Is It Possible to Do Mathematics Research Without a PhD?

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Aiming to study mathematics and engage in research without formal university enrollment is feasible. Individuals can dedicate 4-5 hours daily to self-study, leveraging resources like online courses, textbooks, and academic papers. Previous experience, such as passing actuary exams, provides a solid foundation in undergraduate-level math. It is possible to conduct mathematical research without a PhD, as many researchers begin their work prior to obtaining their doctorate. Engaging with online communities and utilizing educational websites can further enhance learning and research opportunities.
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Good evening,

I really want to study mathematics, to learn to do (at least some level) of mathematic research. I am at a point in my life where I will not be able to pursue these studies in a university because of my commitment to the court calendar. I could devote 4-5 hours a day to study, but not during the time when classes are in session. I have passed several actuary exams and have a proficiency in undergraduate level math. To become a mathematician, to eventually make some contribution to the field (even many years from now) is a dream of mine. Is there a non-traditional way to pursue a path to being a mathematician? What would you recommend as a good course of study for the next year?

Thank you for your advice and input.
 
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Thank you!
 
Is it possible to do research in mathematics without a PhD?
 
NYStateofMind said:
Is it possible to do research in mathematics without a PhD?

Yes. How do you think people get a PhD.
 
Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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