4 ms·

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 a

by j2kun 3y ago

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.

wadd1e 3y ago
>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.
chongli 3y ago
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!
- sfpotter 3y ago
  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.
  - chongli 3y ago
    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.
    - sfpotter 3y ago
      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.
      - 13415 3y ago
        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.
- j2kun 3y ago
  > catch them off guard and put them on the spot 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.
DrDroop 3y ago
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.
- BalinKing 3y ago
  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.
Someone 3y ago
> 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.

by j2kun 3y ago

wadd1e 3y ago

>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.

chongli 3y ago

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!

sfpotter 3y ago
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.
- chongli 3y ago
  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.
  - sfpotter 3y ago
    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.
    - 13415 3y ago
      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.
j2kun 3y ago
> catch them off guard and put them on the spot 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.

DrDroop 3y ago

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.

BalinKing 3y ago
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.

Someone 3y ago

> 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.