Theorems that impeded progressWhat are some famous rejections of correct mathematics?How to unify various reconstruction theorems (Gabriel-Rosenberg, Tannaka,Balmers)Theorems first published in textbooks?Theorems that are 'obvious' but hard to proveAn undergraduate's guide to the foundational theorems of logicProofs that inspire and teachExamples of major theorems with very hard proofs that have NOT dramatically improved over timeHistory of preservation theorems in forcing theoryAre there any Algebraic Geometry Theorems that were proved using Combinatorics?Did Euler prove theorems by example?Theorems demoted back to conjectures

Theorems that impeded progress


What are some famous rejections of correct mathematics?How to unify various reconstruction theorems (Gabriel-Rosenberg, Tannaka,Balmers)Theorems first published in textbooks?Theorems that are 'obvious' but hard to proveAn undergraduate's guide to the foundational theorems of logicProofs that inspire and teachExamples of major theorems with very hard proofs that have NOT dramatically improved over timeHistory of preservation theorems in forcing theoryAre there any Algebraic Geometry Theorems that were proved using Combinatorics?Did Euler prove theorems by example?Theorems demoted back to conjectures













3












$begingroup$


It may be that certain theorems, when proved true, counterintuitively retard
progress in certain domains. Lloyd Trefethen provides two examples:



  • Faber's Theorem on polynomial interpolation

  • Squire's Theorem on hydrodynamic instability


Trefethen, Lloyd N. "Inverse Yogiisms." Notices of the American Mathematical Society 63, no. 11 (2016).
Also: The Best Writing on Mathematics 2017 6 (2017): 28.
Google books link.




In my own experience, I have witnessed the several negative-results theorems in




Marvin Minsky and Seymour A. Papert.
Perceptrons: An Introduction to Computational Geometry , 1969.
MIT Press.




impede progress in neural-net research for more than a decade.1




Q. What are other examples of theorems whose (correct) proofs (possibly temporarily)
suppressed research advancement in mathematical subfields?






1
Olazaran, Mikel. "A sociological study of the official history of the perceptrons controversy." Social Studies of Science 26, no. 3 (1996): 611-659.
Abstract: "[...]I devote particular attention to the proofs and arguments of Minsky and Papert, which were interpreted as showing that further progress in neural nets was not possible, and that this approach to AI had to be abandoned.[...]"
RG link.








share|cite|improve this question









$endgroup$







  • 1




    $begingroup$
    I remember reading, I believe in some other MO post, about how whereas Donaldson's work on smooth 4 manifolds launched a vibrant program of research with invariants coming from physics, Freedman's contemporaneous work on topological 4 manifolds essentially ended the study of topological 4 manifolds. But maybe that's not what you mean by "impeded progress"
    $endgroup$
    – Sam Hopkins
    33 mins ago










  • $begingroup$
    @SamHopkins: I am seeking more misleading impeding, as opposed to closing off a line of investigation. Certainly when a line has terminated, that's it. But there are also misleading endings, which are not terminations afterall.
    $endgroup$
    – Joseph O'Rourke
    20 mins ago
















3












$begingroup$


It may be that certain theorems, when proved true, counterintuitively retard
progress in certain domains. Lloyd Trefethen provides two examples:



  • Faber's Theorem on polynomial interpolation

  • Squire's Theorem on hydrodynamic instability


Trefethen, Lloyd N. "Inverse Yogiisms." Notices of the American Mathematical Society 63, no. 11 (2016).
Also: The Best Writing on Mathematics 2017 6 (2017): 28.
Google books link.




In my own experience, I have witnessed the several negative-results theorems in




Marvin Minsky and Seymour A. Papert.
Perceptrons: An Introduction to Computational Geometry , 1969.
MIT Press.




impede progress in neural-net research for more than a decade.1




Q. What are other examples of theorems whose (correct) proofs (possibly temporarily)
suppressed research advancement in mathematical subfields?






1
Olazaran, Mikel. "A sociological study of the official history of the perceptrons controversy." Social Studies of Science 26, no. 3 (1996): 611-659.
Abstract: "[...]I devote particular attention to the proofs and arguments of Minsky and Papert, which were interpreted as showing that further progress in neural nets was not possible, and that this approach to AI had to be abandoned.[...]"
RG link.








share|cite|improve this question









$endgroup$







  • 1




    $begingroup$
    I remember reading, I believe in some other MO post, about how whereas Donaldson's work on smooth 4 manifolds launched a vibrant program of research with invariants coming from physics, Freedman's contemporaneous work on topological 4 manifolds essentially ended the study of topological 4 manifolds. But maybe that's not what you mean by "impeded progress"
    $endgroup$
    – Sam Hopkins
    33 mins ago










  • $begingroup$
    @SamHopkins: I am seeking more misleading impeding, as opposed to closing off a line of investigation. Certainly when a line has terminated, that's it. But there are also misleading endings, which are not terminations afterall.
    $endgroup$
    – Joseph O'Rourke
    20 mins ago














3












3








3





$begingroup$


It may be that certain theorems, when proved true, counterintuitively retard
progress in certain domains. Lloyd Trefethen provides two examples:



  • Faber's Theorem on polynomial interpolation

  • Squire's Theorem on hydrodynamic instability


Trefethen, Lloyd N. "Inverse Yogiisms." Notices of the American Mathematical Society 63, no. 11 (2016).
Also: The Best Writing on Mathematics 2017 6 (2017): 28.
Google books link.




In my own experience, I have witnessed the several negative-results theorems in




Marvin Minsky and Seymour A. Papert.
Perceptrons: An Introduction to Computational Geometry , 1969.
MIT Press.




impede progress in neural-net research for more than a decade.1




Q. What are other examples of theorems whose (correct) proofs (possibly temporarily)
suppressed research advancement in mathematical subfields?






1
Olazaran, Mikel. "A sociological study of the official history of the perceptrons controversy." Social Studies of Science 26, no. 3 (1996): 611-659.
Abstract: "[...]I devote particular attention to the proofs and arguments of Minsky and Papert, which were interpreted as showing that further progress in neural nets was not possible, and that this approach to AI had to be abandoned.[...]"
RG link.








share|cite|improve this question









$endgroup$




It may be that certain theorems, when proved true, counterintuitively retard
progress in certain domains. Lloyd Trefethen provides two examples:



  • Faber's Theorem on polynomial interpolation

  • Squire's Theorem on hydrodynamic instability


Trefethen, Lloyd N. "Inverse Yogiisms." Notices of the American Mathematical Society 63, no. 11 (2016).
Also: The Best Writing on Mathematics 2017 6 (2017): 28.
Google books link.




In my own experience, I have witnessed the several negative-results theorems in




Marvin Minsky and Seymour A. Papert.
Perceptrons: An Introduction to Computational Geometry , 1969.
MIT Press.




impede progress in neural-net research for more than a decade.1




Q. What are other examples of theorems whose (correct) proofs (possibly temporarily)
suppressed research advancement in mathematical subfields?






1
Olazaran, Mikel. "A sociological study of the official history of the perceptrons controversy." Social Studies of Science 26, no. 3 (1996): 611-659.
Abstract: "[...]I devote particular attention to the proofs and arguments of Minsky and Papert, which were interpreted as showing that further progress in neural nets was not possible, and that this approach to AI had to be abandoned.[...]"
RG link.





ho.history-overview big-picture






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 40 mins ago









Joseph O'RourkeJoseph O'Rourke

86.2k16237709




86.2k16237709







  • 1




    $begingroup$
    I remember reading, I believe in some other MO post, about how whereas Donaldson's work on smooth 4 manifolds launched a vibrant program of research with invariants coming from physics, Freedman's contemporaneous work on topological 4 manifolds essentially ended the study of topological 4 manifolds. But maybe that's not what you mean by "impeded progress"
    $endgroup$
    – Sam Hopkins
    33 mins ago










  • $begingroup$
    @SamHopkins: I am seeking more misleading impeding, as opposed to closing off a line of investigation. Certainly when a line has terminated, that's it. But there are also misleading endings, which are not terminations afterall.
    $endgroup$
    – Joseph O'Rourke
    20 mins ago













  • 1




    $begingroup$
    I remember reading, I believe in some other MO post, about how whereas Donaldson's work on smooth 4 manifolds launched a vibrant program of research with invariants coming from physics, Freedman's contemporaneous work on topological 4 manifolds essentially ended the study of topological 4 manifolds. But maybe that's not what you mean by "impeded progress"
    $endgroup$
    – Sam Hopkins
    33 mins ago










  • $begingroup$
    @SamHopkins: I am seeking more misleading impeding, as opposed to closing off a line of investigation. Certainly when a line has terminated, that's it. But there are also misleading endings, which are not terminations afterall.
    $endgroup$
    – Joseph O'Rourke
    20 mins ago








1




1




$begingroup$
I remember reading, I believe in some other MO post, about how whereas Donaldson's work on smooth 4 manifolds launched a vibrant program of research with invariants coming from physics, Freedman's contemporaneous work on topological 4 manifolds essentially ended the study of topological 4 manifolds. But maybe that's not what you mean by "impeded progress"
$endgroup$
– Sam Hopkins
33 mins ago




$begingroup$
I remember reading, I believe in some other MO post, about how whereas Donaldson's work on smooth 4 manifolds launched a vibrant program of research with invariants coming from physics, Freedman's contemporaneous work on topological 4 manifolds essentially ended the study of topological 4 manifolds. But maybe that's not what you mean by "impeded progress"
$endgroup$
– Sam Hopkins
33 mins ago












$begingroup$
@SamHopkins: I am seeking more misleading impeding, as opposed to closing off a line of investigation. Certainly when a line has terminated, that's it. But there are also misleading endings, which are not terminations afterall.
$endgroup$
– Joseph O'Rourke
20 mins ago





$begingroup$
@SamHopkins: I am seeking more misleading impeding, as opposed to closing off a line of investigation. Certainly when a line has terminated, that's it. But there are also misleading endings, which are not terminations afterall.
$endgroup$
– Joseph O'Rourke
20 mins ago











1 Answer
1






active

oldest

votes


















5












$begingroup$

I don't know the history, but I've heard it said that the realization that higher homotopy groups are abelian lead to people thinking the notion was useless for some time.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    Who realized "that higher homotopy groups are abelian"? Could you provide more details, citations?
    $endgroup$
    – Joseph O'Rourke
    16 mins ago






  • 1




    $begingroup$
    @JosephO'Rourke: see mathoverflow.net/a/13902/25028
    $endgroup$
    – Sam Hopkins
    13 mins ago











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1 Answer
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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









5












$begingroup$

I don't know the history, but I've heard it said that the realization that higher homotopy groups are abelian lead to people thinking the notion was useless for some time.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    Who realized "that higher homotopy groups are abelian"? Could you provide more details, citations?
    $endgroup$
    – Joseph O'Rourke
    16 mins ago






  • 1




    $begingroup$
    @JosephO'Rourke: see mathoverflow.net/a/13902/25028
    $endgroup$
    – Sam Hopkins
    13 mins ago















5












$begingroup$

I don't know the history, but I've heard it said that the realization that higher homotopy groups are abelian lead to people thinking the notion was useless for some time.






share|cite|improve this answer











$endgroup$












  • $begingroup$
    Who realized "that higher homotopy groups are abelian"? Could you provide more details, citations?
    $endgroup$
    – Joseph O'Rourke
    16 mins ago






  • 1




    $begingroup$
    @JosephO'Rourke: see mathoverflow.net/a/13902/25028
    $endgroup$
    – Sam Hopkins
    13 mins ago













5












5








5





$begingroup$

I don't know the history, but I've heard it said that the realization that higher homotopy groups are abelian lead to people thinking the notion was useless for some time.






share|cite|improve this answer











$endgroup$



I don't know the history, but I've heard it said that the realization that higher homotopy groups are abelian lead to people thinking the notion was useless for some time.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 27 mins ago









José Hdz. Stgo.

5,24734877




5,24734877










answered 30 mins ago









Daniel McLauryDaniel McLaury

290217




290217











  • $begingroup$
    Who realized "that higher homotopy groups are abelian"? Could you provide more details, citations?
    $endgroup$
    – Joseph O'Rourke
    16 mins ago






  • 1




    $begingroup$
    @JosephO'Rourke: see mathoverflow.net/a/13902/25028
    $endgroup$
    – Sam Hopkins
    13 mins ago
















  • $begingroup$
    Who realized "that higher homotopy groups are abelian"? Could you provide more details, citations?
    $endgroup$
    – Joseph O'Rourke
    16 mins ago






  • 1




    $begingroup$
    @JosephO'Rourke: see mathoverflow.net/a/13902/25028
    $endgroup$
    – Sam Hopkins
    13 mins ago















$begingroup$
Who realized "that higher homotopy groups are abelian"? Could you provide more details, citations?
$endgroup$
– Joseph O'Rourke
16 mins ago




$begingroup$
Who realized "that higher homotopy groups are abelian"? Could you provide more details, citations?
$endgroup$
– Joseph O'Rourke
16 mins ago




1




1




$begingroup$
@JosephO'Rourke: see mathoverflow.net/a/13902/25028
$endgroup$
– Sam Hopkins
13 mins ago




$begingroup$
@JosephO'Rourke: see mathoverflow.net/a/13902/25028
$endgroup$
– Sam Hopkins
13 mins ago

















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