in these sites I’d be a physicist or mathematician or an independent researcher? I don’t know about publishing papers. At the best, I can access arXiv and Google Scholar on my internet connection. I don’t think I’d be actively ‘contributing’ to research or advancing the frontiers of knowledge. At the best, I guess I can try answer questions on SE sites.

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The short answer is: you can't replicate it.

The longer answer is: yes, you might be able to talk intelligently to someone who has a background in the field, but as previous poster mentioned, the reason why one goes to grad school is not just to learn the material, but to have access to resources. These resources are physical, but they are also mental. Part of what grad school gives you is access to people who have extensive knowledge in the field, can help direct you in your research, as well as provide crucial feedback. Without this one-on-one and group interaction, it is IMO impossible to become a researcher on par with a professional academic.

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Is it possible to become a researcher on your own? In theory, yes, but in practice there are many obstacles for unaffiliated scientists without PhDs. It also depends on what you mean by independent research.

First of all, Gerard 't Hooft spends a significant amount of space on that website encouraging aspiring physicists to go to school. He's not advocating independent science without formal education. The PhD has been designed to train people to be researchers, and it's difficult to obtain that kind of formal training without an equivalent experience. You can read all the books in the world about theoretical physics; that doesn't make you a researcher. That just means you know a lot about theoretical physics. Researchers don't just consume knowledge; they produce it using a specific set of methodologies and communicate it to other scientists in pretty specific ways.

Second, there are structures in place that make it difficult even for independent scientists with a PhD to do research. First, there's the cost of the work itself. Theoretical physics and pure math may be pretty inexpensive without the need for fancy equipment, but you'd still need a small budget - and a salary to provide you with the time to do the research. But nobody is going to pay or give a grant to an unaffiliated non-PhD holding person to do theoretical physics research. Universities aren't going to hire you as a faculty member. The PhD is the qualification for that. And part of NSF grant evaluations is the environment in which you do the work. So you'd have to hold another full-time job to pay the bills, limiting your time to do research. Then there's the background reading. Academic journals are very expensive, and most scientists access them through subscriptions their university or institutional library has paid for. I know physics has a tradition on arXiv, but not everything is on there - especially the foundational work. Speaking on the lecture circuit will also be difficult without an institutional affiliation: people won't invite you to speak places, and submitting to conferences as an independent scholar will likely be a challenge.

So contributing to the formal conversation of science is going to be nigh impossible without the formal training of a PhD program and an apprenticeship with a practicing physicist (which is essentially what it is). If you wanted to do science as a hobbyist, there's more possibility for that. You could blog about your findings, or post them on arXiv yourself, or find some other way to disseminate. If you live nearby a university, you could audit graduate classes and attend seminars and lectures. You could read a lot on your own. It won't be the same as a career as a researcher, but only you can determine what level of participation is acceptable for you.

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