And it seems like bashing high education is the cool thing to do nowadays.
It seems to be particularly common around here. Perhaps because most of the people around here have degrees in CS, which is something relatively easy to self-teach. If you hang around on a forum with a bunch of mathematicians or molecular biologists I doubt you'd be hearing the same "blah blah, university is useless" memes.
By mathematicians, do you mean the tiny fraction of people with math PhD's employed as math profs, quants or "the machine learning guy"?
Or do you include the much larger set of mathematicians who couldn't find a job as mathematicians, and now work as high school math teachers, community college adjuncts or business analysts?
I'm a member of the former set. Most of the people I went to school with are members of the latter. School was fun, but no one is under the illusion it was a good career move.
Are you saying mathematics teachers shouldn't require a degree in math in teach high school mathematics? That a student who have recently graduated is qualified enough to teach the year below him? That a business analyst would do a better job without a major in statistics? Community college adjuncts who teach math don't need anything beyond high school math classes? If not then I think you were beside the point.
University is definitely useful for at least some subset of the population.
You don't need a PhD or even an MS in math to teach high school/CC math. The business analyst, for the most part, doesn't need to know math beyond means and standard deviations. Note: I'm interpreting "mathematician" to mean "math Ph.D." or "person who does/did research in math", which is typically the way the term is used.
Most people with a math degree don't use even a small fraction of their training. I do, but I'm in the minority. (Also worth noting that most of what I use I didn't learn in school.)
We started with 11. One left in the first year. 3 more failed to graduate after 4-7 years. 5 people got postdocs. Of the 5 with postdocs, 2 left the country (one involuntarily), I left academia to work in the private sector, and one I haven't kept in touch with. So at most, 2 are on the tenure track in the US [1].
This was Rutgers - at Princeton, the ratio would be a bit better, at NJIT it would be worse. Don't even ask about podunk state.
It's a shitty career path. Unless you are fantastically good, don't waste your time.
[1] My adviser told me I could have been on the tenure track if I wanted to. Since I didn't put it to the test by applying for such jobs, I won't claim it as true.
No degree will guarantee you a job. Professional degrees (law, engn, accounting, medicine etc) will come close, if you want to work in a profession.
Every other course will just give you a better chance of getting a job, and help you perform better once you get there. A math grad can solve all kinds of problems that other people will just shrug their shoulders at. That's always useful.
Academia in general is a dangerous career path though. Too many people on the ground floor (i.e. every undergrad who can't think of a better thing than grad school), too much glamor keeping them there, very bureaucratic organizations, and a complete mismatch between work (research) and funding (students).
Physics is probably worse. In math, you are either in the game or eliminated. In physics, you can eliminated but still doing grunt work for low pay in someone's lab.
I'm surprised you use Mathematics as an example of a field that's hard to self teach. I actually think Mathematics is one of the easiest fields to self-teach in - you really only need books / video lectures, some paper and pencils, and your brain. It's even less demanding than programming in that sense!
There are also several famous self-taught Mathematicians.
Programming is easy to self-teach because you can immediately verify whether you've got it right -- compile and run, see if it works.
Mathematics is harder to verify, though easier than (say) physics because you can test yourself by proving theorems. However, your proofs might be wrong because you're under some misconception. And, as the other response said, it requires an incredible amount of discipline.
Ramanujan was probably the last great self-taught mathematician, and I'm sure most would say he could have been a helluva lot greater if only he'd been sent off to Oxford at sixteen instead of twenty-seven.
The fundamental things being taught to math majors are how to distinguish between valid and invalid reasoning, and how to produce arguments (proofs) that contain only valid reasoning.
For better or worse, the way these skills are taught is to pick a couple of subjects (like analysis, algebra, or number theory) and demand that students produce dozens of proofs, which are then mercilessly picked apart by professors and grad students. That negative reinforcement is combined with lectures that (should) consist entirely of good examples of mathematical reasoning, at that's an Education.
(The fact that students may also pick up a few facts about analysis or algebra is just a bonus, it's not the main point.)
You can certainly get the good examples from books and video lectures, but not the experience of having your arguments criticized by experts. This part is crucial -- it's just as easy to miss the flaws in your own proofs, especially your early attempts, as it is to miss the flaws in your own programs. (Worse, it's perfectly possible to reach a conclusion that's correct through an invalid argument. You're wrong, but you'll never be able to find evidence against your conclusion.) Feedback from experts is essential.
You also need lots and lots of self-discipline. Of course, that is true for serious study in any field, but unlike many fields no one would call a mathematician someone who wasn't serious about it.
"Which is ye surest character of a true Mathematical Genius, learned these of his own inclination & by his owne industry without a teacher."
— Isaac Newton
In many respects, math has a totally unfair advantage over every other subject you could possibly study in college because it can be learned almost without needing any other people. Well, living people that is, as you do need the books of long deceased thinkers. (I'd say this also applies to philosophy, and hardly anything else). You just need to be willing to spend enormous amounts of time alone in contemplation reading.
The sole cause of man's unhappiness is that he does not know how to stay quietly in his room.
— Blaise Pascal
There's also a very limited social component layer such as you would find in medicine, law, politics, economics, et al. To become a doctor, or any kind of "professional", sure, it requires a massive social apparatus on top of a high degree of actual learning. You have to have connections, know the right people, say the right and popular things to them, be supported and credentialed by the leadership and their agenda, and basically imposture one's self into mimicking whatever behaviors and traits are specific to and dominant in whatever professional field you're studying. Eventually your identity morphs into this set of learned behaviors, and it's almost entirely built upon your position in some type of social hierarchy.
Not so with math. You either know some theorem and the proof, or you don't. How much you know and how advanced you are is entirely dependent upon what you have worked through on your own. What new stuff you can create only comes from what old stuff you already know. None of this has anything to do with interacting with people. Sure, you can benefit by talking to other mathematicians, attending lectures, conferences, teaching others, etc, but at the end of the day, at some point, you still have to sit down and learn the material by yourself. And if you don't do that, it doesn't matter how much of a social butterfly you are—you can't be a mathematician.
No man is an island, but I imagine a Robinson Crusoe type figure would have no such problems becoming a mathematician on a desert island, given enough math books(and some kind of Internet connection).
Well, it was a lot easier to be self-taught in Newton's day... there wasn't that much to learn! You could read Euclid and you're be mostly done. Newton alone probably made learning mathematics at least three times harder during his career.
Anyway, if you're trying to make me regret choosing mathematics as one of my examples, y'all have won. I see no molecular biologists have popped up to advocate for self-taught molecular biology.
I've read that the last Universal mathematicians we've had were Chebyshev and Poincare, who could claim to know "all of math", and who were active in research in nearly every sub-field. It's been over 50 years since their time, and much like the fabled Renaissance Man, that frontier is now closed.
Perhaps because most of the people around here have degrees in CS, which is something relatively easy to self-teach.
Except that it isn't. The problem is that computer programming is easy to self-teach (indeed, that's pretty much the only way it can be taught) and many people confuse computer programming with computer science.
Also MBA degrees are bashed periodically; but I don't think engineering and medical school degrees are.
Edit: and for the Humanities and MBA, the reasons I usually see for bashing are more like "not worth spending the time to learn" than "easy to self-teach".
It seems to be particularly common around here. Perhaps because most of the people around here have degrees in CS, which is something relatively easy to self-teach. If you hang around on a forum with a bunch of mathematicians or molecular biologists I doubt you'd be hearing the same "blah blah, university is useless" memes.