Undirected research is quite possible outside the university system. Perhaps you've heard of Bell Labs? When the government still subsidized them [1], they did plenty of undirected research. In the university system, about 50% of the money the government has earmarked for research is actually used for that purpose. At Bell Labs, the number was close to 100%.

Most grant supported research groups do plenty of undirected research, and the NSF rarely objects when a project makes discoveries not listed in the grant proposal.

You are telling me that (roughly) doubling the amount of money devoted to research will harm research? I really don't understand the mechanism by which that would happen.

"If you can only do, no one will benefit from your knowledge."

Let me be very precise, since you seem to want to misinterpret what I wrote.

A researcher's skill set: generating new knowledge and spreading it to other researchers, and eventually practitioners. This is done through published papers, presentations at conferences, conversation and source code. Generating new knowledge is the primary skill here - other researchers will usually go to great effort to understand it.

A teacher's skill set: understanding existing knowledge and spreading it to people with no background in a classroom setting. The primary skill is motivation and understand people very different from you (e.g., premeds who hate math rather than other math Ph.D.s), and maintaining discipline. The goal is to convey existing knowledge, so creating new knowledge (the primary skill of a researcher) is more or less irrelevant.

There are not that many people who have both of these skill sets. I only had the researcher's skill set, and I know many people with the teacher's skill set.

Also, by "waste", I was referring to general university waste - overpaid and under worked administrators, duplicate offices, etc. If you ever work at a university, you will realize how wasteful they are.

[1] I believe the system was that every dollar AT&T lost at Bell Labs was deducted from their tax bill.

>You are telling me that (roughly) doubling the amount of money devoted to research will harm research? I really don't understand the mechanism by which that would happen.

Again, because you are taking that money away from education. Good education is a fundamental part of good research. They don't need to be in the same building, but they do need to have the same people involved, if only that the researcher was at some point educated.

>There are not that many people who have both of these skill sets. I only had the researcher's skill set, and I know many people with the teacher's skill set.

It doesn't matter. You should try to teach anyway. If you're any good at what you do your experience will be worth something to the people you teach. You experience is in many ways more valuable in teaching 30 students for a year than it is applying that experience. Education is a multiplier, not simply additive.

Obviously, you need both. But trying to do each in a vacuum is short-sighted.

I'm confused - first you wanted education to subsidize research. Wouldn't that have been taking money away from education, back when you believed that was the status quo? It seems as if your fundamental assumption is that the status quo must be correct.

In any case, yes, I agree with you that most researchers will need to have some sort of undergrad education. I don't see any reason why that education should be provided by researchers - cheap adjunct professors seem to do a reasonably good job at it.

(I do agree that a PhD program will need to be taught by researchers, since it is basically just an apprenticeship.)

As for teaching, my experience was worth considerably less to my students than a better ability to explain simple concepts would have been. The fact that I developed a nice outgoing wave filter for the Schrodinger equation did not help my fashion business student who barely knew algebra. It didn't even help the top 2-3 students who were breezing through my class, who might (possibly) have understood the concept of a PDE, or at least nodded along as if they did.

What might have helped them was someone who (like them) struggled with calculus, mastered it, and knew where the difficult points were. It also might have helped to have someone who could get to know students, understand how they learn best, and then tailor the lessons to suit them. Or someone who can look at a sea of blank faces and determine when they are confused. Unfortunately, that person wasn't me. I know a number of people who are that person, but only a small fraction of them have published anything beyond their PhD thesis.