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Pressure to defend the relevance of one's area of mathematics
Toposophy vs Set theoretical multiverse philosophyBadiou and MathematicsLogic in mathematics and philosophyEssential reads in the philosophy of mathematics and set theorySine and Archimedes' derivation of the area of the circleIs there an observer dependent mathematics?Mathematicians with Aphantasia (Inability to Visualize Things in One's Mind)When must one strengthen one's induction hypothesis?Why aren't functions used predominantly as a model for mathematics instead of set theory etc.?Does this axiomatic system satisfy requirements for founding mathematics?Set-theoretical foundations of Mathematics with only bounded quantifiers
$begingroup$
I am a set theorist. Since I began to study this subject, I became increasingly aware of negative attitudes about it. These were expressed both from an internal and an external perspective. By the “internal perspective,” I mean a constant expression of worry from set theorists and logicians about the relevance of their work to the broader community / “real world”, with these worries sometimes leading to career-defining decisions on the direction of research.
For me, this situation is unwanted. I studied set theory because I thought it was interesting, not because I wanted to be a soldier in some kind of movement. Furthermore, I don’t see why an area needs defending when it produces a lot of deep theorems. That part is hard enough.
Does this kind of political situation plague other areas of mathematics? In what areas are scholars free to study according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject?
set-theory lo.logic soft-question mathematical-philosophy
$endgroup$
|
show 14 more comments
$begingroup$
I am a set theorist. Since I began to study this subject, I became increasingly aware of negative attitudes about it. These were expressed both from an internal and an external perspective. By the “internal perspective,” I mean a constant expression of worry from set theorists and logicians about the relevance of their work to the broader community / “real world”, with these worries sometimes leading to career-defining decisions on the direction of research.
For me, this situation is unwanted. I studied set theory because I thought it was interesting, not because I wanted to be a soldier in some kind of movement. Furthermore, I don’t see why an area needs defending when it produces a lot of deep theorems. That part is hard enough.
Does this kind of political situation plague other areas of mathematics? In what areas are scholars free to study according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject?
set-theory lo.logic soft-question mathematical-philosophy
$endgroup$
6
$begingroup$
+1, nice question; another area where I’ve seen this type of internal negative attitude expressed is category theory, for example in this discussion where Sridhar was asked at one point to explain what the ‘payoff’ for categorical versions of set theoretical constructions were for ‘classical mathematics’... ;) (mathoverflow.net/questions/318996/…) I would also like to understand why these demands are made more often of people working in arguably very ‘abstract’ branches of mathematics.
$endgroup$
– Alec Rhea
12 hours ago
4
$begingroup$
I think I've heard similar worries from those in lattice theory. It wouldn't surprise me much if semigroup theorists felt similarly plagued. On the opposite end, I would expect algebraic geometry and algebraic number theory don't suffer as much from this kind of worry (not to speak of hard analysis). Incidentally, Monroe: do you subscribe to FOM? You can find there lots of robust assertions about the relevance of set theory to mathematics generally.
$endgroup$
– Todd Trimble♦
11 hours ago
12
$begingroup$
In a sense, it is plaguing mathematics as a whole. Right now most pure mathematics is considered as "irrelevant" for the needs of the society. I would say it is a problem with the society rather than with pure mathematics, but it still can get rather irritating, especially when hiring is concerned. I have never heard before that such attitudes exist within mathematics itself towards set theory or anything else, but, perhaps, the general layman "What is in it for me?" approach to the valuation of things has spread to the math. community as well.
$endgroup$
– fedja
11 hours ago
14
$begingroup$
I think part of the problem is that some mathematicians think set theory is only about foundations. It may be worthwhile to emphasize other aspects of set theory, for example (my favorite) infinitary combinatorics.
$endgroup$
– Andreas Blass
10 hours ago
4
$begingroup$
@fedja I completely agree with the first part of your comment, but I think that such attitudes are quite prevalent within mathematics as well. A lot of mathematicians think that the kind of math they do (or are at least familiar with) is the most interesting. For instance, if you are a job candidate in logic for a department with no logic, then it is hard to generate interest unless you are proving things in areas other people there are working in.
$endgroup$
– Kimball
7 hours ago
|
show 14 more comments
$begingroup$
I am a set theorist. Since I began to study this subject, I became increasingly aware of negative attitudes about it. These were expressed both from an internal and an external perspective. By the “internal perspective,” I mean a constant expression of worry from set theorists and logicians about the relevance of their work to the broader community / “real world”, with these worries sometimes leading to career-defining decisions on the direction of research.
For me, this situation is unwanted. I studied set theory because I thought it was interesting, not because I wanted to be a soldier in some kind of movement. Furthermore, I don’t see why an area needs defending when it produces a lot of deep theorems. That part is hard enough.
Does this kind of political situation plague other areas of mathematics? In what areas are scholars free to study according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject?
set-theory lo.logic soft-question mathematical-philosophy
$endgroup$
I am a set theorist. Since I began to study this subject, I became increasingly aware of negative attitudes about it. These were expressed both from an internal and an external perspective. By the “internal perspective,” I mean a constant expression of worry from set theorists and logicians about the relevance of their work to the broader community / “real world”, with these worries sometimes leading to career-defining decisions on the direction of research.
For me, this situation is unwanted. I studied set theory because I thought it was interesting, not because I wanted to be a soldier in some kind of movement. Furthermore, I don’t see why an area needs defending when it produces a lot of deep theorems. That part is hard enough.
Does this kind of political situation plague other areas of mathematics? In what areas are scholars free to study according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject?
set-theory lo.logic soft-question mathematical-philosophy
set-theory lo.logic soft-question mathematical-philosophy
edited 1 hour ago
community wiki
3 revs, 2 users 67%
Monroe Eskew
6
$begingroup$
+1, nice question; another area where I’ve seen this type of internal negative attitude expressed is category theory, for example in this discussion where Sridhar was asked at one point to explain what the ‘payoff’ for categorical versions of set theoretical constructions were for ‘classical mathematics’... ;) (mathoverflow.net/questions/318996/…) I would also like to understand why these demands are made more often of people working in arguably very ‘abstract’ branches of mathematics.
$endgroup$
– Alec Rhea
12 hours ago
4
$begingroup$
I think I've heard similar worries from those in lattice theory. It wouldn't surprise me much if semigroup theorists felt similarly plagued. On the opposite end, I would expect algebraic geometry and algebraic number theory don't suffer as much from this kind of worry (not to speak of hard analysis). Incidentally, Monroe: do you subscribe to FOM? You can find there lots of robust assertions about the relevance of set theory to mathematics generally.
$endgroup$
– Todd Trimble♦
11 hours ago
12
$begingroup$
In a sense, it is plaguing mathematics as a whole. Right now most pure mathematics is considered as "irrelevant" for the needs of the society. I would say it is a problem with the society rather than with pure mathematics, but it still can get rather irritating, especially when hiring is concerned. I have never heard before that such attitudes exist within mathematics itself towards set theory or anything else, but, perhaps, the general layman "What is in it for me?" approach to the valuation of things has spread to the math. community as well.
$endgroup$
– fedja
11 hours ago
14
$begingroup$
I think part of the problem is that some mathematicians think set theory is only about foundations. It may be worthwhile to emphasize other aspects of set theory, for example (my favorite) infinitary combinatorics.
$endgroup$
– Andreas Blass
10 hours ago
4
$begingroup$
@fedja I completely agree with the first part of your comment, but I think that such attitudes are quite prevalent within mathematics as well. A lot of mathematicians think that the kind of math they do (or are at least familiar with) is the most interesting. For instance, if you are a job candidate in logic for a department with no logic, then it is hard to generate interest unless you are proving things in areas other people there are working in.
$endgroup$
– Kimball
7 hours ago
|
show 14 more comments
6
$begingroup$
+1, nice question; another area where I’ve seen this type of internal negative attitude expressed is category theory, for example in this discussion where Sridhar was asked at one point to explain what the ‘payoff’ for categorical versions of set theoretical constructions were for ‘classical mathematics’... ;) (mathoverflow.net/questions/318996/…) I would also like to understand why these demands are made more often of people working in arguably very ‘abstract’ branches of mathematics.
$endgroup$
– Alec Rhea
12 hours ago
4
$begingroup$
I think I've heard similar worries from those in lattice theory. It wouldn't surprise me much if semigroup theorists felt similarly plagued. On the opposite end, I would expect algebraic geometry and algebraic number theory don't suffer as much from this kind of worry (not to speak of hard analysis). Incidentally, Monroe: do you subscribe to FOM? You can find there lots of robust assertions about the relevance of set theory to mathematics generally.
$endgroup$
– Todd Trimble♦
11 hours ago
12
$begingroup$
In a sense, it is plaguing mathematics as a whole. Right now most pure mathematics is considered as "irrelevant" for the needs of the society. I would say it is a problem with the society rather than with pure mathematics, but it still can get rather irritating, especially when hiring is concerned. I have never heard before that such attitudes exist within mathematics itself towards set theory or anything else, but, perhaps, the general layman "What is in it for me?" approach to the valuation of things has spread to the math. community as well.
$endgroup$
– fedja
11 hours ago
14
$begingroup$
I think part of the problem is that some mathematicians think set theory is only about foundations. It may be worthwhile to emphasize other aspects of set theory, for example (my favorite) infinitary combinatorics.
$endgroup$
– Andreas Blass
10 hours ago
4
$begingroup$
@fedja I completely agree with the first part of your comment, but I think that such attitudes are quite prevalent within mathematics as well. A lot of mathematicians think that the kind of math they do (or are at least familiar with) is the most interesting. For instance, if you are a job candidate in logic for a department with no logic, then it is hard to generate interest unless you are proving things in areas other people there are working in.
$endgroup$
– Kimball
7 hours ago
6
6
$begingroup$
+1, nice question; another area where I’ve seen this type of internal negative attitude expressed is category theory, for example in this discussion where Sridhar was asked at one point to explain what the ‘payoff’ for categorical versions of set theoretical constructions were for ‘classical mathematics’... ;) (mathoverflow.net/questions/318996/…) I would also like to understand why these demands are made more often of people working in arguably very ‘abstract’ branches of mathematics.
$endgroup$
– Alec Rhea
12 hours ago
$begingroup$
+1, nice question; another area where I’ve seen this type of internal negative attitude expressed is category theory, for example in this discussion where Sridhar was asked at one point to explain what the ‘payoff’ for categorical versions of set theoretical constructions were for ‘classical mathematics’... ;) (mathoverflow.net/questions/318996/…) I would also like to understand why these demands are made more often of people working in arguably very ‘abstract’ branches of mathematics.
$endgroup$
– Alec Rhea
12 hours ago
4
4
$begingroup$
I think I've heard similar worries from those in lattice theory. It wouldn't surprise me much if semigroup theorists felt similarly plagued. On the opposite end, I would expect algebraic geometry and algebraic number theory don't suffer as much from this kind of worry (not to speak of hard analysis). Incidentally, Monroe: do you subscribe to FOM? You can find there lots of robust assertions about the relevance of set theory to mathematics generally.
$endgroup$
– Todd Trimble♦
11 hours ago
$begingroup$
I think I've heard similar worries from those in lattice theory. It wouldn't surprise me much if semigroup theorists felt similarly plagued. On the opposite end, I would expect algebraic geometry and algebraic number theory don't suffer as much from this kind of worry (not to speak of hard analysis). Incidentally, Monroe: do you subscribe to FOM? You can find there lots of robust assertions about the relevance of set theory to mathematics generally.
$endgroup$
– Todd Trimble♦
11 hours ago
12
12
$begingroup$
In a sense, it is plaguing mathematics as a whole. Right now most pure mathematics is considered as "irrelevant" for the needs of the society. I would say it is a problem with the society rather than with pure mathematics, but it still can get rather irritating, especially when hiring is concerned. I have never heard before that such attitudes exist within mathematics itself towards set theory or anything else, but, perhaps, the general layman "What is in it for me?" approach to the valuation of things has spread to the math. community as well.
$endgroup$
– fedja
11 hours ago
$begingroup$
In a sense, it is plaguing mathematics as a whole. Right now most pure mathematics is considered as "irrelevant" for the needs of the society. I would say it is a problem with the society rather than with pure mathematics, but it still can get rather irritating, especially when hiring is concerned. I have never heard before that such attitudes exist within mathematics itself towards set theory or anything else, but, perhaps, the general layman "What is in it for me?" approach to the valuation of things has spread to the math. community as well.
$endgroup$
– fedja
11 hours ago
14
14
$begingroup$
I think part of the problem is that some mathematicians think set theory is only about foundations. It may be worthwhile to emphasize other aspects of set theory, for example (my favorite) infinitary combinatorics.
$endgroup$
– Andreas Blass
10 hours ago
$begingroup$
I think part of the problem is that some mathematicians think set theory is only about foundations. It may be worthwhile to emphasize other aspects of set theory, for example (my favorite) infinitary combinatorics.
$endgroup$
– Andreas Blass
10 hours ago
4
4
$begingroup$
@fedja I completely agree with the first part of your comment, but I think that such attitudes are quite prevalent within mathematics as well. A lot of mathematicians think that the kind of math they do (or are at least familiar with) is the most interesting. For instance, if you are a job candidate in logic for a department with no logic, then it is hard to generate interest unless you are proving things in areas other people there are working in.
$endgroup$
– Kimball
7 hours ago
$begingroup$
@fedja I completely agree with the first part of your comment, but I think that such attitudes are quite prevalent within mathematics as well. A lot of mathematicians think that the kind of math they do (or are at least familiar with) is the most interesting. For instance, if you are a job candidate in logic for a department with no logic, then it is hard to generate interest unless you are proving things in areas other people there are working in.
$endgroup$
– Kimball
7 hours ago
|
show 14 more comments
4 Answers
4
active
oldest
votes
$begingroup$
Overall, people in academia in general and mathematicians in particular are very lucky in being free to study (and being able to make a good living) according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject. In fact even within our disciplines we have a lot of freedom to pursue our individual visions and tastes. (To appreciate how lucky we are compare the situation with musicians, writers, artists, film directors, actors, ...)
Relations with other areas of mathematics or outside mathematics are nice but they are one (and not necessarily a major one) among variety of criteria to appreciate mathematical progress.
I think we do have some duty to try to explain what we are doing outside our community and even outside the mathematical community. (But also this task is easier in some areas and harder in others.)
Another thing that I found useful in similar contexts is the "sure thing principle". Given an unwanted situation that has no implication on your action why worry about it at all too much. For example, suppose a paper you wrote and regard as a good paper is rejected. If the rejection was unjust then the conclusion is: "Improve your paper", and if the rejection was just then the conclusion is "Improve your paper".
$endgroup$
1
$begingroup$
+1 but not sure about the last paragraph. The hope is that by discussing it, I can either get some feedback that allows me to understand and accept the situation, or move some logicians to be a little less self-deprecating.
$endgroup$
– Monroe Eskew
2 hours ago
$begingroup$
@MonroeEskew, you are correct! I was carried away a little, so I updated my answer. Discussions and understanding can be useful even in cases where the sure-thing strategy is a good first approximation.
$endgroup$
– Gil Kalai
1 hour ago
$begingroup$
Ok but I still don’t get your point. There are logicians who make decisions on the direction of research according whether they think it will be seen as relevant by a larger group. So I’m wondering if i should join them in this practice or whether they should relax and do what’s interesting.
$endgroup$
– Monroe Eskew
1 hour ago
$begingroup$
My point is that you should relax and do what’s interesting and important to the best of your judgement.
$endgroup$
– Gil Kalai
1 hour ago
add a comment |
$begingroup$
Timothy Gowers' essay,
Gowers, William Timothy. "The two cultures of mathematics." Mathematics: Frontiers and Perspectives 65 (2000): 65.
PDF download
seems relevantly analogous:
"Loosely speaking, I mean the distinction between mathematicians who regard their central
aim as being to solve problems, and those who are more concerned with building and
understanding theories."
$endgroup$
5
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
11 hours ago
2
$begingroup$
I am a person who is guilty of a subconscious bias against set theory and this answer does not agree with my feelings regarding it (though maybe others have different experiences). I tend to think of set theorists as some sort of aliens so different from 'normal' mathematicians so that the division of mathematics into two cultures is not even applicable to them.
$endgroup$
– schematic_boi
8 hours ago
2
$begingroup$
@MonroeEskew of course, consciously I realize that they are same as the rest of us, but subconsciously I am not sure I am so accepting. I am not a master of introspection, but the reason is probably the following. While usual mathematicians tend to study something fairly concrete (e.g. Galois group of the rationals, or homotopy groups of spheres), set theorists study some meta-mathematical statements. The particular aspect that freaks me out is that the objects I am studying might not even exist if I change the axioms.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
I realize that my opinion does not accurately reflect the daily life of a set theorist, but the OP was asking about negative attitudes so they kind of brought it on themselves. To clarify, if I were in a situation where my decisions would impact the careers of some set theorists, I would try to correct for my biases but it does not seem possible to eradicate them. I think there were experiments in which police officers had to quickly decide if a suspect was armed or not, and black people were judged to be armed more frequently. Not all of those police officers thought of themselves as racist.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
@schematic_boi But I think this may be the core issue (for you and many others). We start with a mathematical statement, and then if it is shown to be independent, it gets re-labeled as meta- mathematical. It doesn't seem entirely fair.
$endgroup$
– Monroe Eskew
5 hours ago
|
show 15 more comments
$begingroup$
Personally, when I started studying Calculus of Finite Differences, and wrote some work related to that and Abel Functions, my professor said "I think we should get you working on some open problems, do you like Number Theory?" He didn't really see the point to Super functions and fractional iteration, and what it can tell us about difference operators on holomorphic functions.
$endgroup$
add a comment |
$begingroup$
This kind of issues plagues the whole of mathematics and TCS, where short-term fads (one can only get grants in "impactful" areas - this is certainly the case in many European countries) and internal politics (why would we hire that person, we'd rather increase our influence by hiring someone very close to our "own" area) dictate funding decisions.
It's basically a fashion industry now, unfortunately.
$endgroup$
$begingroup$
I guess TCS= Theoretical Computer Science, after checking on acronyms.thefreedictionary.com/TCS
$endgroup$
– YCor
4 mins ago
add a comment |
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4 Answers
4
active
oldest
votes
4 Answers
4
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Overall, people in academia in general and mathematicians in particular are very lucky in being free to study (and being able to make a good living) according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject. In fact even within our disciplines we have a lot of freedom to pursue our individual visions and tastes. (To appreciate how lucky we are compare the situation with musicians, writers, artists, film directors, actors, ...)
Relations with other areas of mathematics or outside mathematics are nice but they are one (and not necessarily a major one) among variety of criteria to appreciate mathematical progress.
I think we do have some duty to try to explain what we are doing outside our community and even outside the mathematical community. (But also this task is easier in some areas and harder in others.)
Another thing that I found useful in similar contexts is the "sure thing principle". Given an unwanted situation that has no implication on your action why worry about it at all too much. For example, suppose a paper you wrote and regard as a good paper is rejected. If the rejection was unjust then the conclusion is: "Improve your paper", and if the rejection was just then the conclusion is "Improve your paper".
$endgroup$
1
$begingroup$
+1 but not sure about the last paragraph. The hope is that by discussing it, I can either get some feedback that allows me to understand and accept the situation, or move some logicians to be a little less self-deprecating.
$endgroup$
– Monroe Eskew
2 hours ago
$begingroup$
@MonroeEskew, you are correct! I was carried away a little, so I updated my answer. Discussions and understanding can be useful even in cases where the sure-thing strategy is a good first approximation.
$endgroup$
– Gil Kalai
1 hour ago
$begingroup$
Ok but I still don’t get your point. There are logicians who make decisions on the direction of research according whether they think it will be seen as relevant by a larger group. So I’m wondering if i should join them in this practice or whether they should relax and do what’s interesting.
$endgroup$
– Monroe Eskew
1 hour ago
$begingroup$
My point is that you should relax and do what’s interesting and important to the best of your judgement.
$endgroup$
– Gil Kalai
1 hour ago
add a comment |
$begingroup$
Overall, people in academia in general and mathematicians in particular are very lucky in being free to study (and being able to make a good living) according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject. In fact even within our disciplines we have a lot of freedom to pursue our individual visions and tastes. (To appreciate how lucky we are compare the situation with musicians, writers, artists, film directors, actors, ...)
Relations with other areas of mathematics or outside mathematics are nice but they are one (and not necessarily a major one) among variety of criteria to appreciate mathematical progress.
I think we do have some duty to try to explain what we are doing outside our community and even outside the mathematical community. (But also this task is easier in some areas and harder in others.)
Another thing that I found useful in similar contexts is the "sure thing principle". Given an unwanted situation that has no implication on your action why worry about it at all too much. For example, suppose a paper you wrote and regard as a good paper is rejected. If the rejection was unjust then the conclusion is: "Improve your paper", and if the rejection was just then the conclusion is "Improve your paper".
$endgroup$
1
$begingroup$
+1 but not sure about the last paragraph. The hope is that by discussing it, I can either get some feedback that allows me to understand and accept the situation, or move some logicians to be a little less self-deprecating.
$endgroup$
– Monroe Eskew
2 hours ago
$begingroup$
@MonroeEskew, you are correct! I was carried away a little, so I updated my answer. Discussions and understanding can be useful even in cases where the sure-thing strategy is a good first approximation.
$endgroup$
– Gil Kalai
1 hour ago
$begingroup$
Ok but I still don’t get your point. There are logicians who make decisions on the direction of research according whether they think it will be seen as relevant by a larger group. So I’m wondering if i should join them in this practice or whether they should relax and do what’s interesting.
$endgroup$
– Monroe Eskew
1 hour ago
$begingroup$
My point is that you should relax and do what’s interesting and important to the best of your judgement.
$endgroup$
– Gil Kalai
1 hour ago
add a comment |
$begingroup$
Overall, people in academia in general and mathematicians in particular are very lucky in being free to study (and being able to make a good living) according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject. In fact even within our disciplines we have a lot of freedom to pursue our individual visions and tastes. (To appreciate how lucky we are compare the situation with musicians, writers, artists, film directors, actors, ...)
Relations with other areas of mathematics or outside mathematics are nice but they are one (and not necessarily a major one) among variety of criteria to appreciate mathematical progress.
I think we do have some duty to try to explain what we are doing outside our community and even outside the mathematical community. (But also this task is easier in some areas and harder in others.)
Another thing that I found useful in similar contexts is the "sure thing principle". Given an unwanted situation that has no implication on your action why worry about it at all too much. For example, suppose a paper you wrote and regard as a good paper is rejected. If the rejection was unjust then the conclusion is: "Improve your paper", and if the rejection was just then the conclusion is "Improve your paper".
$endgroup$
Overall, people in academia in general and mathematicians in particular are very lucky in being free to study (and being able to make a good living) according to the standards of their discipline, without feeling pressure to defend the relevance of their whole subject. In fact even within our disciplines we have a lot of freedom to pursue our individual visions and tastes. (To appreciate how lucky we are compare the situation with musicians, writers, artists, film directors, actors, ...)
Relations with other areas of mathematics or outside mathematics are nice but they are one (and not necessarily a major one) among variety of criteria to appreciate mathematical progress.
I think we do have some duty to try to explain what we are doing outside our community and even outside the mathematical community. (But also this task is easier in some areas and harder in others.)
Another thing that I found useful in similar contexts is the "sure thing principle". Given an unwanted situation that has no implication on your action why worry about it at all too much. For example, suppose a paper you wrote and regard as a good paper is rejected. If the rejection was unjust then the conclusion is: "Improve your paper", and if the rejection was just then the conclusion is "Improve your paper".
edited 27 mins ago
community wiki
4 revs
Gil Kalai
1
$begingroup$
+1 but not sure about the last paragraph. The hope is that by discussing it, I can either get some feedback that allows me to understand and accept the situation, or move some logicians to be a little less self-deprecating.
$endgroup$
– Monroe Eskew
2 hours ago
$begingroup$
@MonroeEskew, you are correct! I was carried away a little, so I updated my answer. Discussions and understanding can be useful even in cases where the sure-thing strategy is a good first approximation.
$endgroup$
– Gil Kalai
1 hour ago
$begingroup$
Ok but I still don’t get your point. There are logicians who make decisions on the direction of research according whether they think it will be seen as relevant by a larger group. So I’m wondering if i should join them in this practice or whether they should relax and do what’s interesting.
$endgroup$
– Monroe Eskew
1 hour ago
$begingroup$
My point is that you should relax and do what’s interesting and important to the best of your judgement.
$endgroup$
– Gil Kalai
1 hour ago
add a comment |
1
$begingroup$
+1 but not sure about the last paragraph. The hope is that by discussing it, I can either get some feedback that allows me to understand and accept the situation, or move some logicians to be a little less self-deprecating.
$endgroup$
– Monroe Eskew
2 hours ago
$begingroup$
@MonroeEskew, you are correct! I was carried away a little, so I updated my answer. Discussions and understanding can be useful even in cases where the sure-thing strategy is a good first approximation.
$endgroup$
– Gil Kalai
1 hour ago
$begingroup$
Ok but I still don’t get your point. There are logicians who make decisions on the direction of research according whether they think it will be seen as relevant by a larger group. So I’m wondering if i should join them in this practice or whether they should relax and do what’s interesting.
$endgroup$
– Monroe Eskew
1 hour ago
$begingroup$
My point is that you should relax and do what’s interesting and important to the best of your judgement.
$endgroup$
– Gil Kalai
1 hour ago
1
1
$begingroup$
+1 but not sure about the last paragraph. The hope is that by discussing it, I can either get some feedback that allows me to understand and accept the situation, or move some logicians to be a little less self-deprecating.
$endgroup$
– Monroe Eskew
2 hours ago
$begingroup$
+1 but not sure about the last paragraph. The hope is that by discussing it, I can either get some feedback that allows me to understand and accept the situation, or move some logicians to be a little less self-deprecating.
$endgroup$
– Monroe Eskew
2 hours ago
$begingroup$
@MonroeEskew, you are correct! I was carried away a little, so I updated my answer. Discussions and understanding can be useful even in cases where the sure-thing strategy is a good first approximation.
$endgroup$
– Gil Kalai
1 hour ago
$begingroup$
@MonroeEskew, you are correct! I was carried away a little, so I updated my answer. Discussions and understanding can be useful even in cases where the sure-thing strategy is a good first approximation.
$endgroup$
– Gil Kalai
1 hour ago
$begingroup$
Ok but I still don’t get your point. There are logicians who make decisions on the direction of research according whether they think it will be seen as relevant by a larger group. So I’m wondering if i should join them in this practice or whether they should relax and do what’s interesting.
$endgroup$
– Monroe Eskew
1 hour ago
$begingroup$
Ok but I still don’t get your point. There are logicians who make decisions on the direction of research according whether they think it will be seen as relevant by a larger group. So I’m wondering if i should join them in this practice or whether they should relax and do what’s interesting.
$endgroup$
– Monroe Eskew
1 hour ago
$begingroup$
My point is that you should relax and do what’s interesting and important to the best of your judgement.
$endgroup$
– Gil Kalai
1 hour ago
$begingroup$
My point is that you should relax and do what’s interesting and important to the best of your judgement.
$endgroup$
– Gil Kalai
1 hour ago
add a comment |
$begingroup$
Timothy Gowers' essay,
Gowers, William Timothy. "The two cultures of mathematics." Mathematics: Frontiers and Perspectives 65 (2000): 65.
PDF download
seems relevantly analogous:
"Loosely speaking, I mean the distinction between mathematicians who regard their central
aim as being to solve problems, and those who are more concerned with building and
understanding theories."
$endgroup$
5
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
11 hours ago
2
$begingroup$
I am a person who is guilty of a subconscious bias against set theory and this answer does not agree with my feelings regarding it (though maybe others have different experiences). I tend to think of set theorists as some sort of aliens so different from 'normal' mathematicians so that the division of mathematics into two cultures is not even applicable to them.
$endgroup$
– schematic_boi
8 hours ago
2
$begingroup$
@MonroeEskew of course, consciously I realize that they are same as the rest of us, but subconsciously I am not sure I am so accepting. I am not a master of introspection, but the reason is probably the following. While usual mathematicians tend to study something fairly concrete (e.g. Galois group of the rationals, or homotopy groups of spheres), set theorists study some meta-mathematical statements. The particular aspect that freaks me out is that the objects I am studying might not even exist if I change the axioms.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
I realize that my opinion does not accurately reflect the daily life of a set theorist, but the OP was asking about negative attitudes so they kind of brought it on themselves. To clarify, if I were in a situation where my decisions would impact the careers of some set theorists, I would try to correct for my biases but it does not seem possible to eradicate them. I think there were experiments in which police officers had to quickly decide if a suspect was armed or not, and black people were judged to be armed more frequently. Not all of those police officers thought of themselves as racist.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
@schematic_boi But I think this may be the core issue (for you and many others). We start with a mathematical statement, and then if it is shown to be independent, it gets re-labeled as meta- mathematical. It doesn't seem entirely fair.
$endgroup$
– Monroe Eskew
5 hours ago
|
show 15 more comments
$begingroup$
Timothy Gowers' essay,
Gowers, William Timothy. "The two cultures of mathematics." Mathematics: Frontiers and Perspectives 65 (2000): 65.
PDF download
seems relevantly analogous:
"Loosely speaking, I mean the distinction between mathematicians who regard their central
aim as being to solve problems, and those who are more concerned with building and
understanding theories."
$endgroup$
5
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
11 hours ago
2
$begingroup$
I am a person who is guilty of a subconscious bias against set theory and this answer does not agree with my feelings regarding it (though maybe others have different experiences). I tend to think of set theorists as some sort of aliens so different from 'normal' mathematicians so that the division of mathematics into two cultures is not even applicable to them.
$endgroup$
– schematic_boi
8 hours ago
2
$begingroup$
@MonroeEskew of course, consciously I realize that they are same as the rest of us, but subconsciously I am not sure I am so accepting. I am not a master of introspection, but the reason is probably the following. While usual mathematicians tend to study something fairly concrete (e.g. Galois group of the rationals, or homotopy groups of spheres), set theorists study some meta-mathematical statements. The particular aspect that freaks me out is that the objects I am studying might not even exist if I change the axioms.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
I realize that my opinion does not accurately reflect the daily life of a set theorist, but the OP was asking about negative attitudes so they kind of brought it on themselves. To clarify, if I were in a situation where my decisions would impact the careers of some set theorists, I would try to correct for my biases but it does not seem possible to eradicate them. I think there were experiments in which police officers had to quickly decide if a suspect was armed or not, and black people were judged to be armed more frequently. Not all of those police officers thought of themselves as racist.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
@schematic_boi But I think this may be the core issue (for you and many others). We start with a mathematical statement, and then if it is shown to be independent, it gets re-labeled as meta- mathematical. It doesn't seem entirely fair.
$endgroup$
– Monroe Eskew
5 hours ago
|
show 15 more comments
$begingroup$
Timothy Gowers' essay,
Gowers, William Timothy. "The two cultures of mathematics." Mathematics: Frontiers and Perspectives 65 (2000): 65.
PDF download
seems relevantly analogous:
"Loosely speaking, I mean the distinction between mathematicians who regard their central
aim as being to solve problems, and those who are more concerned with building and
understanding theories."
$endgroup$
Timothy Gowers' essay,
Gowers, William Timothy. "The two cultures of mathematics." Mathematics: Frontiers and Perspectives 65 (2000): 65.
PDF download
seems relevantly analogous:
"Loosely speaking, I mean the distinction between mathematicians who regard their central
aim as being to solve problems, and those who are more concerned with building and
understanding theories."
answered 12 hours ago
community wiki
Joseph O'Rourke
5
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
11 hours ago
2
$begingroup$
I am a person who is guilty of a subconscious bias against set theory and this answer does not agree with my feelings regarding it (though maybe others have different experiences). I tend to think of set theorists as some sort of aliens so different from 'normal' mathematicians so that the division of mathematics into two cultures is not even applicable to them.
$endgroup$
– schematic_boi
8 hours ago
2
$begingroup$
@MonroeEskew of course, consciously I realize that they are same as the rest of us, but subconsciously I am not sure I am so accepting. I am not a master of introspection, but the reason is probably the following. While usual mathematicians tend to study something fairly concrete (e.g. Galois group of the rationals, or homotopy groups of spheres), set theorists study some meta-mathematical statements. The particular aspect that freaks me out is that the objects I am studying might not even exist if I change the axioms.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
I realize that my opinion does not accurately reflect the daily life of a set theorist, but the OP was asking about negative attitudes so they kind of brought it on themselves. To clarify, if I were in a situation where my decisions would impact the careers of some set theorists, I would try to correct for my biases but it does not seem possible to eradicate them. I think there were experiments in which police officers had to quickly decide if a suspect was armed or not, and black people were judged to be armed more frequently. Not all of those police officers thought of themselves as racist.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
@schematic_boi But I think this may be the core issue (for you and many others). We start with a mathematical statement, and then if it is shown to be independent, it gets re-labeled as meta- mathematical. It doesn't seem entirely fair.
$endgroup$
– Monroe Eskew
5 hours ago
|
show 15 more comments
5
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
11 hours ago
2
$begingroup$
I am a person who is guilty of a subconscious bias against set theory and this answer does not agree with my feelings regarding it (though maybe others have different experiences). I tend to think of set theorists as some sort of aliens so different from 'normal' mathematicians so that the division of mathematics into two cultures is not even applicable to them.
$endgroup$
– schematic_boi
8 hours ago
2
$begingroup$
@MonroeEskew of course, consciously I realize that they are same as the rest of us, but subconsciously I am not sure I am so accepting. I am not a master of introspection, but the reason is probably the following. While usual mathematicians tend to study something fairly concrete (e.g. Galois group of the rationals, or homotopy groups of spheres), set theorists study some meta-mathematical statements. The particular aspect that freaks me out is that the objects I am studying might not even exist if I change the axioms.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
I realize that my opinion does not accurately reflect the daily life of a set theorist, but the OP was asking about negative attitudes so they kind of brought it on themselves. To clarify, if I were in a situation where my decisions would impact the careers of some set theorists, I would try to correct for my biases but it does not seem possible to eradicate them. I think there were experiments in which police officers had to quickly decide if a suspect was armed or not, and black people were judged to be armed more frequently. Not all of those police officers thought of themselves as racist.
$endgroup$
– schematic_boi
5 hours ago
2
$begingroup$
@schematic_boi But I think this may be the core issue (for you and many others). We start with a mathematical statement, and then if it is shown to be independent, it gets re-labeled as meta- mathematical. It doesn't seem entirely fair.
$endgroup$
– Monroe Eskew
5 hours ago
5
5
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
11 hours ago
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
11 hours ago
2
2
$begingroup$
I am a person who is guilty of a subconscious bias against set theory and this answer does not agree with my feelings regarding it (though maybe others have different experiences). I tend to think of set theorists as some sort of aliens so different from 'normal' mathematicians so that the division of mathematics into two cultures is not even applicable to them.
$endgroup$
– schematic_boi
8 hours ago
$begingroup$
I am a person who is guilty of a subconscious bias against set theory and this answer does not agree with my feelings regarding it (though maybe others have different experiences). I tend to think of set theorists as some sort of aliens so different from 'normal' mathematicians so that the division of mathematics into two cultures is not even applicable to them.
$endgroup$
– schematic_boi
8 hours ago
2
2
$begingroup$
@MonroeEskew of course, consciously I realize that they are same as the rest of us, but subconsciously I am not sure I am so accepting. I am not a master of introspection, but the reason is probably the following. While usual mathematicians tend to study something fairly concrete (e.g. Galois group of the rationals, or homotopy groups of spheres), set theorists study some meta-mathematical statements. The particular aspect that freaks me out is that the objects I am studying might not even exist if I change the axioms.
$endgroup$
– schematic_boi
5 hours ago
$begingroup$
@MonroeEskew of course, consciously I realize that they are same as the rest of us, but subconsciously I am not sure I am so accepting. I am not a master of introspection, but the reason is probably the following. While usual mathematicians tend to study something fairly concrete (e.g. Galois group of the rationals, or homotopy groups of spheres), set theorists study some meta-mathematical statements. The particular aspect that freaks me out is that the objects I am studying might not even exist if I change the axioms.
$endgroup$
– schematic_boi
5 hours ago
2
2
$begingroup$
I realize that my opinion does not accurately reflect the daily life of a set theorist, but the OP was asking about negative attitudes so they kind of brought it on themselves. To clarify, if I were in a situation where my decisions would impact the careers of some set theorists, I would try to correct for my biases but it does not seem possible to eradicate them. I think there were experiments in which police officers had to quickly decide if a suspect was armed or not, and black people were judged to be armed more frequently. Not all of those police officers thought of themselves as racist.
$endgroup$
– schematic_boi
5 hours ago
$begingroup$
I realize that my opinion does not accurately reflect the daily life of a set theorist, but the OP was asking about negative attitudes so they kind of brought it on themselves. To clarify, if I were in a situation where my decisions would impact the careers of some set theorists, I would try to correct for my biases but it does not seem possible to eradicate them. I think there were experiments in which police officers had to quickly decide if a suspect was armed or not, and black people were judged to be armed more frequently. Not all of those police officers thought of themselves as racist.
$endgroup$
– schematic_boi
5 hours ago
2
2
$begingroup$
@schematic_boi But I think this may be the core issue (for you and many others). We start with a mathematical statement, and then if it is shown to be independent, it gets re-labeled as meta- mathematical. It doesn't seem entirely fair.
$endgroup$
– Monroe Eskew
5 hours ago
$begingroup$
@schematic_boi But I think this may be the core issue (for you and many others). We start with a mathematical statement, and then if it is shown to be independent, it gets re-labeled as meta- mathematical. It doesn't seem entirely fair.
$endgroup$
– Monroe Eskew
5 hours ago
|
show 15 more comments
$begingroup$
Personally, when I started studying Calculus of Finite Differences, and wrote some work related to that and Abel Functions, my professor said "I think we should get you working on some open problems, do you like Number Theory?" He didn't really see the point to Super functions and fractional iteration, and what it can tell us about difference operators on holomorphic functions.
$endgroup$
add a comment |
$begingroup$
Personally, when I started studying Calculus of Finite Differences, and wrote some work related to that and Abel Functions, my professor said "I think we should get you working on some open problems, do you like Number Theory?" He didn't really see the point to Super functions and fractional iteration, and what it can tell us about difference operators on holomorphic functions.
$endgroup$
add a comment |
$begingroup$
Personally, when I started studying Calculus of Finite Differences, and wrote some work related to that and Abel Functions, my professor said "I think we should get you working on some open problems, do you like Number Theory?" He didn't really see the point to Super functions and fractional iteration, and what it can tell us about difference operators on holomorphic functions.
$endgroup$
Personally, when I started studying Calculus of Finite Differences, and wrote some work related to that and Abel Functions, my professor said "I think we should get you working on some open problems, do you like Number Theory?" He didn't really see the point to Super functions and fractional iteration, and what it can tell us about difference operators on holomorphic functions.
answered 11 hours ago
community wiki
Richard Diagram
add a comment |
add a comment |
$begingroup$
This kind of issues plagues the whole of mathematics and TCS, where short-term fads (one can only get grants in "impactful" areas - this is certainly the case in many European countries) and internal politics (why would we hire that person, we'd rather increase our influence by hiring someone very close to our "own" area) dictate funding decisions.
It's basically a fashion industry now, unfortunately.
$endgroup$
$begingroup$
I guess TCS= Theoretical Computer Science, after checking on acronyms.thefreedictionary.com/TCS
$endgroup$
– YCor
4 mins ago
add a comment |
$begingroup$
This kind of issues plagues the whole of mathematics and TCS, where short-term fads (one can only get grants in "impactful" areas - this is certainly the case in many European countries) and internal politics (why would we hire that person, we'd rather increase our influence by hiring someone very close to our "own" area) dictate funding decisions.
It's basically a fashion industry now, unfortunately.
$endgroup$
$begingroup$
I guess TCS= Theoretical Computer Science, after checking on acronyms.thefreedictionary.com/TCS
$endgroup$
– YCor
4 mins ago
add a comment |
$begingroup$
This kind of issues plagues the whole of mathematics and TCS, where short-term fads (one can only get grants in "impactful" areas - this is certainly the case in many European countries) and internal politics (why would we hire that person, we'd rather increase our influence by hiring someone very close to our "own" area) dictate funding decisions.
It's basically a fashion industry now, unfortunately.
$endgroup$
This kind of issues plagues the whole of mathematics and TCS, where short-term fads (one can only get grants in "impactful" areas - this is certainly the case in many European countries) and internal politics (why would we hire that person, we'd rather increase our influence by hiring someone very close to our "own" area) dictate funding decisions.
It's basically a fashion industry now, unfortunately.
answered 9 mins ago
community wiki
Dima Pasechnik
$begingroup$
I guess TCS= Theoretical Computer Science, after checking on acronyms.thefreedictionary.com/TCS
$endgroup$
– YCor
4 mins ago
add a comment |
$begingroup$
I guess TCS= Theoretical Computer Science, after checking on acronyms.thefreedictionary.com/TCS
$endgroup$
– YCor
4 mins ago
$begingroup$
I guess TCS= Theoretical Computer Science, after checking on acronyms.thefreedictionary.com/TCS
$endgroup$
– YCor
4 mins ago
$begingroup$
I guess TCS= Theoretical Computer Science, after checking on acronyms.thefreedictionary.com/TCS
$endgroup$
– YCor
4 mins ago
add a comment |
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6
$begingroup$
+1, nice question; another area where I’ve seen this type of internal negative attitude expressed is category theory, for example in this discussion where Sridhar was asked at one point to explain what the ‘payoff’ for categorical versions of set theoretical constructions were for ‘classical mathematics’... ;) (mathoverflow.net/questions/318996/…) I would also like to understand why these demands are made more often of people working in arguably very ‘abstract’ branches of mathematics.
$endgroup$
– Alec Rhea
12 hours ago
4
$begingroup$
I think I've heard similar worries from those in lattice theory. It wouldn't surprise me much if semigroup theorists felt similarly plagued. On the opposite end, I would expect algebraic geometry and algebraic number theory don't suffer as much from this kind of worry (not to speak of hard analysis). Incidentally, Monroe: do you subscribe to FOM? You can find there lots of robust assertions about the relevance of set theory to mathematics generally.
$endgroup$
– Todd Trimble♦
11 hours ago
12
$begingroup$
In a sense, it is plaguing mathematics as a whole. Right now most pure mathematics is considered as "irrelevant" for the needs of the society. I would say it is a problem with the society rather than with pure mathematics, but it still can get rather irritating, especially when hiring is concerned. I have never heard before that such attitudes exist within mathematics itself towards set theory or anything else, but, perhaps, the general layman "What is in it for me?" approach to the valuation of things has spread to the math. community as well.
$endgroup$
– fedja
11 hours ago
14
$begingroup$
I think part of the problem is that some mathematicians think set theory is only about foundations. It may be worthwhile to emphasize other aspects of set theory, for example (my favorite) infinitary combinatorics.
$endgroup$
– Andreas Blass
10 hours ago
4
$begingroup$
@fedja I completely agree with the first part of your comment, but I think that such attitudes are quite prevalent within mathematics as well. A lot of mathematicians think that the kind of math they do (or are at least familiar with) is the most interesting. For instance, if you are a job candidate in logic for a department with no logic, then it is hard to generate interest unless you are proving things in areas other people there are working in.
$endgroup$
– Kimball
7 hours ago