Controversial area of mathematics
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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
asked 45 mins ago
Monroe EskewMonroe Eskew
8,02412263
$endgroup$
add a comment |
$begingroup$
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
asked 45 mins ago
Monroe EskewMonroe Eskew
8,02412263
$endgroup$
$begingroup$
+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
34 mins ago
$begingroup$
@AlecRhea Fair enough. I would say I was trying to understand the impact of something on my area coming from outside, so I used the language of “applications” to make my point rhetorically. This may have been unfair.
$endgroup$
– Monroe Eskew
28 mins ago
$begingroup$
It's completely understandable, and I think this provides a lens on the set theory issue as well -- set theory has been touted and accepted as 'the' rigorous foundation for mathematics for decades (excepting some developments in category theory), but an analyst or algebraic geometer can have a completely healthy and productive career without ever really understanding any of the deeper constructions in set theory. I think requests for applications and consequences in fields outside set theory are usually attempts to get a grasp on an abstract branch of mathematics from a familiar perspective.
$endgroup$
– Alec Rhea
19 mins ago
$begingroup$
If you (and your colleagues) have enough funding, no worries. I suspect it is not the research area so much as the economics plus the psychology of the players. While my research path is primarily my own responsibility and my own fault, I believe it was influenced by how certain players viewed Universal Algebra at the time. Not all of the players were universal algebraists. Gerhard "Politics Isn't For The Individual" Paseman, 2019.04.27.
$endgroup$
– Gerhard Paseman
7 mins ago
add a comment |
$begingroup$
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
asked 45 mins ago
Monroe EskewMonroe Eskew
8,02412263
$endgroup$
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
asked 45 mins ago
Monroe EskewMonroe Eskew
8,02412263
asked 45 mins ago
Monroe EskewMonroe Eskew
8,02412263
asked 45 mins ago
Monroe EskewMonroe Eskew
8,02412263
asked 45 mins ago
Monroe EskewMonroe Eskew
8,02412263
asked 45 mins ago
Monroe EskewMonroe Eskew
8,02412263
8,02412263
$begingroup$
+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
34 mins ago
$begingroup$
@AlecRhea Fair enough. I would say I was trying to understand the impact of something on my area coming from outside, so I used the language of “applications” to make my point rhetorically. This may have been unfair.
$endgroup$
– Monroe Eskew
28 mins ago
$begingroup$
It's completely understandable, and I think this provides a lens on the set theory issue as well -- set theory has been touted and accepted as 'the' rigorous foundation for mathematics for decades (excepting some developments in category theory), but an analyst or algebraic geometer can have a completely healthy and productive career without ever really understanding any of the deeper constructions in set theory. I think requests for applications and consequences in fields outside set theory are usually attempts to get a grasp on an abstract branch of mathematics from a familiar perspective.
$endgroup$
– Alec Rhea
19 mins ago
$begingroup$
If you (and your colleagues) have enough funding, no worries. I suspect it is not the research area so much as the economics plus the psychology of the players. While my research path is primarily my own responsibility and my own fault, I believe it was influenced by how certain players viewed Universal Algebra at the time. Not all of the players were universal algebraists. Gerhard "Politics Isn't For The Individual" Paseman, 2019.04.27.
$endgroup$
– Gerhard Paseman
7 mins ago
add a comment |
$begingroup$
+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
34 mins ago
$begingroup$
@AlecRhea Fair enough. I would say I was trying to understand the impact of something on my area coming from outside, so I used the language of “applications” to make my point rhetorically. This may have been unfair.
$endgroup$
– Monroe Eskew
28 mins ago
$begingroup$
It's completely understandable, and I think this provides a lens on the set theory issue as well -- set theory has been touted and accepted as 'the' rigorous foundation for mathematics for decades (excepting some developments in category theory), but an analyst or algebraic geometer can have a completely healthy and productive career without ever really understanding any of the deeper constructions in set theory. I think requests for applications and consequences in fields outside set theory are usually attempts to get a grasp on an abstract branch of mathematics from a familiar perspective.
$endgroup$
– Alec Rhea
19 mins ago
$begingroup$
If you (and your colleagues) have enough funding, no worries. I suspect it is not the research area so much as the economics plus the psychology of the players. While my research path is primarily my own responsibility and my own fault, I believe it was influenced by how certain players viewed Universal Algebra at the time. Not all of the players were universal algebraists. Gerhard "Politics Isn't For The Individual" Paseman, 2019.04.27.
$endgroup$
– Gerhard Paseman
7 mins 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
34 mins 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
34 mins ago
$begingroup$
@AlecRhea Fair enough. I would say I was trying to understand the impact of something on my area coming from outside, so I used the language of “applications” to make my point rhetorically. This may have been unfair.
$endgroup$
– Monroe Eskew
28 mins ago
$begingroup$
@AlecRhea Fair enough. I would say I was trying to understand the impact of something on my area coming from outside, so I used the language of “applications” to make my point rhetorically. This may have been unfair.
$endgroup$
– Monroe Eskew
28 mins ago
$begingroup$
It's completely understandable, and I think this provides a lens on the set theory issue as well -- set theory has been touted and accepted as 'the' rigorous foundation for mathematics for decades (excepting some developments in category theory), but an analyst or algebraic geometer can have a completely healthy and productive career without ever really understanding any of the deeper constructions in set theory. I think requests for applications and consequences in fields outside set theory are usually attempts to get a grasp on an abstract branch of mathematics from a familiar perspective.
$endgroup$
– Alec Rhea
19 mins ago
$begingroup$
It's completely understandable, and I think this provides a lens on the set theory issue as well -- set theory has been touted and accepted as 'the' rigorous foundation for mathematics for decades (excepting some developments in category theory), but an analyst or algebraic geometer can have a completely healthy and productive career without ever really understanding any of the deeper constructions in set theory. I think requests for applications and consequences in fields outside set theory are usually attempts to get a grasp on an abstract branch of mathematics from a familiar perspective.
$endgroup$
– Alec Rhea
19 mins ago
$begingroup$
If you (and your colleagues) have enough funding, no worries. I suspect it is not the research area so much as the economics plus the psychology of the players. While my research path is primarily my own responsibility and my own fault, I believe it was influenced by how certain players viewed Universal Algebra at the time. Not all of the players were universal algebraists. Gerhard "Politics Isn't For The Individual" Paseman, 2019.04.27.
$endgroup$
– Gerhard Paseman
7 mins ago
$begingroup$
If you (and your colleagues) have enough funding, no worries. I suspect it is not the research area so much as the economics plus the psychology of the players. While my research path is primarily my own responsibility and my own fault, I believe it was influenced by how certain players viewed Universal Algebra at the time. Not all of the players were universal algebraists. Gerhard "Politics Isn't For The Individual" Paseman, 2019.04.27.
$endgroup$
– Gerhard Paseman
7 mins ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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."
answered 25 mins ago
Joseph O'RourkeJoseph O'Rourke
86.7k16240714
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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."
answered 25 mins ago
Joseph O'RourkeJoseph O'Rourke
86.7k16240714
$endgroup$
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."
answered 25 mins ago
Joseph O'RourkeJoseph O'Rourke
86.7k16240714
$endgroup$
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."
answered 25 mins ago
Joseph O'RourkeJoseph O'Rourke
86.7k16240714
$endgroup$
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 25 mins ago
Joseph O'RourkeJoseph O'Rourke
86.7k16240714
answered 25 mins ago
Joseph O'RourkeJoseph O'Rourke
86.7k16240714
answered 25 mins ago
Joseph O'RourkeJoseph O'Rourke
86.7k16240714
answered 25 mins ago
Joseph O'RourkeJoseph O'Rourke
86.7k16240714
86.7k16240714
add a comment |
add a comment |
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$begingroup$
+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
34 mins ago
$begingroup$
@AlecRhea Fair enough. I would say I was trying to understand the impact of something on my area coming from outside, so I used the language of “applications” to make my point rhetorically. This may have been unfair.
$endgroup$
– Monroe Eskew
28 mins ago
$begingroup$
It's completely understandable, and I think this provides a lens on the set theory issue as well -- set theory has been touted and accepted as 'the' rigorous foundation for mathematics for decades (excepting some developments in category theory), but an analyst or algebraic geometer can have a completely healthy and productive career without ever really understanding any of the deeper constructions in set theory. I think requests for applications and consequences in fields outside set theory are usually attempts to get a grasp on an abstract branch of mathematics from a familiar perspective.
$endgroup$
– Alec Rhea
19 mins ago
$begingroup$
If you (and your colleagues) have enough funding, no worries. I suspect it is not the research area so much as the economics plus the psychology of the players. While my research path is primarily my own responsibility and my own fault, I believe it was influenced by how certain players viewed Universal Algebra at the time. Not all of the players were universal algebraists. Gerhard "Politics Isn't For The Individual" Paseman, 2019.04.27.
$endgroup$
– Gerhard Paseman
7 mins ago