People are welcome to do whatever they like. I'm expressing an opinion, my value judgement, that the math done for its own sake is just not as beautiful to me as math that has applications.
You call it laziness, and I call it a refined view built up over decades of study and repeatedly hearing mathematicians bullshit and be misinformed about how applicable their work is.
>that the math done for its own sake is just not as beautiful to me as math that has applications.
The point that the person who you're replying to is making is that you dont know the distinction between maths done for its own sake and maths that has applications until potentially hundreds of years later.
If you want to read a more thorough defence of the value of pure mathematics research, I recommend that you read A Mathematician's Apology by G.H. Hardy. Hardy witnessed first-hand the beginnings of the applications of his field, number theory, to cryptography. At that time, the only use for cryptography was in warfare so as a committed pacifist you can well imagine how much this upset him.
misinformed about how applicable their work is
I think I know exactly what you're talking about and it's unfair. I've also seen it happen to scientists across the spectrum. A question from a journalist or other layperson -- about the applicability of their research -- to catch them off guard and put them on the spot, designed to humble them and make the questioner feel superior. You never hear this sort of question levelled at painters, sculptors, musicians, writers, game designers, or any other artist!
It's different. Painters, sculptors, musicians, etc. are all doing something which is ultimately in service of making others happy and fulfilled. A mathematician or scientist working on something terribly narrow and abstruse is arguably only working on something in service of making themselves happy and fulfilled. Since they are frequently supported by taxpayer money, asking whether what they're working on is worth that expense is totally legitimate. The idea that we can't question the legitimacy or applicability of research because we can't predict how useful that research will be useful in 300 years is dumb.
If you want to be taken seriously, it's better to spend some time dwelling on whether you are responsibly fulfilling your obligation to society. For many professors, I think this could easily be addressed by shifting the focus away from research back to where it belongs: teaching.
On the other hand, if there are potential commercial applications 10-20 years in the future, it may not be the best idea for the government to fund the research. The topic is already concrete enough for the market, and it could be a waste of tax money to fund it. There is a lot more money in commercial research than publicly funded research. The government should focus on funding topics where the applications are too uncertain or too far in the future to make sense in the market.
Since they are frequently supported by taxpayer money, asking whether what they're working on is worth that expense is totally legitimate.
That's not the deal they signed up for. They were told that they were going into a purely theoretical field. To turn around and demand applications is called a bait-and-switch.
For many professors, I think this could easily be addressed by shifting the focus away from research back to where it belongs: teaching.
Same as above. The universities hired these professors on the basis of their research. If they want teaching staff they should hire teachers. The researchers will seek greener pastures elsewhere.
As for taxpayers demanding applications? Vote for it! Give the money to DARPA or Johns Hopkins instead of Princeton IAS. But to demand that theoreticians come up with applications on the spot is disingenuous.
Most people don't have the luxury of tenure. Frankly, most people don't have the luxury of a single career that's well paying throughout their professional life. If funding dried up tomorrow and every number theory professor was out on their ear, that wouldn't be a bait and switch. That would be a uniquely nice and pleasant situation for them coming to an end.
It's probably also good to contextualize this historically. The NSF has only existed since 1950. The high degree of funding for pure math let alone the rest of science and engineering could easily be a historical blip.
I don't really care what happens to people who are currently employed doing some kind of useless research in academia. Indeed, they got hired for it. I'm simply pointing out that it's totally fair and reasonable for anyone to ask whether it's a good idea to employ people this way. Your earlier comment seems to suggest that you don't think it's OK for people to call this into question.
I'm also not particularly worried about it. I'm not sure how much money IAS gets, but my guess is that DARPA and the DOE get a hell of a lot more, which (at least in my opinion ;-) ) is good.
It may be fair but it's definitely not reasonable. Progress in mathematics has foreshadowed practical applicability sometimes by centuries. It's short-sighted to consider applications outside of mathematics in the hiring of mathematicians.
In that context, it's worth noting that research mathematicians almost always mean "applications to other fields of mathematics" when they talk about the applicability of their research.
I don't agree. You're basically sticking your head in the sand saying that because there have been unanticipated benefits sometimes hundreds of years later, we can't even attempt to decide what research is valuable.
If the public is paying for research, it is both fair and reasonable to ask questions about its utility. It's as simple as that.
It’s totally fine if you want to say “defund pure mathematics!” I was complaining about the bait-and-switch people do when they take someone who was hired to do pure mathematics and then demand applications from them. It’s disingenuous and unfair. Likewise for the superstar researcher who is demanded to teach!
How many pure mathematicians have gotten tenure in math departments and were subsequently forced to work on "applications"? Do you have any actual examples?
How many superstar researchers have been forced to teach against their will? If they're working as a regular, tenure-track professor, then teaching is part of their job. The word doctor comes from the Latin word for teacher!
You didn’t say “defund pure mathematics” but you implied it with your original statement:
A mathematician or scientist working on something terribly narrow and abstruse is arguably only working on something in service of making themselves happy and fulfilled. Since they are frequently supported by taxpayer money, asking whether what they're working on is worth that expense is totally legitimate
To me this reads as “pure mathematics is a taxpayer-funded hobby that provides no value to society.” Is that an unfair reading? I don’t know how else to parse the statement that mathematicians are ”arguably only working on something in service of making themselves happy and fulfilled.” If that is what they’re doing then why shouldn’t they be defunded?
As for teaching, plenty of pure mathematicians do teach graduate students. Asking a world-leading number theorist to teach first year algebra class is silly though. Universities hire dedicated teaching faculty for those courses. Many of the expert researchers are terrible at teaching.
I also want to add that the reason universities covet superstar researchers (in any field) is because they bring in grant money (paying for themselves and then some) and because research elevates the profile of the school in the world rankings. The best schools have the best researchers but that doesn’t mean they provide the best education. Trying to fix this is an enormous challenge because you’ve got to tackle the issue of schools competing against each other for students. The losing schools are going bankrupt [1].
I'm not saying we should defund math. I'm saying that it's perfectly fair and reasonable to think through how much sense it makes to allocate research funds for pure math. More specifically, I'm pushing because on the idea that it isn't okay to discuss this because past math successes have been useful in other areas. People really seem to cling to this argument and it doesn't make any sense to me. Maybe, at the end of the day, after thinking about it, it will make sense to continue funding pure math or even fund it more.
I agree that having a top number theorist teach Algebra I is a waste, but it's not a waste having them teaching undergraduate abstract algebra or number theory. The bigger issue is that in many places, there is very little expectation of teaching quality. I'm not sure this is connected to the issue of competition over students. The average math undergrad isn't picking a school based on how many Fields medalists it has.
I should say that I took number theory in undergrad from a top number theorist, and he was a phenomenally good teacher. I could have taken abstract algebra from him, too, if I had timed it right. Taking the craft of teaching seriously and being a good researcher aren't mutually exclusive!
No, it's the researchers who first claim their work is applicable, in their papers, in lectures, etc. I have read entire books with titles like "Applications of X" and later discover all the claimed applications were unrealistic.
Hardy was a prickish snob who claimed in that book that any math that can be applied is dull.
> that the math done for its own sake is just not as beautiful to me as math that has applications.
I think the reverse. In general, the math done for its own sake will be more beautiful.
Think of it this way: mathematicians doing math to get some place will accept to take a long path that’s ugly and/or extremely dull, as long as it gets them there; mathematicians doing math for math’s sake will prefer to walk nicer paths.
But of course, beauty is in the eye of the beholder; those who define ‘beautiful’ as ‘has direct application’ will disagree.
This is the reason I prefer the intuitionist view of mathematics vs the more common platonic view. Something as simple as the Pythagorean theorem is true because it has found so many ways to solve practical problems, the Sumerians and Egyptians basically worshiped that formula.
I really don't think that intuitionism has that much to do with practical application—rather, it's a view about what it means for something to be "true" in the first place. That is to say, whether an intuitionist accepts a piece of mathematics is not contingent on if it has any practical applications.
I suppose one could argue that something proven in an intuitionistic manner would have a higher probability of being practically useful (since it could e.g. be extracted into an algorithm), but IMO any such correlation is pretty weak.
You call it laziness, and I call it a refined view built up over decades of study and repeatedly hearing mathematicians bullshit and be misinformed about how applicable their work is.