PhD is not strictly necessary, but the process and training that results in a PhD degree is.
Case in point, Freeman Dyson, brilliant mathematician/math-physicist, never got a PhD degree, but did research work all his life. Note, he was deeply embedded in the research community, and pretty much everyone he collaborated with, was a PhD or eventually got a PhD (meaning he went through the motions just like other researchers).
Final note, the process and training required to be able to conduct research is massively undernurtured, i.e., in my opinion, most PhD graduates are barely an iota better-trained than MS graduates these days. This is getting increasingly true as world population grows, and PhD diplomas get handed out willy nilly (a topic I could go on at for hours). In short, Sturgeon's law is in full swing.
> PhD is not strictly necessary, but the process and training that results in a PhD degree is.
I was just about to post the same. I just finished a master's in math (in fact, with additional coursework in physics and statistics I've almost completed two master's) and I don't feel ready to tackle outstanding math problems.
And the PhD students I knew were receiving a lot of help from their mentors as they learned how to tackle outstanding problems.
There's just so much to learn to contribute to research math these days, it's hard to imagine anyone learning it all on their own.
Freeman Dyson studied in very unusual circumstances and got more support than most PhD students. He was regularly playing billiard and discussing math with famous professors at age 17. From his collection of letters "Maker of Patterns":
>I arrived as a seventeen-year-old undergraduate at Trinity College, Cambridge, in September 1941. It was a great time to get an education, in the middle of World War II. The famous old professors were all there, but there were hardly any students.
>I have fixed up all my lectures now, they are: Hardy on Fourier series, Besicovitch on integration, Dirac on quantum mechanics, Pars on dynamics. The lectures are very select; Hardy has an audience of four, Besicovitch three, Pars four, and Dirac about twenty
Here's a video of him speaking about the PhD system, part of a great interview series: https://youtu.be/DzC1IRYN_Ps?t=98
(“It is an evil system and it has ruined many lives”)
Case in point, Freeman Dyson, brilliant mathematician/math-physicist, never got a PhD degree, but did research work all his life. Note, he was deeply embedded in the research community, and pretty much everyone he collaborated with, was a PhD or eventually got a PhD (meaning he went through the motions just like other researchers).
Final note, the process and training required to be able to conduct research is massively undernurtured, i.e., in my opinion, most PhD graduates are barely an iota better-trained than MS graduates these days. This is getting increasingly true as world population grows, and PhD diplomas get handed out willy nilly (a topic I could go on at for hours). In short, Sturgeon's law is in full swing.