Nothing good will happen: a mathematics professor can teach 3 courses per semester. The tuition for a 3 credit semester course is about 600 bucks (well, that varies but it is not an atypical figure). Assuming we pack 100 students into one class, the revenue is 180,000.

The football season ticket at the MSU Spartan stadium costs 300 bucks. They boast that they have steady sales of 60,000 per season. The revenue is 18,000,000 (not counting one game ticket sale revenue, side events, etc.)

Moral: one football coach is worth at least 100 math professors. Besides nobody really understands what those crazy nerds are really doing and the subject they teach is boring, incomprehensible, and has nothing to do with the everyday life of 99.999% of the population. Compare it to the breath taking football games, which attract throngs of people, be it sunshine or rain, and keep even more glued to the TV screens every evening.

Nah, Richard, if we let the market forces in, we'll just lose our jobs: nobody really needs a PhD to teach that "domain is x, I repeat, x; it is not y, which is the range!" and "to differentiate, put the power p down as a factor and reduce it by 1 in the degree of the monomial", and all those fancy graduate courses are run at loss, not at profit.

Some of us will survive doing consulting for those few industries that haven't moved to China or India yet. The rest will either leave the country, or die out as professionals.

Physics is a huge part of gym, as is biology. Not sure about chemistry, but I think simple logic alone should get science teachers at least paid equally. Who wants a bunch of kids running wild without a clue of the forces acting on and in their body?

I agree with fedja.Market forces should not control us(I am just a school student but I know that someday I shall be in a position similar to fedja).The point is fedja has summed it well when he implies that common people have no idea of what we are doing and would not appreciate what we do.Market forces will wreck havoc with our job security and destroy mathematics as a whole.

I shall provide an example.The various upheavals in the USSR affected economy, sciences and everything with the exception of mathematics(Well, our brains are our labs, aren't they!) for the simple reason that the dictators didn't understand it properly.They found it harmless.Now, in a capitalist economy the same is true except that if the market had the power to, it would have thrown fedja and prospective professors out of their jobs as what they do is not "useful".

You're talking about college football coaches, not middle and high school gym teachers. You're comparing apples and oranges here.

Besides, college football isn't a market, either -- ask the players. In a real market setting, what you're calling "college football" would disassociate from schools entirely. Instead, the schools exploit the free labor of the players to subsidize administrative positions and extract donations from alums. It's quite a racket.

As for the college situation, I know this may be heretical to say, but maybe it wouldn't be a bad thing if fewer people were studying some of the things they're studying. There are way too many people racking up way too much debt pursuing useless degrees. If the schools themselves had some skin in that game (i.e., make them eat some of the student loan losses), I think this might be different. At the very least, they might have some incentive to give some guidance. Although they may simply be incapable of it.

I'd also wager that the vast majority of high school football teams are heavily subsidized, and are not funded by "market forces" like ticket sales. Take away some of these subsidies, and an awful lot of these teams would disappear. Considering the incidence of head injuries in the game (and I'm a big pro football fan, not a hater), I think shutting down 50-70% of high school football programs (well, outside of Texas) might be a very good thing.

Well, Richard, I'm just talking about the setting I am familiar with . True, I project my observations from one setting to another without providing sufficient justification but I don't think it is a completely ridiculous projection.

If you want me to be more serious, the "market forces", as I see them have 3 main points:

1) The philosophy (meaning of life, whatever) is given by one sentence "dollars now".

2) The complete moral code is given by "loss=bad, profit=good".

That would be still not so terrible if not for the third principle

3) The future is discounted at the rate of 3% per year or so.

What the last thing really means is that if we have an option to double the profits for the next 20 years and burn the planet down afterwards, it is a good thing to do. We cannot double the profits yet, just to raise them by about 10%, so we sort of care of the next 60 years but the time beyond that is of little value for both the market and the human being as a biological entity, so nobody seems to really mind if the civilization ends a century later. I do not argue that dictatorship or other kind of full government control is much better: the corresponding three principles there (substitute "power" for "dollars" and increase the discount rate to 6%) are even worse. Still, it is naive to use "free market" as a universal solution. It is efficient for the distribution of tangible consumer goods but that's where its usefulness ends.

Schools and Universities deal with upbringing the next generation, which will kick in in 15 to 20 years from the moment the education process starts, i.e., somewhere on the very horizon of the things the market cares of today. The remote profit one can get from that future generation discounted according to the standard exponential law barely offsets the expense incurred during the upbringing. The reason we care about the children in general and children education in particular is entirely orthogonal (if not opposite) to the market interests. The problem is that the sexual desire and motherly instinct are good enough to produce children in (more than) sufficient quantities but aren't nearly half as good to ensure their proper mental development. The veneer of intelligence is still rather thin and needs a lot of effort to maintain. What adds to the difficulty is that you can now enjoy all benefits of modern science without understanding any of it. So why bother learning those dull subjects? And why worry if your kids learn them or not? It is the happiness and self-confidence we want for our children, not the exhausting work and constant feeling of your own stupidity, right?

As to university administration, I assure you that I like it no more than you do. Ironically, it is that very administration who represents the "market thinking" at the colleges and a lot of our effort is spent fighting their bright ideas.

As to "it would be not so bad if fewer people pursued PhD", I would agree if we could figure out in the beginning who will finally make it and if the development of science needed just new great ideas rather than a lot of mundane work. Alas, neither seems to be true. We try to educate everybody not because everybody can learn (that is a humanistic myth, IMHO) but because a clever person can come from anywhere. True, we need fewer PhD's than we produce, perhaps, much fewer, but what do you propose to do with those who are not good enough to come to the very top but not bad enough to be discarded immediately? After all, many of them enjoy it and we've sort of experimented with their lives when keeping them in the school and university walls for 16 years shaping their brains in some strange ways.
I'm very far from being a humanist, i.e., claiming that every human life has value, but I'm very far from just discarding lives because they are insufficiently efficient either.

Anyway, I'm on the same side with you when you say that the salary inequality should be reversed. I only disagree with you when you say that the market forces will do it. The knowledge is not fashionable and there isn't much demand for it. You know it yourself: your books are beyond any comparison with Steven King's (or even Joanne Rowling's) in terms of quality and value, and which are selling better and read more? Note that in both cases it is the kids and the parents who choose what to read: neither "Introduction to Counting ...", nor "Harry Potter" is a compulsory reading at school. Neither one is prohibited from being read either. And the prices for the full series are comparable. That's market for you and it is the same for me and many other people who try to see beyond the 60 year horizon. It lets us survive if we work hard enough but that's about it.

I find particularly ironic that you're arguing "we need lots of PhD students because we don't know which ones will succeed" and I'm arguing that we don't need "experts" (centralized knowledge) determining what the right wages are for this or that profession because the market (distributed local knowledge) is going to determine better what the right wages are. FWIW, I basically agree with you about the PhD situation -- those students aren't being forced into those positions, and there's not much of a false surplus or shortage. At any rate, something much more like the market exists in the PhD universe that is producing your desired outcome than exists in K-12, where the outcome is something you and I both lament.

I think you're reading a lot more into my comments than are present. I'm merely saying that some market forces at all on school wages would be a good thing. (There are nearly none now.) Math and science teachers are scarcer and more valuable than history teachers and PE teachers. If there were a real market, this would be immediately apparent. You can get a sense for this by looking at places where there is a market -- online classes, tutoring, SAT prep, etc., are all much larger in math than in history. Much larger. As in, order of magnitude larger. I'd also expect that these markets are also an order of magnitude larger than personal preparation for athletics outside the schools. There simply isn't an equivalent of Kaplan or Mathnasium or Kumon or anything like that in athletics. There are a few AoPS equivalents here and there, but nothing with the broad audience of the many outlets to help kids in math. The market is pretty clear on this: math is more valuable than PE in K-12 education.

If there were school choice, and schools were free to pay whatever they want to whatever teachers, I'd wager that math and science teachers would get paid a lot more than gym teachers in nearly every school in the country, because results in those areas simply mean more to most parents paying the bills. (This is all turned sideways in college, where alumni giving and TV contracts are what the football program is all about.)

You and I simply disagree on markets versus centralized control by fiat. Products of our environments, perhaps. I've become much, much more pro-market since starting AoPS.

As for the market in books that you mention, I like to think that you're right in comparing the intrinsic "value" of our work versus Stephen King. But he is operating in a much larger market than I am -- bringing a tenth the value to 1000 times as many people has him doing OK. I cannot compete with him in that market. He can't compete with us in ours, but I'm sure he's not losing any sleep over that.

As for people preferring what they enjoy over what's good for them, well, I much prefer the resulting outcome (more kids reading Harry Potter than Intro Counting) to forcing my values on them (or, worse yet from my point of view, having their values forced on me).

The PhD thing was a sideline, of course. We do not even disagree too much on the drawbacks of "centralized authority" in the wage determination (though it would be interesting to look at private college prep. schools where they really can pay whatever teacher whatever they want and where the parents are even more likely to care more about good education. My impression is that on average they pay their teachers less, not more than public schools but it is difficult to find reliable data, so I may be misinformed here).

The key disagreement comes from your implicit opinion that the market looks for the best qualified labor force and my opinion that the market looks for the most cost effective labor force. Truly qualified math. teachers are scarce, I do not disagree with that. But the outcome of the teaching at school is hard to measure and one can always "curve the grades" (moreover, there is a strong pressure to do it), so "the most cost effective" translates into "the cheapest" and "semi-qualified" math. teachers are abundant (I admit that the fault is ours (college) not yours, because we give those masters degrees too easily).

As to "forcing your values on the kids", the problem is that if you don't do it when they are 12, we have to do it when they are 20.
And at that age it is both painful and inefficient. All those "business calculus", "intuitive calculus", etc. courses are pure mockery and, in all honesty, I would strongly prefer forcing all the students who take them (a multitude, really) to read a few introductory AoPS books at the age of 12 or 13. Moreover, I'm doing it with my daughter. She's not a math. person at all but, since she'll be force-fed math. at some point no matter what, I prefer to make sure that what is pushed down her throat is real food and that it is done at the age when she still can swallow and digest it without upsetting her stomach too much .

Fair points, both. I refer to the points that the market produces "cost-effective" solutions and the point that instilling values in young people is important. (I may be less confident than you that this instilling of values can actually be pulled off by parents' and teachers' actions as much as genes and peers.)

The former is particularly depressing when applied to education. I suspect that you are correct that if everything were fully market-oriented, then most teachers would get paid less. (I don't think the private school market can tell us much about this by comparing to public schools; there are all sorts of distortions when you try to compare the two. But my instinct is that you are correct.) There would be some outliers -- some very successful schools that recruit outstanding teachers, pay them well, and garner a high price (from whomever, be it the state or the students' parents). On the other hand, many schools would probably be even lower-paying, reflecting the fact that society does not value education as it is currently constituted very highly. Here's the depressing point: society is very likely correct in that assessment.

Of course, in time (a lot of time), the market might solve this problem by moving towards an educational system that actually is more valuable, but it would be a long, torturous road. I'm not certain the market would bring about such an outcome, but I'm pretty confident that a non-market system like the one we have now won't do anything to increase that perceived value of education by, you know, actually increasing the value of education.

Well, maybe you are right. The only thing I know for sure about market forces in education is that at Saint-Petersburg university (Russia) the law department offers for-fee legal services to the students who failed their math. exams and the lawyers really come and try to argue that the grade was not "fair" and the exam procedure itself was not "compliant with the law" or whatever. This and a few other things show that even if the market forces are capable of bringing us up eventually, they'll start with sending us to a deep dive down. I do not disagree that when an "artificial order" of things is destroyed, this dive is inevitable. I am only afraid that this dive may be so deep that nobody will emerge on the other side to embrace the "natural order" to come.

Can a non-market system provide good education and qualified teachers? I would argue that Russia did it under the communist rule. The "market experiment" in Russia is almost 20 years old by now. It is still in its diving phase as far as education is concerned.

Wow, those comments are like mini essays!