[te_platt]

My oldest brother had a real love of mathematics and got a masters degree but never even applied to a PhD program. When I asked him about it he just said he was tired of working on other people's problems.

He had a quiet programming position in a large company that gave him time to work on personal projects. Among other things he volunteered at the local schools teaching "fun" math. I guess I'm just agreeing with you about finding something that inspires you and go with it.

[selimthegrim]

I don’t know what PhD program your brother was looking at but ideally candidacy committees won’t pass you unless you chose the problem or made it your own. Where your brother is right is that forming such a ideal committee is mostly politics.

[Eridrus]

I don't know about math, but in CS, a lot of funding comes from specific grants, so you'll be working on something related to what your advisor got grant funding for.

[QuercusMax]

Regardless of grants, etc., your general area of work is going to be based on what the faculty members' focuses are. But in any case, you'll probably still be doing your own sub-piece of some larger effort. You wouldn't choose an advisor at random, so this isn't really relevant.

I mean, if you're interested in astrophysics, you shouldn't go to a school where the Physics department is focused on nuclear physics!

[te_platt]

I think you are right on both points. There were more details and his answer was just a quick way to say:

He didn't care about the status of having a PhD

He didn't need a PhD to advance his career

He was having fun doing math stuff anyway

[proginthebox]

Selecting an approachable problem is also a skill that more experienced people have and often the younger people don't. Some problems are just not ready to be tackled because the field hasn't developed for it yet. It is a risk factor between choosing your own problem and floundering through the quagmire or getting help in choosing a problem you have confidence in solving in some years.

While I appreciate your brother's personal choice, to each their own after all. There is quite a lot of merit in your PhD advisor helping you in choosing a problem. That being said, good advisors provide students with an array of good problems out of which the student can choose one they are the most passionate about. This is what happened with me, I was provided with around 7 different choices to make. In the end, I chose 2 of them even though I wanted to chose 3 more but couldn't because of lack of time.