Controversial area of mathematicsToposophy vs Set theoretical multiverse philosophyHow platonistic is your...
Controversial area of mathematics
Toposophy vs Set theoretical multiverse philosophyHow platonistic is your attitude towards mathematics?Badiou and MathematicsLogic in mathematics and philosophyEssential reads in the philosophy of mathematics and set theoryEuler's mathematics in terms of modern theories?Is there an observer dependent mathematics?Meta$^{n{-}th}$ mathematicsWhy 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 3 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
$endgroup$
1
$begingroup$
+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
2 hours 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
2 hours 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
2 hours 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
1 hour ago
2
$begingroup$
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♦
1 hour ago
|
show 3 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
asked 2 hours ago
community wiki
Monroe Eskew
1
$begingroup$
+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
2 hours 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
2 hours 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
2 hours 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
1 hour ago
2
$begingroup$
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♦
1 hour ago
|
show 3 more comments
1
$begingroup$
+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
2 hours 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
2 hours 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
2 hours 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
1 hour ago
2
$begingroup$
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♦
1 hour ago
1
1
$begingroup$
+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
2 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
2 hours 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
2 hours 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
2 hours 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
2 hours 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
2 hours 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
1 hour 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
1 hour ago
2
2
$begingroup$
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♦
1 hour 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♦
1 hour ago
|
show 3 more comments
2 Answers
2
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."
$endgroup$
$begingroup$
I think one could make a case that astronomers and data scientists / statisticians are in a similar relationship to physicists and mathematicians, respectively.
$endgroup$
– Joseph O'Rourke
1 hour ago
1
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
1 hour ago
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 |
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2 Answers
2
active
oldest
votes
2 Answers
2
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."
$endgroup$
$begingroup$
I think one could make a case that astronomers and data scientists / statisticians are in a similar relationship to physicists and mathematicians, respectively.
$endgroup$
– Joseph O'Rourke
1 hour ago
1
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
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."
$endgroup$
$begingroup$
I think one could make a case that astronomers and data scientists / statisticians are in a similar relationship to physicists and mathematicians, respectively.
$endgroup$
– Joseph O'Rourke
1 hour ago
1
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
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."
$endgroup$
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 2 hours ago
community wiki
Joseph O'Rourke
$begingroup$
I think one could make a case that astronomers and data scientists / statisticians are in a similar relationship to physicists and mathematicians, respectively.
$endgroup$
– Joseph O'Rourke
1 hour ago
1
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
1 hour ago
add a comment |
$begingroup$
I think one could make a case that astronomers and data scientists / statisticians are in a similar relationship to physicists and mathematicians, respectively.
$endgroup$
– Joseph O'Rourke
1 hour ago
1
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
1 hour ago
$begingroup$
I think one could make a case that astronomers and data scientists / statisticians are in a similar relationship to physicists and mathematicians, respectively.
$endgroup$
– Joseph O'Rourke
1 hour ago
$begingroup$
I think one could make a case that astronomers and data scientists / statisticians are in a similar relationship to physicists and mathematicians, respectively.
$endgroup$
– Joseph O'Rourke
1 hour ago
1
1
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
1 hour ago
$begingroup$
I'm confused. Which one is set theory? I feel that it's both.
$endgroup$
– Asaf Karagila
1 hour ago
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.
$endgroup$
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 1 hour ago
community wiki
Richard Diagram
add a comment |
add a comment |
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1
$begingroup$
+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
2 hours 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
2 hours 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
2 hours 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
1 hour ago
2
$begingroup$
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♦
1 hour ago