Maybe a better advisor would have helped them find a research topic that engaged them? I really didn't care much about traffic. I cared about Chaos Theory and MDOT had free traffic data and DEC was willing to loan me some hardware. That's it.

I mean, I like traffic now. Back then? I was just meh... But it was something I could bite into and really see where Chaos Theory techniques could apply to understanding traffic. Which is to say, quite well - actually. But, I digress...

A great advisor really, really helps.

Doing a phd in machine learning and working at a high paying tech company is still a money losing competition due to the opportunity cost. Getting a masters and then working for 5 years gives you at least a half million dollar head start.

I like where your head is at. This is the type of math we should be doing.

On the other hand, someone has to do the PhDs in order to invent things like machine learning. That is also math we should be doing.

There is this notion (that I find quite convincing) that people tend to be overly optimistic as to their prospects (to become a successful entrepreneur/professor/etc.), and that leads them to decisions that are suboptimal for themselves (as they overestimate the likelihood of a big exit/tenure/etc.), but are good (optimal?) for society, because it encourages more people to take these huge risks, some of which do pay off.

> That is also math we should be doing.

There are things that should not only be seen in narrow economic terms, though. If someone wants to run their own business, or increase the stock of knowledge, or seek enlightenment in meditation retreats, that's perfectly ok, even if they don't strictly optimise their expected monetary payoff.

Lots of other areas where people are interested in machine learning and willing to pay good money. Biotech, pharma and medical, and oil/geology are just a few areas off the top of my head.