Examples of Mathematical Papers that Contain a Kind of Research Report
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What are examples of well received mathematical papers in which the author provides detail on how a surprising solution to a problem has been found.
I am especially looking for papers that also document the dead ends of investigation, i.e. ideas that seemed promising but lead nowhere, and where the motivation and inspiration that lead to the right ideas came from.
By "surprising solution" I mean solutions that feel right at first reading and it isn't clear why they haven't been found earlier.
mathematical-writing
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show 9 more comments
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What are examples of well received mathematical papers in which the author provides detail on how a surprising solution to a problem has been found.
I am especially looking for papers that also document the dead ends of investigation, i.e. ideas that seemed promising but lead nowhere, and where the motivation and inspiration that lead to the right ideas came from.
By "surprising solution" I mean solutions that feel right at first reading and it isn't clear why they haven't been found earlier.
mathematical-writing
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31
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A long time ago, a referee asked for more information on how we had gone about finding the solution to the problem. We added half a page on that. Then we got a new report saying "the authors carry on like they solved the Riemann Hypothesis".
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– Brendan McKay
Nov 21 '18 at 10:15
18
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@BrendanMcKay its too sad that it seems to be imperative in mathematics to keep up the impression mathematicians don't experience emotions when doing research; no wonder that mathematics is judged as dry and the most undesirable thing to do.
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– Manfred Weis
Nov 21 '18 at 10:26
8
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I'm surprised JR Stallings' paper "How Not To Prove The Poincaré Conjecture" has not yet been mentioned.
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– Sam Hopkins
Nov 21 '18 at 16:15
5
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Not a paper, but Villani's "Birth of a Theorem" does that kind of thing in detail.
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– Piyush Grover
Nov 21 '18 at 17:17
5
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Dirac in Recollections of an exciting era (1977) recounts how he came up with his matrices while trying to “take the square root of a sum of four squares”.
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– Francois Ziegler
Nov 21 '18 at 18:40
|
show 9 more comments
$begingroup$
What are examples of well received mathematical papers in which the author provides detail on how a surprising solution to a problem has been found.
I am especially looking for papers that also document the dead ends of investigation, i.e. ideas that seemed promising but lead nowhere, and where the motivation and inspiration that lead to the right ideas came from.
By "surprising solution" I mean solutions that feel right at first reading and it isn't clear why they haven't been found earlier.
mathematical-writing
$endgroup$
What are examples of well received mathematical papers in which the author provides detail on how a surprising solution to a problem has been found.
I am especially looking for papers that also document the dead ends of investigation, i.e. ideas that seemed promising but lead nowhere, and where the motivation and inspiration that lead to the right ideas came from.
By "surprising solution" I mean solutions that feel right at first reading and it isn't clear why they haven't been found earlier.
mathematical-writing
mathematical-writing
asked Nov 21 '18 at 7:25
community wiki
Manfred Weis
31
$begingroup$
A long time ago, a referee asked for more information on how we had gone about finding the solution to the problem. We added half a page on that. Then we got a new report saying "the authors carry on like they solved the Riemann Hypothesis".
$endgroup$
– Brendan McKay
Nov 21 '18 at 10:15
18
$begingroup$
@BrendanMcKay its too sad that it seems to be imperative in mathematics to keep up the impression mathematicians don't experience emotions when doing research; no wonder that mathematics is judged as dry and the most undesirable thing to do.
$endgroup$
– Manfred Weis
Nov 21 '18 at 10:26
8
$begingroup$
I'm surprised JR Stallings' paper "How Not To Prove The Poincaré Conjecture" has not yet been mentioned.
$endgroup$
– Sam Hopkins
Nov 21 '18 at 16:15
5
$begingroup$
Not a paper, but Villani's "Birth of a Theorem" does that kind of thing in detail.
$endgroup$
– Piyush Grover
Nov 21 '18 at 17:17
5
$begingroup$
Dirac in Recollections of an exciting era (1977) recounts how he came up with his matrices while trying to “take the square root of a sum of four squares”.
$endgroup$
– Francois Ziegler
Nov 21 '18 at 18:40
|
show 9 more comments
31
$begingroup$
A long time ago, a referee asked for more information on how we had gone about finding the solution to the problem. We added half a page on that. Then we got a new report saying "the authors carry on like they solved the Riemann Hypothesis".
$endgroup$
– Brendan McKay
Nov 21 '18 at 10:15
18
$begingroup$
@BrendanMcKay its too sad that it seems to be imperative in mathematics to keep up the impression mathematicians don't experience emotions when doing research; no wonder that mathematics is judged as dry and the most undesirable thing to do.
$endgroup$
– Manfred Weis
Nov 21 '18 at 10:26
8
$begingroup$
I'm surprised JR Stallings' paper "How Not To Prove The Poincaré Conjecture" has not yet been mentioned.
$endgroup$
– Sam Hopkins
Nov 21 '18 at 16:15
5
$begingroup$
Not a paper, but Villani's "Birth of a Theorem" does that kind of thing in detail.
$endgroup$
– Piyush Grover
Nov 21 '18 at 17:17
5
$begingroup$
Dirac in Recollections of an exciting era (1977) recounts how he came up with his matrices while trying to “take the square root of a sum of four squares”.
$endgroup$
– Francois Ziegler
Nov 21 '18 at 18:40
31
31
$begingroup$
A long time ago, a referee asked for more information on how we had gone about finding the solution to the problem. We added half a page on that. Then we got a new report saying "the authors carry on like they solved the Riemann Hypothesis".
$endgroup$
– Brendan McKay
Nov 21 '18 at 10:15
$begingroup$
A long time ago, a referee asked for more information on how we had gone about finding the solution to the problem. We added half a page on that. Then we got a new report saying "the authors carry on like they solved the Riemann Hypothesis".
$endgroup$
– Brendan McKay
Nov 21 '18 at 10:15
18
18
$begingroup$
@BrendanMcKay its too sad that it seems to be imperative in mathematics to keep up the impression mathematicians don't experience emotions when doing research; no wonder that mathematics is judged as dry and the most undesirable thing to do.
$endgroup$
– Manfred Weis
Nov 21 '18 at 10:26
$begingroup$
@BrendanMcKay its too sad that it seems to be imperative in mathematics to keep up the impression mathematicians don't experience emotions when doing research; no wonder that mathematics is judged as dry and the most undesirable thing to do.
$endgroup$
– Manfred Weis
Nov 21 '18 at 10:26
8
8
$begingroup$
I'm surprised JR Stallings' paper "How Not To Prove The Poincaré Conjecture" has not yet been mentioned.
$endgroup$
– Sam Hopkins
Nov 21 '18 at 16:15
$begingroup$
I'm surprised JR Stallings' paper "How Not To Prove The Poincaré Conjecture" has not yet been mentioned.
$endgroup$
– Sam Hopkins
Nov 21 '18 at 16:15
5
5
$begingroup$
Not a paper, but Villani's "Birth of a Theorem" does that kind of thing in detail.
$endgroup$
– Piyush Grover
Nov 21 '18 at 17:17
$begingroup$
Not a paper, but Villani's "Birth of a Theorem" does that kind of thing in detail.
$endgroup$
– Piyush Grover
Nov 21 '18 at 17:17
5
5
$begingroup$
Dirac in Recollections of an exciting era (1977) recounts how he came up with his matrices while trying to “take the square root of a sum of four squares”.
$endgroup$
– Francois Ziegler
Nov 21 '18 at 18:40
$begingroup$
Dirac in Recollections of an exciting era (1977) recounts how he came up with his matrices while trying to “take the square root of a sum of four squares”.
$endgroup$
– Francois Ziegler
Nov 21 '18 at 18:40
|
show 9 more comments
9 Answers
9
active
oldest
votes
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Richard P. Stanley's How the Upper Bound Conjecture was proved ends with two morals:
- The shortest path may not be the best.
- Even if you don’t arrive at your destination, the journey can still be
worthwhile.
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4
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These kind of papers surely deserve more awareness and should be recommended to novices to mathematical research.
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– Manfred Weis
Nov 21 '18 at 8:17
1
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@DavidRicherby Looking at your edit, I should probably mention that the picture is mostly my fault. For a more detailed explanation, see here.
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– Martin Sleziak
Nov 21 '18 at 21:33
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@MartinSleziak Ah. Makes sense, now. I didn't look at the edit history before removing it.
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– David Richerby
Nov 21 '18 at 21:35
add a comment |
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The paper
Rawnsley, John; Schmid, Wilfried; Wolf, Joseph A., Singular unitary representations and indefinite harmonic theory, J. Funct. Anal. 51, 1-114 (1983). ZBL0511.22005.
contains an unusual “Historical Note” (pp. 102–107). E.g.:
For various reasons one expects to get $mu_n$ by... That does not work directly because... In 1975, S & W tried... At that point it became clear that an intrinsic higher $L_2$ cohomology theory was needed... In 1977, R & W looked... They did not see how to... This was the point at which S & W had been stopped... During the following academic year B succeeded in... but the method did not extend past... R & W made some progress in... These results were not published formally because... During the summer of 1979, S & W discussed the apparent disparity and clarified... then carried out a computation... then looked at the case... Thus the original S & W problem was settled... At the end of the summer of 1980, S & W saw that... could be simplified... The present version was completed in... There are two important parallel developments which we understood only after... (etc.)
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add a comment |
$begingroup$
The prime example is Euler's papers. This style is out of fashion in 20th century.
Polya in Mathematics and Plausible reasoning discusses this question at length and
even reproduces completely (in English) one of Euler's papers (on partitions).
Of the 20th century examples I can mention
MR1555091 Malmquist, J. Sur les fonctions a un nombre fini de branches définies par les équations différentielles du premier ordre. Acta Math. 36 (1913), no. 1, 297–343.
$endgroup$
add a comment |
$begingroup$
Ryan Williams provides a Casual Tour Around a Circuit Complexity Bound (the bound in question being that NEXP lacks nonuniform polysized ACC circuits) which may fit the bill, although I believe that Williams's goal is to give a motivated exposition rather than a 100% historically accurate account of how he came up with his proof.
$endgroup$
add a comment |
$begingroup$
A nice example is the article "The method of undetermined generalization and specialization, illustrated with Fred Galvin's amazing proof of the Dinitz Conjecture" by Doron Zeilberger in Amer. Math. Monthly 103, no. 3, 233-239, 1996 (see also here for a freely accessible version).
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add a comment |
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The first example that came to mind was
MR0270881 (42 #5764) van der Waerden, B. L. How the proof of Baudet's conjecture was found. 1971 Studies in Pure Mathematics (Presented to Richard Rado) pp. 251–260 Academic Press, London.
There, van der Waerden describes some of the history as well as his proof of his well-known theorem.
Another example:
MR2245898 (2007j:05091) Seymour, Paul. How the proof of the strong perfect graph conjecture was found. Gaz. Math. No. 109 (2006), 69–83.
From Wilson's review in Mathematical Reviews: "In this interesting and revealing paper, Seymour describes in graphic terms their assaults on the problem, the difficulties they came across, and the means they used to overcome these difficulties."
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add a comment |
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I think David Hayes article "The Partial Zeta Functions of a Real Quadratic Number Field Evaluated at $s=0$" fits here. First, the result is kind of surprising and, a priori, unexpected. Also, he explains the motivation that led him to his result. Finally, he explains why his approach works and why another approach did not work for him.
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add a comment |
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Another type of example. Textbooks on non-Euclidean geometry may often begin with a chapter on historical failed attempts to prove the Parallel Postulate.
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add a comment |
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I enjoy The genesis of the Macdonald polynomial statistics, complete with journal entries, and detailed descriptions of the experimental method.
This paper describes how the researchers came up with a nice formula for the combinatorial (aka modified) Macdonald polynomials.
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add a comment |
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9 Answers
9
active
oldest
votes
9 Answers
9
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Richard P. Stanley's How the Upper Bound Conjecture was proved ends with two morals:
- The shortest path may not be the best.
- Even if you don’t arrive at your destination, the journey can still be
worthwhile.
$endgroup$
4
$begingroup$
These kind of papers surely deserve more awareness and should be recommended to novices to mathematical research.
$endgroup$
– Manfred Weis
Nov 21 '18 at 8:17
1
$begingroup$
@DavidRicherby Looking at your edit, I should probably mention that the picture is mostly my fault. For a more detailed explanation, see here.
$endgroup$
– Martin Sleziak
Nov 21 '18 at 21:33
$begingroup$
@MartinSleziak Ah. Makes sense, now. I didn't look at the edit history before removing it.
$endgroup$
– David Richerby
Nov 21 '18 at 21:35
add a comment |
$begingroup$
Richard P. Stanley's How the Upper Bound Conjecture was proved ends with two morals:
- The shortest path may not be the best.
- Even if you don’t arrive at your destination, the journey can still be
worthwhile.
$endgroup$
4
$begingroup$
These kind of papers surely deserve more awareness and should be recommended to novices to mathematical research.
$endgroup$
– Manfred Weis
Nov 21 '18 at 8:17
1
$begingroup$
@DavidRicherby Looking at your edit, I should probably mention that the picture is mostly my fault. For a more detailed explanation, see here.
$endgroup$
– Martin Sleziak
Nov 21 '18 at 21:33
$begingroup$
@MartinSleziak Ah. Makes sense, now. I didn't look at the edit history before removing it.
$endgroup$
– David Richerby
Nov 21 '18 at 21:35
add a comment |
$begingroup$
Richard P. Stanley's How the Upper Bound Conjecture was proved ends with two morals:
- The shortest path may not be the best.
- Even if you don’t arrive at your destination, the journey can still be
worthwhile.
$endgroup$
Richard P. Stanley's How the Upper Bound Conjecture was proved ends with two morals:
- The shortest path may not be the best.
- Even if you don’t arrive at your destination, the journey can still be
worthwhile.
edited Nov 21 '18 at 17:11
community wiki
4 revs, 2 users 87%
Bjørn Kjos-Hanssen
4
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These kind of papers surely deserve more awareness and should be recommended to novices to mathematical research.
$endgroup$
– Manfred Weis
Nov 21 '18 at 8:17
1
$begingroup$
@DavidRicherby Looking at your edit, I should probably mention that the picture is mostly my fault. For a more detailed explanation, see here.
$endgroup$
– Martin Sleziak
Nov 21 '18 at 21:33
$begingroup$
@MartinSleziak Ah. Makes sense, now. I didn't look at the edit history before removing it.
$endgroup$
– David Richerby
Nov 21 '18 at 21:35
add a comment |
4
$begingroup$
These kind of papers surely deserve more awareness and should be recommended to novices to mathematical research.
$endgroup$
– Manfred Weis
Nov 21 '18 at 8:17
1
$begingroup$
@DavidRicherby Looking at your edit, I should probably mention that the picture is mostly my fault. For a more detailed explanation, see here.
$endgroup$
– Martin Sleziak
Nov 21 '18 at 21:33
$begingroup$
@MartinSleziak Ah. Makes sense, now. I didn't look at the edit history before removing it.
$endgroup$
– David Richerby
Nov 21 '18 at 21:35
4
4
$begingroup$
These kind of papers surely deserve more awareness and should be recommended to novices to mathematical research.
$endgroup$
– Manfred Weis
Nov 21 '18 at 8:17
$begingroup$
These kind of papers surely deserve more awareness and should be recommended to novices to mathematical research.
$endgroup$
– Manfred Weis
Nov 21 '18 at 8:17
1
1
$begingroup$
@DavidRicherby Looking at your edit, I should probably mention that the picture is mostly my fault. For a more detailed explanation, see here.
$endgroup$
– Martin Sleziak
Nov 21 '18 at 21:33
$begingroup$
@DavidRicherby Looking at your edit, I should probably mention that the picture is mostly my fault. For a more detailed explanation, see here.
$endgroup$
– Martin Sleziak
Nov 21 '18 at 21:33
$begingroup$
@MartinSleziak Ah. Makes sense, now. I didn't look at the edit history before removing it.
$endgroup$
– David Richerby
Nov 21 '18 at 21:35
$begingroup$
@MartinSleziak Ah. Makes sense, now. I didn't look at the edit history before removing it.
$endgroup$
– David Richerby
Nov 21 '18 at 21:35
add a comment |
$begingroup$
The paper
Rawnsley, John; Schmid, Wilfried; Wolf, Joseph A., Singular unitary representations and indefinite harmonic theory, J. Funct. Anal. 51, 1-114 (1983). ZBL0511.22005.
contains an unusual “Historical Note” (pp. 102–107). E.g.:
For various reasons one expects to get $mu_n$ by... That does not work directly because... In 1975, S & W tried... At that point it became clear that an intrinsic higher $L_2$ cohomology theory was needed... In 1977, R & W looked... They did not see how to... This was the point at which S & W had been stopped... During the following academic year B succeeded in... but the method did not extend past... R & W made some progress in... These results were not published formally because... During the summer of 1979, S & W discussed the apparent disparity and clarified... then carried out a computation... then looked at the case... Thus the original S & W problem was settled... At the end of the summer of 1980, S & W saw that... could be simplified... The present version was completed in... There are two important parallel developments which we understood only after... (etc.)
$endgroup$
add a comment |
$begingroup$
The paper
Rawnsley, John; Schmid, Wilfried; Wolf, Joseph A., Singular unitary representations and indefinite harmonic theory, J. Funct. Anal. 51, 1-114 (1983). ZBL0511.22005.
contains an unusual “Historical Note” (pp. 102–107). E.g.:
For various reasons one expects to get $mu_n$ by... That does not work directly because... In 1975, S & W tried... At that point it became clear that an intrinsic higher $L_2$ cohomology theory was needed... In 1977, R & W looked... They did not see how to... This was the point at which S & W had been stopped... During the following academic year B succeeded in... but the method did not extend past... R & W made some progress in... These results were not published formally because... During the summer of 1979, S & W discussed the apparent disparity and clarified... then carried out a computation... then looked at the case... Thus the original S & W problem was settled... At the end of the summer of 1980, S & W saw that... could be simplified... The present version was completed in... There are two important parallel developments which we understood only after... (etc.)
$endgroup$
add a comment |
$begingroup$
The paper
Rawnsley, John; Schmid, Wilfried; Wolf, Joseph A., Singular unitary representations and indefinite harmonic theory, J. Funct. Anal. 51, 1-114 (1983). ZBL0511.22005.
contains an unusual “Historical Note” (pp. 102–107). E.g.:
For various reasons one expects to get $mu_n$ by... That does not work directly because... In 1975, S & W tried... At that point it became clear that an intrinsic higher $L_2$ cohomology theory was needed... In 1977, R & W looked... They did not see how to... This was the point at which S & W had been stopped... During the following academic year B succeeded in... but the method did not extend past... R & W made some progress in... These results were not published formally because... During the summer of 1979, S & W discussed the apparent disparity and clarified... then carried out a computation... then looked at the case... Thus the original S & W problem was settled... At the end of the summer of 1980, S & W saw that... could be simplified... The present version was completed in... There are two important parallel developments which we understood only after... (etc.)
$endgroup$
The paper
Rawnsley, John; Schmid, Wilfried; Wolf, Joseph A., Singular unitary representations and indefinite harmonic theory, J. Funct. Anal. 51, 1-114 (1983). ZBL0511.22005.
contains an unusual “Historical Note” (pp. 102–107). E.g.:
For various reasons one expects to get $mu_n$ by... That does not work directly because... In 1975, S & W tried... At that point it became clear that an intrinsic higher $L_2$ cohomology theory was needed... In 1977, R & W looked... They did not see how to... This was the point at which S & W had been stopped... During the following academic year B succeeded in... but the method did not extend past... R & W made some progress in... These results were not published formally because... During the summer of 1979, S & W discussed the apparent disparity and clarified... then carried out a computation... then looked at the case... Thus the original S & W problem was settled... At the end of the summer of 1980, S & W saw that... could be simplified... The present version was completed in... There are two important parallel developments which we understood only after... (etc.)
answered Nov 21 '18 at 12:00
community wiki
Francois Ziegler
add a comment |
add a comment |
$begingroup$
The prime example is Euler's papers. This style is out of fashion in 20th century.
Polya in Mathematics and Plausible reasoning discusses this question at length and
even reproduces completely (in English) one of Euler's papers (on partitions).
Of the 20th century examples I can mention
MR1555091 Malmquist, J. Sur les fonctions a un nombre fini de branches définies par les équations différentielles du premier ordre. Acta Math. 36 (1913), no. 1, 297–343.
$endgroup$
add a comment |
$begingroup$
The prime example is Euler's papers. This style is out of fashion in 20th century.
Polya in Mathematics and Plausible reasoning discusses this question at length and
even reproduces completely (in English) one of Euler's papers (on partitions).
Of the 20th century examples I can mention
MR1555091 Malmquist, J. Sur les fonctions a un nombre fini de branches définies par les équations différentielles du premier ordre. Acta Math. 36 (1913), no. 1, 297–343.
$endgroup$
add a comment |
$begingroup$
The prime example is Euler's papers. This style is out of fashion in 20th century.
Polya in Mathematics and Plausible reasoning discusses this question at length and
even reproduces completely (in English) one of Euler's papers (on partitions).
Of the 20th century examples I can mention
MR1555091 Malmquist, J. Sur les fonctions a un nombre fini de branches définies par les équations différentielles du premier ordre. Acta Math. 36 (1913), no. 1, 297–343.
$endgroup$
The prime example is Euler's papers. This style is out of fashion in 20th century.
Polya in Mathematics and Plausible reasoning discusses this question at length and
even reproduces completely (in English) one of Euler's papers (on partitions).
Of the 20th century examples I can mention
MR1555091 Malmquist, J. Sur les fonctions a un nombre fini de branches définies par les équations différentielles du premier ordre. Acta Math. 36 (1913), no. 1, 297–343.
edited Nov 21 '18 at 16:22
community wiki
2 revs, 2 users 92%
Alexandre Eremenko
add a comment |
add a comment |
$begingroup$
Ryan Williams provides a Casual Tour Around a Circuit Complexity Bound (the bound in question being that NEXP lacks nonuniform polysized ACC circuits) which may fit the bill, although I believe that Williams's goal is to give a motivated exposition rather than a 100% historically accurate account of how he came up with his proof.
$endgroup$
add a comment |
$begingroup$
Ryan Williams provides a Casual Tour Around a Circuit Complexity Bound (the bound in question being that NEXP lacks nonuniform polysized ACC circuits) which may fit the bill, although I believe that Williams's goal is to give a motivated exposition rather than a 100% historically accurate account of how he came up with his proof.
$endgroup$
add a comment |
$begingroup$
Ryan Williams provides a Casual Tour Around a Circuit Complexity Bound (the bound in question being that NEXP lacks nonuniform polysized ACC circuits) which may fit the bill, although I believe that Williams's goal is to give a motivated exposition rather than a 100% historically accurate account of how he came up with his proof.
$endgroup$
Ryan Williams provides a Casual Tour Around a Circuit Complexity Bound (the bound in question being that NEXP lacks nonuniform polysized ACC circuits) which may fit the bill, although I believe that Williams's goal is to give a motivated exposition rather than a 100% historically accurate account of how he came up with his proof.
answered Nov 21 '18 at 18:24
community wiki
Timothy Chow
add a comment |
add a comment |
$begingroup$
A nice example is the article "The method of undetermined generalization and specialization, illustrated with Fred Galvin's amazing proof of the Dinitz Conjecture" by Doron Zeilberger in Amer. Math. Monthly 103, no. 3, 233-239, 1996 (see also here for a freely accessible version).
$endgroup$
add a comment |
$begingroup$
A nice example is the article "The method of undetermined generalization and specialization, illustrated with Fred Galvin's amazing proof of the Dinitz Conjecture" by Doron Zeilberger in Amer. Math. Monthly 103, no. 3, 233-239, 1996 (see also here for a freely accessible version).
$endgroup$
add a comment |
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A nice example is the article "The method of undetermined generalization and specialization, illustrated with Fred Galvin's amazing proof of the Dinitz Conjecture" by Doron Zeilberger in Amer. Math. Monthly 103, no. 3, 233-239, 1996 (see also here for a freely accessible version).
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A nice example is the article "The method of undetermined generalization and specialization, illustrated with Fred Galvin's amazing proof of the Dinitz Conjecture" by Doron Zeilberger in Amer. Math. Monthly 103, no. 3, 233-239, 1996 (see also here for a freely accessible version).
edited Nov 22 '18 at 16:18
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2 revs, 2 users 67%
Abdelmalek Abdesselam
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The first example that came to mind was
MR0270881 (42 #5764) van der Waerden, B. L. How the proof of Baudet's conjecture was found. 1971 Studies in Pure Mathematics (Presented to Richard Rado) pp. 251–260 Academic Press, London.
There, van der Waerden describes some of the history as well as his proof of his well-known theorem.
Another example:
MR2245898 (2007j:05091) Seymour, Paul. How the proof of the strong perfect graph conjecture was found. Gaz. Math. No. 109 (2006), 69–83.
From Wilson's review in Mathematical Reviews: "In this interesting and revealing paper, Seymour describes in graphic terms their assaults on the problem, the difficulties they came across, and the means they used to overcome these difficulties."
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add a comment |
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The first example that came to mind was
MR0270881 (42 #5764) van der Waerden, B. L. How the proof of Baudet's conjecture was found. 1971 Studies in Pure Mathematics (Presented to Richard Rado) pp. 251–260 Academic Press, London.
There, van der Waerden describes some of the history as well as his proof of his well-known theorem.
Another example:
MR2245898 (2007j:05091) Seymour, Paul. How the proof of the strong perfect graph conjecture was found. Gaz. Math. No. 109 (2006), 69–83.
From Wilson's review in Mathematical Reviews: "In this interesting and revealing paper, Seymour describes in graphic terms their assaults on the problem, the difficulties they came across, and the means they used to overcome these difficulties."
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add a comment |
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The first example that came to mind was
MR0270881 (42 #5764) van der Waerden, B. L. How the proof of Baudet's conjecture was found. 1971 Studies in Pure Mathematics (Presented to Richard Rado) pp. 251–260 Academic Press, London.
There, van der Waerden describes some of the history as well as his proof of his well-known theorem.
Another example:
MR2245898 (2007j:05091) Seymour, Paul. How the proof of the strong perfect graph conjecture was found. Gaz. Math. No. 109 (2006), 69–83.
From Wilson's review in Mathematical Reviews: "In this interesting and revealing paper, Seymour describes in graphic terms their assaults on the problem, the difficulties they came across, and the means they used to overcome these difficulties."
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The first example that came to mind was
MR0270881 (42 #5764) van der Waerden, B. L. How the proof of Baudet's conjecture was found. 1971 Studies in Pure Mathematics (Presented to Richard Rado) pp. 251–260 Academic Press, London.
There, van der Waerden describes some of the history as well as his proof of his well-known theorem.
Another example:
MR2245898 (2007j:05091) Seymour, Paul. How the proof of the strong perfect graph conjecture was found. Gaz. Math. No. 109 (2006), 69–83.
From Wilson's review in Mathematical Reviews: "In this interesting and revealing paper, Seymour describes in graphic terms their assaults on the problem, the difficulties they came across, and the means they used to overcome these difficulties."
answered Nov 21 '18 at 15:02
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Andrés E. Caicedo
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I think David Hayes article "The Partial Zeta Functions of a Real Quadratic Number Field Evaluated at $s=0$" fits here. First, the result is kind of surprising and, a priori, unexpected. Also, he explains the motivation that led him to his result. Finally, he explains why his approach works and why another approach did not work for him.
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add a comment |
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I think David Hayes article "The Partial Zeta Functions of a Real Quadratic Number Field Evaluated at $s=0$" fits here. First, the result is kind of surprising and, a priori, unexpected. Also, he explains the motivation that led him to his result. Finally, he explains why his approach works and why another approach did not work for him.
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add a comment |
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I think David Hayes article "The Partial Zeta Functions of a Real Quadratic Number Field Evaluated at $s=0$" fits here. First, the result is kind of surprising and, a priori, unexpected. Also, he explains the motivation that led him to his result. Finally, he explains why his approach works and why another approach did not work for him.
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I think David Hayes article "The Partial Zeta Functions of a Real Quadratic Number Field Evaluated at $s=0$" fits here. First, the result is kind of surprising and, a priori, unexpected. Also, he explains the motivation that led him to his result. Finally, he explains why his approach works and why another approach did not work for him.
edited Nov 22 '18 at 16:21
community wiki
2 revs, 2 users 67%
EFinat-S
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Another type of example. Textbooks on non-Euclidean geometry may often begin with a chapter on historical failed attempts to prove the Parallel Postulate.
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add a comment |
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Another type of example. Textbooks on non-Euclidean geometry may often begin with a chapter on historical failed attempts to prove the Parallel Postulate.
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add a comment |
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Another type of example. Textbooks on non-Euclidean geometry may often begin with a chapter on historical failed attempts to prove the Parallel Postulate.
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Another type of example. Textbooks on non-Euclidean geometry may often begin with a chapter on historical failed attempts to prove the Parallel Postulate.
answered Nov 21 '18 at 18:14
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Gerald Edgar
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I enjoy The genesis of the Macdonald polynomial statistics, complete with journal entries, and detailed descriptions of the experimental method.
This paper describes how the researchers came up with a nice formula for the combinatorial (aka modified) Macdonald polynomials.
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I enjoy The genesis of the Macdonald polynomial statistics, complete with journal entries, and detailed descriptions of the experimental method.
This paper describes how the researchers came up with a nice formula for the combinatorial (aka modified) Macdonald polynomials.
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add a comment |
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I enjoy The genesis of the Macdonald polynomial statistics, complete with journal entries, and detailed descriptions of the experimental method.
This paper describes how the researchers came up with a nice formula for the combinatorial (aka modified) Macdonald polynomials.
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I enjoy The genesis of the Macdonald polynomial statistics, complete with journal entries, and detailed descriptions of the experimental method.
This paper describes how the researchers came up with a nice formula for the combinatorial (aka modified) Macdonald polynomials.
answered Dec 10 '18 at 7:28
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Per Alexandersson
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A long time ago, a referee asked for more information on how we had gone about finding the solution to the problem. We added half a page on that. Then we got a new report saying "the authors carry on like they solved the Riemann Hypothesis".
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– Brendan McKay
Nov 21 '18 at 10:15
18
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@BrendanMcKay its too sad that it seems to be imperative in mathematics to keep up the impression mathematicians don't experience emotions when doing research; no wonder that mathematics is judged as dry and the most undesirable thing to do.
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– Manfred Weis
Nov 21 '18 at 10:26
8
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I'm surprised JR Stallings' paper "How Not To Prove The Poincaré Conjecture" has not yet been mentioned.
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– Sam Hopkins
Nov 21 '18 at 16:15
5
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Not a paper, but Villani's "Birth of a Theorem" does that kind of thing in detail.
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– Piyush Grover
Nov 21 '18 at 17:17
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Dirac in Recollections of an exciting era (1977) recounts how he came up with his matrices while trying to “take the square root of a sum of four squares”.
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– Francois Ziegler
Nov 21 '18 at 18:40