Yes, a lot of math is useless -- "Publish or Perish" for research mathematicians

  • Thread starter hatsoff
  • Start date
  • #1
20
1
I've published a dozen or so research level math papers (most with co-authors), and every single one of them is utterly pointless. I do it because that's what research mathematicians have to do in order to get and keep a professorship. Publish or perish, as the old saying goes.

I believe a lot of my colleagues secretly know this, although few will admit it openly.

This needs to change. Now. And I believe the best way to do it is for referees to reject papers unless they can be shown to have a use.

Some argue that maths which currently have no use might find some use in the future. But a moment's reflection should reveal how bad this argument is. Sure, anything is possible. So maybe some currently useless math paper might find a future application. But why think it will? Taking wild guesses is incredibly inefficient. Moreover, a lot of math has the appearance of having no hope for a future application.
 
Last edited by a moderator:
  • Like
Likes Grands

Answers and Replies

  • #2
Do you have any examples of what you would consider "useless" mathematics?
 
  • #3
20
1
Sure. The constructions of hereditarily indecomposable spaces. Classifying closed ideals in operator algebras. Pretty much anything in number theory (other than the cryptography stuff). Etc.
 
Last edited:
  • #4
13,807
10,955
I am of the contrary opinion. To judge mathematics by its applications fundamentally contradicts the way mathematics is done and developed. I think that mathematics is a toolbox and whether a tool is needed or not cannot be decided beforehand. The fact alone that so many different fields of science use it, from economics over politics, social sciences, natural sciences and finally mathematics itself, makes it impossible for any person to be able to make such a decision. E.g. I never would have thought to find cohomology theory in physics, abstract algebra in biology or algebraic geometry in information science. So whether and when a result is or will be useless, is simply an example of an undecidable truth.
 
  • Like
Likes Auto-Didact, gleem, dextercioby and 2 others
  • #5
20
1
I am of the contrary opinion. To judge mathematics by its applications fundamentally contradicts the way mathematics is done and developed. I think that mathematics is a toolbox and whether a tool is needed or not cannot be decided beforehand. The fact alone that so many different fields of science use it, from economics over politics, social sciences, natural sciences and finally mathematics itself, makes it impossible for any person to be able to make such a decision. E.g. I never would have thought to find cohomology theory in physics, abstract algebra in biology or algebraic geometry in information science. So whether and when a result is or will be useless, is simply an example of an undecidable truth.
It sounds like you aren't really disagreeing with my first point about a lot of math *currently* being useless. If I understand you correctly, you're saying "okay, we don't have any use for it right now now but we might find some use for it in the future." Is that right?

But I think that's a bad policy. It's shooting blind, a very inefficient method. And I am aware that you can produce examples of math which started off being useless but we eventually found a use for it. I think the classical examples are some results in number theory which originally had no use but eventually found applications in cryptography. But it seems to me that such examples are the exception rather than the rule. Most math which was originally useless has, as far as I can tell, stayed useless.

Moreover, a lot of math is really hard to imagine how it could ever be useful. Take the HI spaces example I mentioned above. That seems to me just spinning our wheels.
 
  • #6
13,807
10,955
It sounds like you aren't really disagreeing with my first point about a lot of math *currently* being useless.
I clearly do, as I pointed out, that useless is an attribute which cannot be associated to any mathematical result. It depends on so many unknowns, some are likely highly personal and thus undecidable by realistic means.
If I understand you correctly, you're saying "okay, we don't have any use for it right now now but we might find some use for it in the future." Is that right?
No, that's not what I said. I say, it does not matter, whether someone in any sense attributed a result as useless, because this person cannot be capable of doing so. I mentioned a few realms which became useful without originally being associated to a certain purpose. This does not allow the conclusion, that I consider this qualifier as necessary. I disrespect the question as such, because I think, mathematics must not be judged by usability at all, and even less in advance. This is not how mathematics works. It is true, that many mathematical results were driven by the necessity of real world problems, but by far not all. There is simply no need to justify mathematical results other than on their own validity. Use them now or later or even not at all. What sense does nilpotency for a Lie algebra make at the start? None. Yet, it is the central tool which classifies all semisimple - and therewith the exact opposite of nilpotent ones - which are nowadays the playground for the standard model, possible extensions and even a kind of starting point for string theory. What if Engel and Lie had thought the way you do? And if someone would manage to classify at least some Lie algebras with non trivial radical, then it would be a useless result in your sense, but mathematically important. I find your position to high degrees disrespectful towards the work of an Andrew Wiles or a Григорий Яковлевич Перельман (Perelman), and even Tao could be mentioned here, since many of his results appear useless. Their results are useless at first glance. But who could say, they will not be used to prove the ERH? And who could have imagined 1859, that cryptologists in 2009 rely on it? And even if not, who cares? A restriction by means of applicability leads inevitably to the end of how mathematical research is done and finally to more unsolved problems in sciences, which might could have used the results.

The goal for mankind is in my opinion to gain knowledge, how irrelevant it might look.
 
  • Like
Likes Auto-Didact and phinds
  • #7
The goal for mankind is in my opinion to gain knowledge, how irrelevant it might look.
This is as good of an opinion as any other. I suppose the OP just has a different opinion as to the worth of some knowledge, perhaps assigning worth based on how practical the knowledge is. It is certainly the right of the OP to hold this opinion but I think it would be inappropriate to impose such a philosophy on academic journals who exist only to provide access to knowledge.

We lose nothing by publishing ideas that may have no practical use right now, but we could lose something by doing the converse.
 
  • Like
Likes russ_watters, Asymptotic and fresh_42
  • #8
StatGuy2000
Education Advisor
1,801
906
To the OP:

If I understand you correctly, you are stating that the only areas of mathematics that have value are those that have a use. Are you thus implying that all of pure mathematics are worthless, and only applied mathematics work should be published? Because after all, the field of pure mathematics involves research into areas of mathematics without regard to, or independent of, any physical application.
 
  • Like
Likes BWV
  • #9
Stephen Tashi
Science Advisor
7,455
1,407
Why single out math as requiring applications? Should we insist all music have a use? - restrict it advertising jingles, little education songs ?

I've published a dozen or so research level math papers (most with co-authors), and every single one of them is utterly pointless. I do it because that's what research mathematicians have to do in order to get and keep a professorship. Publish or perish, as the old saying goes.
Is there anything about publish-or-perish that prevents a participant from studying mathematics that is useful? Was specialization in your current field something you had no say about?
 
  • Like
Likes russ_watters
  • #10
BWV
703
649
Perhaps its not inherently useless, but one has to consider the opportunity cost. Could these high level skills be put to better use? What percentage of the population should be engaged in researching esoteric math topics that do not have a clear application? The answer is of course not zero, but is it too high or too low? Would many of these professors contribute more by focusing more attention on teaching rather than publishing?
 
  • #11
StoneTemplePython
Science Advisor
Gold Member
2019 Award
1,173
573
What sense does nilpotency for a Lie algebra make at the start? None. Yet, it is the central tool which classifies all semisimple - and therewith the exact opposite of nilpotent ones - which are nowadays the playground for the standard model, possible extensions and even a kind of starting point for string theory. What if Engel and Lie had thought the way you do?
or better, regarding Sophus Lie:
- - - -
He read little of the works of the great mathematical classicists and he understood even less... [what Lie] provides us with is a doctrine of methods of little use whose barren formalism... must repel a reader of educated taste... The problem of examining continuous groups is novel... His results are trivial, and his virtually insignificant applications demonstrate that a problem solved by Euler and Lagrange in a natural way may be solved by means of his methods in a much more complicated manner.
-Frobenius
- - - -
source:
http://www.math.wisc.edu/hans/frob.pdf
 
  • Like
Likes PeroK, kith, krater and 3 others
  • #12
20
1
This is as good of an opinion as any other. I suppose the OP just has a different opinion as to the worth of some knowledge, perhaps assigning worth based on how practical the knowledge is. It is certainly the right of the OP to hold this opinion but I think it would be inappropriate to impose such a philosophy on academic journals who exist only to provide access to knowledge.

We lose nothing by publishing ideas that may have no practical use right now, but we could lose something by doing the converse.
But that's not true. We lose a lot. Oogles of money is funneled into promoting all this useless math, e.g. research grants and conference budgets. Research professors are paid six-digit figures and only teach a few classes per year because the bulk of their time is spent writing pointless papers.

What's worse, mathematicians are taught not to care whether their work might have a practical application. That's what happened to me, by the way. I was pushed so hard into playing the publishing game that I didn't realize until it was too late that my field was utterly ridiculous. Now I don't have the time to go back and do it right. I'm stuck with utterly useless skills, and the only way for me to get tenure is to pretend the work means something when I know full well that it doesn't.
 
  • #13
f95toli
Science Advisor
Gold Member
3,053
550
But that's not true. We lose a lot. Oogles of money is funneled into promoting all this useless math, e.g. research grants and conference budgets. Research professors are paid six-digit figures and only teach a few classes per year because the bulk of their time is spent writing pointless papers.
But this is true for research in just about any fields. The vast majority of the knowledge we "produce" will never be of practical use. There are lots of examples in e.g. physics of whole fields of research that at the time appeared to be very promising but later turned out to be a dead end. This is just the nature of research.
Moreover, even when it comes to fundamental research in "applied" topics (say solid state physics) we can't be sure something will be useful; when I write a research proposal I always have to say "this might turn out to be useful for X, Y or Z" (in 10-15 years) but this is always just a best guess.

Note that this is true even for very applied fields; an obvious example would be the pharmaceutical industry: only a tiny proportion of all drugs turn out to be useful; and there will be scientists who have spent well over ten years developing a drug just to discover that it has no effect at all during the first clinical trial .

Note also the the flipside can be true: sometimes a field "dies" just to be re-discovered 20-30 year later when the results turn out to be useful for another field which did not even exist when the original research was done.
 
  • Like
Likes Asymptotic, NFuller, russ_watters and 1 other person
  • #14
russ_watters
Mentor
19,938
6,410
I am of the contrary opinion. To judge mathematics by its applications fundamentally contradicts the way mathematics is done and developed. I think that mathematics is a toolbox and whether a tool is needed or not cannot be decided beforehand.
I agree with this, but would go further to say that it surprises me for a mathematician (or scientist) NOT to have a worldview that knowledge in and of itself is a positive thing. Much of cosmology and astronomy, for example, will never have practical applications; we study them merely because we want to Know.
 
  • #15
russ_watters
Mentor
19,938
6,410
It sounds like you aren't really disagreeing with my first point about a lot of math *currently* being useless. If I understand you correctly, you're saying "okay, we don't have any use for it right now now but we might find some use for it in the future." Is that right?

But I think that's a bad policy. It's shooting blind, a very inefficient method...

Moreover, a lot of math is really hard to imagine how it could ever be useful. Take the HI spaces example I mentioned above. That seems to me just spinning our wheels.
No, speaking just for myself, I agree that some science/math will never have practical applications, but imo, that truth is just completely irrelevant. "Usefulness" is a constraint that you want, but does not in general get applied by others.
 
  • #16
13,807
10,955
"Usefulness" is a constraint that you want, but does not in general get applied by others.
Yes, and it is simply not us (as a species). I'm sure there would have been easier ways to keep track of the seasons than to build Stonehenge, the Maya pyramids or even the Nebra sky disc.
 
  • Like
Likes russ_watters
  • #17
Wooj Amon
If you think of math as an art, and that you are employed as an artist as part of an art business, then your career is to produce art. Maybe that doesn't mean someone buys it right away, or that a customer asked for it, but that's not your motivation nor are you being paid to be concerned about it. If you love producing art just for the joy of it and you're getting paid for doing something you love, then you're golden. But if you want to produce art upon request and actually care about someone buying your art and putting it to use, then you need to get into a different kind of art business -- go into industry as an applied mathematician for NASA or Lockheed Martin or some other gig.
 
  • Like
Likes pinball1970, kith, mathwonk and 2 others
  • #18
Pythagorean
Gold Member
4,210
270
You should experience a biomedical science conference, where everybody is curing cancer. I much prefer the "intellectual merit" factor to the "broader impact" factor for fund acquisition.
 
  • Like
Likes fresh_42
  • #19
mathwonk
Science Advisor
Homework Helper
11,058
1,246
". Pretty much anything in number theory (other than the cryptography stuff). Etc."

This is amusing to me since cryptography was a use that was found years later for research in number theory that had been thought completely useless before, i.e. when it was done. (my colleagues Carl Pomerance, Robert Rumely, and Red Alford, were active practitioners in the number theory research that [now] informs cryptography.)
 
  • #20
20
1
". Pretty much anything in number theory (other than the cryptography stuff). Etc."

This is amusing to me since cryptography was a use that was found years later for research in number theory that had been thought completely useless before, i.e. when it was done. (my colleagues Carl Pomerance, Robert Rumely, and Red Alford, were active practitioners in the number theory research that [now] informs cryptography.)
Well there are a couple of things to keep in mind, here. The first is this: would the (presumably small) part of number theory which is useful for cryptography have been developed anyway, once crypographers understood how it might be useful? Sure, we would have had to wait longer for the development. But wouldn't it have been more efficient in the long run to wait until we knew what would probably be useful before allocating the effort?

The second thing I want to keep in mind is this: It's easy to zoom in on cryptography, but let's not forget that for every useful theorem there seem to be a hundred more that are completely useless. Even if we miss out on some useful cryptography results in number theory, we have to balance that against all the stuff we're losing because thousands of brilliant mathematicians are pouring their effort into generating a bunch of useless nonsense. What are we missing out on, that they might have invented or developed instead by doing something useful with their talents?

To put it another way: I don't deny that some formerly-useless math has (and will) turn out to be useful after all. But the issue here is one of efficiency. As an analogy, if you fire a gun blindly, you're bound to hit something eventually. But isn't it better to take careful aim first, even if it takes longer?
 
  • #21
But how can you decide beforehand what will be useful? If, at this very moment, I asked you to compile a list of mathematics that we could develop which will be useful for us, I think that your list would be awfully short compared to we do actually find to be useful in the future.

If I'm not making myself clear, all I am saying is that what you think will be useful is most likely a subset of what will actually be useful, and by conducting our research in the manner that prescribe, we are going to handicap ourselves.
 
  • Like
Likes pinball1970
  • #22
mathwonk
Science Advisor
Homework Helper
11,058
1,246
I have the impression that the OP is for some unexplained reason, in a research position at an academic institution, even though he/she (I assume he) hates what he does there and finds no excitement, joy, or fulfillment from it at all. If so, I suggest you look for another job at once. If you have PhD level math skills and training you may well find a job that does do "useful" work and pays 2 or 3 (or even 10) times what you are making now. And your absence would make room for someone with real enthusiasm for academics and thus who has more of a chance to do some research we might appreciate. I am currently reading the red book of algebraic geometry by a fields medalist and loving it for its intellectual depth and scope. This book adds significantly to the richness of the knowledge base of humankind, and we are lucky the researcher wrote it, although up to now the results seem useless in the real world. (At least they don't do any harm.) I suggest you try to take this goal with your own work or else find another field where you are really engaged by the challenge of each day.

I want to suggest however that there is a chance you really are talented and insightful enough to actually make useful progess in your area, but it helps to want to and try to do so. perhaps you are just discouraged by the "rat race". if so, you owe yourself a career can enjoy, you have worked hard and sacrificed a lot to get this far. don't be afraid to commit to something you can care about.

good luck.
 
Last edited:
  • Like
Likes StatGuy2000, pinball1970 and Mark44
  • #23
Drakkith
Staff Emeritus
Science Advisor
21,013
4,829
What are we missing out on, that they might have invented or developed instead by doing something useful with their talents?
Surely less than by restricting research to only those fields which we think will lead to 'useful' results within a short timeframe. I think that mindset will slightly increase the rate of discovery within those areas we deem as useful, but will drastically delay discoveries in other areas

To put it another way: I don't deny that some formerly-useless math has (and will) turn out to be useful after all. But the issue here is one of efficiency. As an analogy, if you fire a gun blindly, you're bound to hit something eventually. But isn't it better to take careful aim first, even if it takes longer?
The problem is that the targets are all initially hidden. Unless you fire blindly you will only ever discover a new target by missing the one you were aiming for, and only if that target is relatively close to the first.
 
  • #24
pinball1970
Gold Member
704
720
I've published a dozen or so research level math papers (most with co-authors), and every single one of them is utterly pointless. I do it because that's what research mathematicians have to do in order to get and keep a professorship. Publish or perish, as the old saying goes.

I believe a lot of my colleagues secretly know this, although few will admit it openly.

This needs to change. Now. And I believe the best way to do it is for referees to reject papers unless they can be shown to have a use.

Some argue that maths which currently have no use might find some use in the future. But a moment's reflection should reveal how bad this argument is. Sure, anything is possible. So maybe some currently useless math paper might find a future application. But why think it will? Taking wild guesses is incredibly inefficient. Moreover, a lot of math has the appearance of having no hope for a future application.
Ill be repeating a little bit but I want to post on this. There is absolutely no way of knowing what work (maybe yours) could be the final piece in the jigsaw for something in the future. The fact you cannot tell right now should be irrelevant surely? You could search in an area of science that is crying out for a mathematical approach to a problem? Presumably you had a love for this subject at some point? During your degree? Your Doctorate? You realize not many people have the ability you have to do what you do and have done? Its a gift. Shame to waste it.
 
  • #25
Dr. Courtney
Education Advisor
Insights Author
Gold Member
3,260
2,402
I've published a dozen or so research level math papers (most with co-authors), and every single one of them is utterly pointless. I do it because that's what research mathematicians have to do in order to get and keep a professorship. Publish or perish, as the old saying goes.

I believe a lot of my colleagues secretly know this, although few will admit it openly.

This needs to change. Now. And I believe the best way to do it is for referees to reject papers unless they can be shown to have a use.

Some argue that maths which currently have no use might find some use in the future. But a moment's reflection should reveal how bad this argument is. Sure, anything is possible. So maybe some currently useless math paper might find a future application. But why think it will? Taking wild guesses is incredibly inefficient. Moreover, a lot of math has the appearance of having no hope for a future application.
What then should be the criteria for getting and keeping math professorships at R1 institutions?

My wife and I have served on the factulty of a number of schools which were not R1 institutions. The criteria at those places tended to be more teaching focused, with a very strong element of affirmative action - STEM departments really needed more women and minority faculty members - so much so that white males had much lower hiring rates.

The Math faculty at the Air Force Academy had a nice balance. Hiring and retention were focused on teaching abilities and accomplishments. Promotion to Associate Professor and Full Professor began to have a research component - but this research component was focussed on publication (rather than funding), the expected rate of publication was one peer-reviewed paper every 18 months (on average), and there was no expectation that papers be in pure mathematics. A math faculty member's publications could be in math education, applied math, or just about any area of science and engineering, with a mild preference for things important to the Air Force. Research that involved undergraduate students was also highly valued, regardless of whether or not it was pure math.

One thing that helped in this regard was that the promotion committees were interdepartmental. The question tended to be closer to "How valuable is your research to the mission of the Air Force Academy?" rather than "How valuable is your research to the Math department?" Not that pure math would have been frowned upon, but it would not be treated as more valuable than more applied math. In addition, the promotion application also had the faculty member list the number of citations for each of their publications. Consequently, my publications in blast physics and ballistics with dozens of citations would have been treated more favorably than pure math publications that often struggle to break double digits in their citations.
 

Related Threads on Yes, a lot of math is useless -- "Publish or Perish" for research mathematicians

Replies
72
Views
14K
Replies
4
Views
1K
Replies
70
Views
9K
Replies
15
Views
3K
Replies
54
Views
5K
  • Poll
  • Last Post
2
Replies
39
Views
2K
Replies
2
Views
425
Replies
10
Views
2K
Replies
25
Views
3K
Top