Short but Substantial Math Papers [closed]

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down vote

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I am looking for short papers that made a significant impact on the mathematics community. I have already seen:
interesting-but-short-math-papers
and, What is the Shortest Ph.D. Thesis? on math overflow, but these weren't quite what I was looking for (although the intersection of the set of answers to this question with the set of answers to either of the above links is likely to be non-trivial)

I am more interested in short and important works of mathematics, not necessarily Ph.D.s (but not necessarily not Ph.D.s either). Things that changed the course of mathematical history, that sort of thing.

Any suggested readings would be very much appreciated.

EDIT:

I realize I was not clear on what I meant by short. around the 20 page or less mark. If it goes higher, but is really something for its size then that is acceptable too.

reference-request soft-question math-history big-list

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edited Aug 31 at 13:07

asked Aug 31 at 13:02

Logan Toll

738417

closed as too broad by m_t_, user133281, Paul Frost, John Ma, HK Lee Sep 1 at 2:39

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  A classic in short papers is John Nash's Equilibrium Points in N-Person Games with $1$ page(something which today would maybe not be considered a paper anymore). With $26$ pages a little over, but compensating this through its impact, could be Goedel's Ueber formal Unentscheidbare Saetze der Principia Mathematica und verwandter System, I.
  – zzuussee
  Aug 31 at 13:14
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  This MO question could also be of interest : mathoverflow.net/questions/7330/… (the first two answers there are the paper by Riemann in Barry Cipra's answer and the Nash one in the comment above).
  – Arnaud D.
  Aug 31 at 13:19
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Levin's paper on universal search problems was only 2 pages long, but introduced the idea of NP-completeness in complexity theory (which might stretch your definition of mathematics a bit).
  – chepner
  Aug 31 at 15:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @chepner: Why is it stretching? P=NP is still an open problem that can be written as an arithmetical sentence (namely one that only quantifies over natural numbers), and even got chosen by the Clay Mathematics Institute as 1 of only 7 Millenium Prize Problems. =)
  – user21820
  Aug 31 at 16:48
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  If Riemann hypothesis is wrong and a counterexample is found, the corresponding paper would be pivotal and extremely short : "BTW, here's a non-trivial zero for Riemann zeta function which is outside the critical line : $a+bi$. kthxbye".
  – Eric Duminil
  Aug 31 at 21:40
  

  
  
  
  

 | 
show 2 more comments

up vote
9
down vote

favorite

7

I am looking for short papers that made a significant impact on the mathematics community. I have already seen:
interesting-but-short-math-papers
and, What is the Shortest Ph.D. Thesis? on math overflow, but these weren't quite what I was looking for (although the intersection of the set of answers to this question with the set of answers to either of the above links is likely to be non-trivial)

I am more interested in short and important works of mathematics, not necessarily Ph.D.s (but not necessarily not Ph.D.s either). Things that changed the course of mathematical history, that sort of thing.

Any suggested readings would be very much appreciated.

EDIT:

I realize I was not clear on what I meant by short. around the 20 page or less mark. If it goes higher, but is really something for its size then that is acceptable too.

reference-request soft-question math-history big-list

share|cite|improve this question

edited Aug 31 at 13:07

asked Aug 31 at 13:02

Logan Toll

738417

closed as too broad by m_t_, user133281, Paul Frost, John Ma, HK Lee Sep 1 at 2:39

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  A classic in short papers is John Nash's Equilibrium Points in N-Person Games with $1$ page(something which today would maybe not be considered a paper anymore). With $26$ pages a little over, but compensating this through its impact, could be Goedel's Ueber formal Unentscheidbare Saetze der Principia Mathematica und verwandter System, I.
  – zzuussee
  Aug 31 at 13:14
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  This MO question could also be of interest : mathoverflow.net/questions/7330/… (the first two answers there are the paper by Riemann in Barry Cipra's answer and the Nash one in the comment above).
  – Arnaud D.
  Aug 31 at 13:19
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Levin's paper on universal search problems was only 2 pages long, but introduced the idea of NP-completeness in complexity theory (which might stretch your definition of mathematics a bit).
  – chepner
  Aug 31 at 15:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @chepner: Why is it stretching? P=NP is still an open problem that can be written as an arithmetical sentence (namely one that only quantifies over natural numbers), and even got chosen by the Clay Mathematics Institute as 1 of only 7 Millenium Prize Problems. =)
  – user21820
  Aug 31 at 16:48
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  If Riemann hypothesis is wrong and a counterexample is found, the corresponding paper would be pivotal and extremely short : "BTW, here's a non-trivial zero for Riemann zeta function which is outside the critical line : $a+bi$. kthxbye".
  – Eric Duminil
  Aug 31 at 21:40
  

  
  
  
  

 | 
show 2 more comments

up vote
9
down vote

favorite

7

up vote
9
down vote

favorite

7

7

I am looking for short papers that made a significant impact on the mathematics community. I have already seen:
interesting-but-short-math-papers
and, What is the Shortest Ph.D. Thesis? on math overflow, but these weren't quite what I was looking for (although the intersection of the set of answers to this question with the set of answers to either of the above links is likely to be non-trivial)

I am more interested in short and important works of mathematics, not necessarily Ph.D.s (but not necessarily not Ph.D.s either). Things that changed the course of mathematical history, that sort of thing.

Any suggested readings would be very much appreciated.

EDIT:

I realize I was not clear on what I meant by short. around the 20 page or less mark. If it goes higher, but is really something for its size then that is acceptable too.

reference-request soft-question math-history big-list

share|cite|improve this question

edited Aug 31 at 13:07

asked Aug 31 at 13:02

Logan Toll

738417

I am looking for short papers that made a significant impact on the mathematics community. I have already seen:
interesting-but-short-math-papers
and, What is the Shortest Ph.D. Thesis? on math overflow, but these weren't quite what I was looking for (although the intersection of the set of answers to this question with the set of answers to either of the above links is likely to be non-trivial)

I am more interested in short and important works of mathematics, not necessarily Ph.D.s (but not necessarily not Ph.D.s either). Things that changed the course of mathematical history, that sort of thing.

Any suggested readings would be very much appreciated.

EDIT:

I realize I was not clear on what I meant by short. around the 20 page or less mark. If it goes higher, but is really something for its size then that is acceptable too.

reference-request soft-question math-history big-list

share|cite|improve this question

edited Aug 31 at 13:07

asked Aug 31 at 13:02

Logan Toll

738417

share|cite|improve this question

share|cite|improve this question

edited Aug 31 at 13:07

edited Aug 31 at 13:07

edited Aug 31 at 13:07

asked Aug 31 at 13:02

Logan Toll

738417

asked Aug 31 at 13:02

Logan Toll

738417

asked Aug 31 at 13:02

Logan Toll

738417

738417

closed as too broad by m_t_, user133281, Paul Frost, John Ma, HK Lee Sep 1 at 2:39

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

closed as too broad by m_t_, user133281, Paul Frost, John Ma, HK Lee Sep 1 at 2:39

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  A classic in short papers is John Nash's Equilibrium Points in N-Person Games with $1$ page(something which today would maybe not be considered a paper anymore). With $26$ pages a little over, but compensating this through its impact, could be Goedel's Ueber formal Unentscheidbare Saetze der Principia Mathematica und verwandter System, I.
  – zzuussee
  Aug 31 at 13:14
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  This MO question could also be of interest : mathoverflow.net/questions/7330/… (the first two answers there are the paper by Riemann in Barry Cipra's answer and the Nash one in the comment above).
  – Arnaud D.
  Aug 31 at 13:19
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Levin's paper on universal search problems was only 2 pages long, but introduced the idea of NP-completeness in complexity theory (which might stretch your definition of mathematics a bit).
  – chepner
  Aug 31 at 15:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @chepner: Why is it stretching? P=NP is still an open problem that can be written as an arithmetical sentence (namely one that only quantifies over natural numbers), and even got chosen by the Clay Mathematics Institute as 1 of only 7 Millenium Prize Problems. =)
  – user21820
  Aug 31 at 16:48
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  If Riemann hypothesis is wrong and a counterexample is found, the corresponding paper would be pivotal and extremely short : "BTW, here's a non-trivial zero for Riemann zeta function which is outside the critical line : $a+bi$. kthxbye".
  – Eric Duminil
  Aug 31 at 21:40
  

  
  
  
  

 | 
show 2 more comments

• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  A classic in short papers is John Nash's Equilibrium Points in N-Person Games with $1$ page(something which today would maybe not be considered a paper anymore). With $26$ pages a little over, but compensating this through its impact, could be Goedel's Ueber formal Unentscheidbare Saetze der Principia Mathematica und verwandter System, I.
  – zzuussee
  Aug 31 at 13:14
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  This MO question could also be of interest : mathoverflow.net/questions/7330/… (the first two answers there are the paper by Riemann in Barry Cipra's answer and the Nash one in the comment above).
  – Arnaud D.
  Aug 31 at 13:19
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Levin's paper on universal search problems was only 2 pages long, but introduced the idea of NP-completeness in complexity theory (which might stretch your definition of mathematics a bit).
  – chepner
  Aug 31 at 15:19
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @chepner: Why is it stretching? P=NP is still an open problem that can be written as an arithmetical sentence (namely one that only quantifies over natural numbers), and even got chosen by the Clay Mathematics Institute as 1 of only 7 Millenium Prize Problems. =)
  – user21820
  Aug 31 at 16:48
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  If Riemann hypothesis is wrong and a counterexample is found, the corresponding paper would be pivotal and extremely short : "BTW, here's a non-trivial zero for Riemann zeta function which is outside the critical line : $a+bi$. kthxbye".
  – Eric Duminil
  Aug 31 at 21:40
  

  
  
  
  

2

2

A classic in short papers is John Nash's Equilibrium Points in N-Person Games with $1$ page(something which today would maybe not be considered a paper anymore). With $26$ pages a little over, but compensating this through its impact, could be Goedel's Ueber formal Unentscheidbare Saetze der Principia Mathematica und verwandter System, I.
– zzuussee
Aug 31 at 13:14

A classic in short papers is John Nash's Equilibrium Points in N-Person Games with $1$ page(something which today would maybe not be considered a paper anymore). With $26$ pages a little over, but compensating this through its impact, could be Goedel's Ueber formal Unentscheidbare Saetze der Principia Mathematica und verwandter System, I.
– zzuussee
Aug 31 at 13:14

3

3

This MO question could also be of interest : mathoverflow.net/questions/7330/… (the first two answers there are the paper by Riemann in Barry Cipra's answer and the Nash one in the comment above).
– Arnaud D.
Aug 31 at 13:19

This MO question could also be of interest : mathoverflow.net/questions/7330/… (the first two answers there are the paper by Riemann in Barry Cipra's answer and the Nash one in the comment above).
– Arnaud D.
Aug 31 at 13:19

Levin's paper on universal search problems was only 2 pages long, but introduced the idea of NP-completeness in complexity theory (which might stretch your definition of mathematics a bit).
– chepner
Aug 31 at 15:19

Levin's paper on universal search problems was only 2 pages long, but introduced the idea of NP-completeness in complexity theory (which might stretch your definition of mathematics a bit).
– chepner
Aug 31 at 15:19

@chepner: Why is it stretching? P=NP is still an open problem that can be written as an arithmetical sentence (namely one that only quantifies over natural numbers), and even got chosen by the Clay Mathematics Institute as 1 of only 7 Millenium Prize Problems. =)
– user21820
Aug 31 at 16:48

@chepner: Why is it stretching? P=NP is still an open problem that can be written as an arithmetical sentence (namely one that only quantifies over natural numbers), and even got chosen by the Clay Mathematics Institute as 1 of only 7 Millenium Prize Problems. =)
– user21820
Aug 31 at 16:48

1

1

If Riemann hypothesis is wrong and a counterexample is found, the corresponding paper would be pivotal and extremely short : "BTW, here's a non-trivial zero for Riemann zeta function which is outside the critical line : $a+bi$. kthxbye".
– Eric Duminil
Aug 31 at 21:40

If Riemann hypothesis is wrong and a counterexample is found, the corresponding paper would be pivotal and extremely short : "BTW, here's a non-trivial zero for Riemann zeta function which is outside the critical line : $a+bi$. kthxbye".
– Eric Duminil
Aug 31 at 21:40

 | 
show 2 more comments

7 Answers
7

active

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up vote
15
down vote

Riemann's short paper, "Über die Anzahl der Primzahlen unter einer gegebenen Grösse," surely qualifies.

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answered Aug 31 at 13:15

community wiki

Barry Cipra

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

add a comment | 

up vote
7
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Not a paper, but definitely significant, is Russell's paradoxical letter to Frege.

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answered Aug 31 at 13:34

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Barry Cipra

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

add a comment | 

up vote
6
down vote

I would recommend Classics of Mathematics, ed. Ronald Calinger. It's got articles from a very broad range of mathematical history, all the way from the Stone Age through 1932 (includes Gödel). Naturally, it does not include later works. Most of the most important ideas in modern mathematics will be found in here somewhere. For more modern topics, I found Love and Math by Edward Frenkel to be excellent.

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answered Aug 31 at 13:10

Adrian Keister

4,04541633

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up vote
5
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Short does not mean a lot of things for me. A paper may be short, but to understand it you may have to read a lot of books. You can read the work of Milnor, he is very well-known for is concise papers which are very well written. Look for example his work on exotic spheres.

Milnor, John W. (1959), "Differentiable structures on spheres", American Journal of Mathematics, 81 (4): 962–972

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edited Aug 31 at 16:44

answered Aug 31 at 13:39

Tsemo Aristide

52.2k11244

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up vote
2
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There is a proof of the non-existence of vector fields on spheres by (Adams and Atiyah ?) that was famously said, could fit on a post card. There is an Indian mathematician named C.P. Ramanujan who wrote a number of very important papers in algebraic geometry and number theory. To the best of my recollection, none of his papers is over 20 pages.

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answered Aug 31 at 19:10

aginensky

1213

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up vote
1
down vote

The Proceedings of the AMS is all about short papers. You could probably search MathSciNet for publications in the Proceedings and sort by citation number to find some winners.

^{I'd do this myself, but I don't have a login right now :c}

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answered Aug 31 at 16:18

community wiki

Mike Pierce

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1
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The Noah Sheets helped me a lot in contest math.

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answered Aug 31 at 21:13

Jason Kim

53516

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  I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae.
  – Arnaud D.
  Sep 3 at 11:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Oh... well then I guess I can't contribute...
  – Jason Kim
  Sep 3 at 16:08
  
  

  
  
  
  

add a comment | 

7 Answers
7

active

oldest

votes

7 Answers
7

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
15
down vote

Riemann's short paper, "Über die Anzahl der Primzahlen unter einer gegebenen Grösse," surely qualifies.

share|cite|improve this answer

answered Aug 31 at 13:15

community wiki

Barry Cipra

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

add a comment | 

up vote
15
down vote

Riemann's short paper, "Über die Anzahl der Primzahlen unter einer gegebenen Grösse," surely qualifies.

share|cite|improve this answer

answered Aug 31 at 13:15

community wiki

Barry Cipra

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

add a comment | 

up vote
15
down vote

up vote
15
down vote

Riemann's short paper, "Über die Anzahl der Primzahlen unter einer gegebenen Grösse," surely qualifies.

share|cite|improve this answer

answered Aug 31 at 13:15

community wiki

Barry Cipra

Riemann's short paper, "Über die Anzahl der Primzahlen unter einer gegebenen Grösse," surely qualifies.

share|cite|improve this answer

answered Aug 31 at 13:15

community wiki

Barry Cipra

share|cite|improve this answer

share|cite|improve this answer

answered Aug 31 at 13:15

answered Aug 31 at 13:15

answered Aug 31 at 13:15

community wiki

Barry Cipra

community wiki

Barry Cipra

community wiki

Barry Cipra

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

1

1

I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
– Barry Cipra
Aug 31 at 13:36

I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
– Barry Cipra
Aug 31 at 13:36

add a comment | 

up vote
7
down vote

Not a paper, but definitely significant, is Russell's paradoxical letter to Frege.

share|cite|improve this answer

answered Aug 31 at 13:34

community wiki

Barry Cipra

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

add a comment | 

up vote
7
down vote

Not a paper, but definitely significant, is Russell's paradoxical letter to Frege.

share|cite|improve this answer

answered Aug 31 at 13:34

community wiki

Barry Cipra

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

add a comment | 

up vote
7
down vote

up vote
7
down vote

Not a paper, but definitely significant, is Russell's paradoxical letter to Frege.

share|cite|improve this answer

answered Aug 31 at 13:34

community wiki

Barry Cipra

Not a paper, but definitely significant, is Russell's paradoxical letter to Frege.

share|cite|improve this answer

answered Aug 31 at 13:34

community wiki

Barry Cipra

share|cite|improve this answer

share|cite|improve this answer

answered Aug 31 at 13:34

answered Aug 31 at 13:34

answered Aug 31 at 13:34

community wiki

Barry Cipra

community wiki

Barry Cipra

community wiki

Barry Cipra

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
  – Barry Cipra
  Aug 31 at 13:36
  
  

  
  
  
  

I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
– Barry Cipra
Aug 31 at 13:36

I've made this answer community wiki so that upvotes can indicate agreement rather than reward.
– Barry Cipra
Aug 31 at 13:36

add a comment | 

up vote
6
down vote

I would recommend Classics of Mathematics, ed. Ronald Calinger. It's got articles from a very broad range of mathematical history, all the way from the Stone Age through 1932 (includes Gödel). Naturally, it does not include later works. Most of the most important ideas in modern mathematics will be found in here somewhere. For more modern topics, I found Love and Math by Edward Frenkel to be excellent.

share|cite|improve this answer

answered Aug 31 at 13:10

Adrian Keister

4,04541633

add a comment | 

up vote
6
down vote

I would recommend Classics of Mathematics, ed. Ronald Calinger. It's got articles from a very broad range of mathematical history, all the way from the Stone Age through 1932 (includes Gödel). Naturally, it does not include later works. Most of the most important ideas in modern mathematics will be found in here somewhere. For more modern topics, I found Love and Math by Edward Frenkel to be excellent.

share|cite|improve this answer

answered Aug 31 at 13:10

Adrian Keister

4,04541633

add a comment | 

up vote
6
down vote

up vote
6
down vote

I would recommend Classics of Mathematics, ed. Ronald Calinger. It's got articles from a very broad range of mathematical history, all the way from the Stone Age through 1932 (includes Gödel). Naturally, it does not include later works. Most of the most important ideas in modern mathematics will be found in here somewhere. For more modern topics, I found Love and Math by Edward Frenkel to be excellent.

share|cite|improve this answer

answered Aug 31 at 13:10

Adrian Keister

4,04541633

I would recommend Classics of Mathematics, ed. Ronald Calinger. It's got articles from a very broad range of mathematical history, all the way from the Stone Age through 1932 (includes Gödel). Naturally, it does not include later works. Most of the most important ideas in modern mathematics will be found in here somewhere. For more modern topics, I found Love and Math by Edward Frenkel to be excellent.

share|cite|improve this answer

answered Aug 31 at 13:10

Adrian Keister

4,04541633

share|cite|improve this answer

share|cite|improve this answer

answered Aug 31 at 13:10

Adrian Keister

4,04541633

answered Aug 31 at 13:10

Adrian Keister

4,04541633

answered Aug 31 at 13:10

Adrian Keister

4,04541633

4,04541633

add a comment | 

add a comment | 

up vote
5
down vote

Short does not mean a lot of things for me. A paper may be short, but to understand it you may have to read a lot of books. You can read the work of Milnor, he is very well-known for is concise papers which are very well written. Look for example his work on exotic spheres.

Milnor, John W. (1959), "Differentiable structures on spheres", American Journal of Mathematics, 81 (4): 962–972

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edited Aug 31 at 16:44

answered Aug 31 at 13:39

Tsemo Aristide

52.2k11244

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up vote
5
down vote

Short does not mean a lot of things for me. A paper may be short, but to understand it you may have to read a lot of books. You can read the work of Milnor, he is very well-known for is concise papers which are very well written. Look for example his work on exotic spheres.

Milnor, John W. (1959), "Differentiable structures on spheres", American Journal of Mathematics, 81 (4): 962–972

share|cite|improve this answer

edited Aug 31 at 16:44

answered Aug 31 at 13:39

Tsemo Aristide

52.2k11244

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up vote
5
down vote

up vote
5
down vote

Short does not mean a lot of things for me. A paper may be short, but to understand it you may have to read a lot of books. You can read the work of Milnor, he is very well-known for is concise papers which are very well written. Look for example his work on exotic spheres.

Milnor, John W. (1959), "Differentiable structures on spheres", American Journal of Mathematics, 81 (4): 962–972

share|cite|improve this answer

edited Aug 31 at 16:44

answered Aug 31 at 13:39

Tsemo Aristide

52.2k11244

Short does not mean a lot of things for me. A paper may be short, but to understand it you may have to read a lot of books. You can read the work of Milnor, he is very well-known for is concise papers which are very well written. Look for example his work on exotic spheres.

Milnor, John W. (1959), "Differentiable structures on spheres", American Journal of Mathematics, 81 (4): 962–972

share|cite|improve this answer

edited Aug 31 at 16:44

answered Aug 31 at 13:39

Tsemo Aristide

52.2k11244

share|cite|improve this answer

share|cite|improve this answer

edited Aug 31 at 16:44

edited Aug 31 at 16:44

edited Aug 31 at 16:44

answered Aug 31 at 13:39

Tsemo Aristide

52.2k11244

answered Aug 31 at 13:39

Tsemo Aristide

52.2k11244

answered Aug 31 at 13:39

Tsemo Aristide

52.2k11244

52.2k11244

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add a comment | 

up vote
2
down vote

There is a proof of the non-existence of vector fields on spheres by (Adams and Atiyah ?) that was famously said, could fit on a post card. There is an Indian mathematician named C.P. Ramanujan who wrote a number of very important papers in algebraic geometry and number theory. To the best of my recollection, none of his papers is over 20 pages.

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answered Aug 31 at 19:10

aginensky

1213

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up vote
2
down vote

There is a proof of the non-existence of vector fields on spheres by (Adams and Atiyah ?) that was famously said, could fit on a post card. There is an Indian mathematician named C.P. Ramanujan who wrote a number of very important papers in algebraic geometry and number theory. To the best of my recollection, none of his papers is over 20 pages.

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answered Aug 31 at 19:10

aginensky

1213

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up vote
2
down vote

up vote
2
down vote

There is a proof of the non-existence of vector fields on spheres by (Adams and Atiyah ?) that was famously said, could fit on a post card. There is an Indian mathematician named C.P. Ramanujan who wrote a number of very important papers in algebraic geometry and number theory. To the best of my recollection, none of his papers is over 20 pages.

share|cite|improve this answer

answered Aug 31 at 19:10

aginensky

1213

There is a proof of the non-existence of vector fields on spheres by (Adams and Atiyah ?) that was famously said, could fit on a post card. There is an Indian mathematician named C.P. Ramanujan who wrote a number of very important papers in algebraic geometry and number theory. To the best of my recollection, none of his papers is over 20 pages.

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answered Aug 31 at 19:10

aginensky

1213

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share|cite|improve this answer

answered Aug 31 at 19:10

aginensky

1213

answered Aug 31 at 19:10

aginensky

1213

answered Aug 31 at 19:10

aginensky

1213

1213

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add a comment | 

up vote
1
down vote

The Proceedings of the AMS is all about short papers. You could probably search MathSciNet for publications in the Proceedings and sort by citation number to find some winners.

^{I'd do this myself, but I don't have a login right now :c}

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answered Aug 31 at 16:18

community wiki

Mike Pierce

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up vote
1
down vote

The Proceedings of the AMS is all about short papers. You could probably search MathSciNet for publications in the Proceedings and sort by citation number to find some winners.

^{I'd do this myself, but I don't have a login right now :c}

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answered Aug 31 at 16:18

community wiki

Mike Pierce

add a comment | 

up vote
1
down vote

up vote
1
down vote

The Proceedings of the AMS is all about short papers. You could probably search MathSciNet for publications in the Proceedings and sort by citation number to find some winners.

^{I'd do this myself, but I don't have a login right now :c}

share|cite|improve this answer

answered Aug 31 at 16:18

community wiki

Mike Pierce

The Proceedings of the AMS is all about short papers. You could probably search MathSciNet for publications in the Proceedings and sort by citation number to find some winners.

^{I'd do this myself, but I don't have a login right now :c}

share|cite|improve this answer

answered Aug 31 at 16:18

community wiki

Mike Pierce

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share|cite|improve this answer

answered Aug 31 at 16:18

answered Aug 31 at 16:18

answered Aug 31 at 16:18

community wiki

Mike Pierce

community wiki

Mike Pierce

community wiki

Mike Pierce

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up vote
1
down vote

The Noah Sheets helped me a lot in contest math.

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answered Aug 31 at 21:13

Jason Kim

53516

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae.
  – Arnaud D.
  Sep 3 at 11:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Oh... well then I guess I can't contribute...
  – Jason Kim
  Sep 3 at 16:08
  
  

  
  
  
  

add a comment | 

up vote
1
down vote

The Noah Sheets helped me a lot in contest math.

share|cite|improve this answer

answered Aug 31 at 21:13

Jason Kim

53516

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae.
  – Arnaud D.
  Sep 3 at 11:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Oh... well then I guess I can't contribute...
  – Jason Kim
  Sep 3 at 16:08
  
  

  
  
  
  

add a comment | 

up vote
1
down vote

up vote
1
down vote

The Noah Sheets helped me a lot in contest math.

share|cite|improve this answer

answered Aug 31 at 21:13

Jason Kim

53516

The Noah Sheets helped me a lot in contest math.

share|cite|improve this answer

answered Aug 31 at 21:13

Jason Kim

53516

share|cite|improve this answer

share|cite|improve this answer

answered Aug 31 at 21:13

Jason Kim

53516

answered Aug 31 at 21:13

Jason Kim

53516

answered Aug 31 at 21:13

Jason Kim

53516

53516

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae.
  – Arnaud D.
  Sep 3 at 11:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Oh... well then I guess I can't contribute...
  – Jason Kim
  Sep 3 at 16:08
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae.
  – Arnaud D.
  Sep 3 at 11:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Oh... well then I guess I can't contribute...
  – Jason Kim
  Sep 3 at 16:08
  
  

  
  
  
  

I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae.
– Arnaud D.
Sep 3 at 11:49

I don't think this qualifies as an answer to the question : it seems to me that OP asks about articles that have had a lot of influence on mathematical research by introducing new ideas. Your link is just a list of known formulae.
– Arnaud D.
Sep 3 at 11:49

Oh... well then I guess I can't contribute...
– Jason Kim
Sep 3 at 16:08

Oh... well then I guess I can't contribute...
– Jason Kim
Sep 3 at 16:08

add a comment |