Exactly. Getting a PhD means 1. taking some advanced math classes 2. hanging around some like-minded people for a few years 3. solving a problem or two, big en

Exactly. Getting a PhD means 1. taking some advanced math classes 2. hanging around some like-minded people for a few years 3. solving a problem or two, big enough to add up to a dissertation 4. publish, with professional help on learning to write 5. getting teaching experience Except for the last item, all these are things every aspiring mathematician would need / want to do anyway. Now, not everyone wants to teach, and at some universities TAs are overburdened. But certainly not all, and I'd argue that teaching experience in a well-strucured programs can teach one a lot of useful communication skills. Working on your own means you can get #3. Not everyone needs #4, and you can get some of #1 online or from books (but harder to find people to talk to). So no, a PhD isn't necessary. But most of the things one would do to get a PhD certainly is useful. Full disclosure: FWIW I have a PhD and work as an academic mathematician.