Mixing
Theorem that von Neumann proved in five minutes.
$begingroup$
In "How To Solve It", George Pólya writes:
"There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain
theorem, and I said it is not proved and it may be difficult. Von
Neumann didn't say anything but after five minutes he raised his hand.
When I called on him he went to the blackboard and proceeded to write
down the proof. After that I was afraid of von Neumann." [2nd ed.
(1957), p. xv]
Could someone tell me please what was that theorem which von Neumann proved?
reference-request math-history
asked Feb 1 '14 at 2:51
Salech RubensteinSalech Rubenstein
4,86212137
$endgroup$
|
show 7 more comments
$begingroup$
In "How To Solve It", George Pólya writes:
"There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain
theorem, and I said it is not proved and it may be difficult. Von
Neumann didn't say anything but after five minutes he raised his hand.
When I called on him he went to the blackboard and proceeded to write
down the proof. After that I was afraid of von Neumann." [2nd ed.
(1957), p. xv]
Could someone tell me please what was that theorem which von Neumann proved?
reference-request math-history
asked Feb 1 '14 at 2:51
Salech RubensteinSalech Rubenstein
4,86212137
$endgroup$
2
$begingroup$
The fly infinite sum?
$endgroup$
– CAGT
Feb 1 '14 at 3:31
13
$begingroup$
@CAGT That's not a "theorem" that "is not proved" and "may be difficult". Polya is probably referring to an open problem here, since he says in other places that when he mentioned open problems in class that Von Neumman would often present him with the solution after class.
$endgroup$
– Bill Dubuque
Feb 1 '14 at 3:52
3
$begingroup$
Is thi srelated to the anecdote about a student coming late to class, copyiing what he thinks is a problem from the blackboard, handing in a solution next time saying "todays homework was quite tricky" - not having noticed that the "homework problem" was in fact an open problem?
$endgroup$
– Hagen von Eitzen
Apr 12 '14 at 20:13
4
$begingroup$
In the book Famous Puzzles of Great Mathematicians it says that George Pólya said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
$endgroup$
– Euna Ko
Apr 17 '14 at 5:44
8
$begingroup$
@HagenvonEitzen You probably mean the story about Dantzig: Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.
$endgroup$
– Martin Sleziak
Jun 9 '14 at 12:19
|
show 7 more comments
$begingroup$
In "How To Solve It", George Pólya writes:
"There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain
theorem, and I said it is not proved and it may be difficult. Von
Neumann didn't say anything but after five minutes he raised his hand.
When I called on him he went to the blackboard and proceeded to write
down the proof. After that I was afraid of von Neumann." [2nd ed.
(1957), p. xv]
Could someone tell me please what was that theorem which von Neumann proved?
reference-request math-history
asked Feb 1 '14 at 2:51
Salech RubensteinSalech Rubenstein
4,86212137
$endgroup$
In "How To Solve It", George Pólya writes:
"There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain
theorem, and I said it is not proved and it may be difficult. Von
Neumann didn't say anything but after five minutes he raised his hand.
When I called on him he went to the blackboard and proceeded to write
down the proof. After that I was afraid of von Neumann." [2nd ed.
(1957), p. xv]
Could someone tell me please what was that theorem which von Neumann proved?
reference-request math-history
reference-request math-history
asked Feb 1 '14 at 2:51
Salech RubensteinSalech Rubenstein
4,86212137
asked Feb 1 '14 at 2:51
Salech RubensteinSalech Rubenstein
4,86212137
asked Feb 1 '14 at 2:51
Salech RubensteinSalech Rubenstein
4,86212137
asked Feb 1 '14 at 2:51
Salech RubensteinSalech Rubenstein
4,86212137
asked Feb 1 '14 at 2:51
Salech RubensteinSalech Rubenstein
4,86212137
4,86212137
2
$begingroup$
The fly infinite sum?
$endgroup$
– CAGT
Feb 1 '14 at 3:31
13
$begingroup$
@CAGT That's not a "theorem" that "is not proved" and "may be difficult". Polya is probably referring to an open problem here, since he says in other places that when he mentioned open problems in class that Von Neumman would often present him with the solution after class.
$endgroup$
– Bill Dubuque
Feb 1 '14 at 3:52
3
$begingroup$
Is thi srelated to the anecdote about a student coming late to class, copyiing what he thinks is a problem from the blackboard, handing in a solution next time saying "todays homework was quite tricky" - not having noticed that the "homework problem" was in fact an open problem?
$endgroup$
– Hagen von Eitzen
Apr 12 '14 at 20:13
4
$begingroup$
In the book Famous Puzzles of Great Mathematicians it says that George Pólya said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
$endgroup$
– Euna Ko
Apr 17 '14 at 5:44
8
$begingroup$
@HagenvonEitzen You probably mean the story about Dantzig: Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.
$endgroup$
– Martin Sleziak
Jun 9 '14 at 12:19
|
show 7 more comments
2
$begingroup$
The fly infinite sum?
$endgroup$
– CAGT
Feb 1 '14 at 3:31
13
$begingroup$
@CAGT That's not a "theorem" that "is not proved" and "may be difficult". Polya is probably referring to an open problem here, since he says in other places that when he mentioned open problems in class that Von Neumman would often present him with the solution after class.
$endgroup$
– Bill Dubuque
Feb 1 '14 at 3:52
3
$begingroup$
Is thi srelated to the anecdote about a student coming late to class, copyiing what he thinks is a problem from the blackboard, handing in a solution next time saying "todays homework was quite tricky" - not having noticed that the "homework problem" was in fact an open problem?
$endgroup$
– Hagen von Eitzen
Apr 12 '14 at 20:13
4
$begingroup$
In the book Famous Puzzles of Great Mathematicians it says that George Pólya said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
$endgroup$
– Euna Ko
Apr 17 '14 at 5:44
8
$begingroup$
@HagenvonEitzen You probably mean the story about Dantzig: Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.
$endgroup$
– Martin Sleziak
Jun 9 '14 at 12:19
2
2
$begingroup$
The fly infinite sum?
$endgroup$
– CAGT
Feb 1 '14 at 3:31
$begingroup$
The fly infinite sum?
$endgroup$
– CAGT
Feb 1 '14 at 3:31
13
13
$begingroup$
@CAGT That's not a "theorem" that "is not proved" and "may be difficult". Polya is probably referring to an open problem here, since he says in other places that when he mentioned open problems in class that Von Neumman would often present him with the solution after class.
$endgroup$
– Bill Dubuque
Feb 1 '14 at 3:52
$begingroup$
@CAGT That's not a "theorem" that "is not proved" and "may be difficult". Polya is probably referring to an open problem here, since he says in other places that when he mentioned open problems in class that Von Neumman would often present him with the solution after class.
$endgroup$
– Bill Dubuque
Feb 1 '14 at 3:52
3
3
$begingroup$
Is thi srelated to the anecdote about a student coming late to class, copyiing what he thinks is a problem from the blackboard, handing in a solution next time saying "todays homework was quite tricky" - not having noticed that the "homework problem" was in fact an open problem?
$endgroup$
– Hagen von Eitzen
Apr 12 '14 at 20:13
$begingroup$
Is thi srelated to the anecdote about a student coming late to class, copyiing what he thinks is a problem from the blackboard, handing in a solution next time saying "todays homework was quite tricky" - not having noticed that the "homework problem" was in fact an open problem?
$endgroup$
– Hagen von Eitzen
Apr 12 '14 at 20:13
4
4
$begingroup$
In the book Famous Puzzles of Great Mathematicians it says that George Pólya said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
$endgroup$
– Euna Ko
Apr 17 '14 at 5:44
$begingroup$
In the book Famous Puzzles of Great Mathematicians it says that George Pólya said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
$endgroup$
– Euna Ko
Apr 17 '14 at 5:44
8
8
$begingroup$
@HagenvonEitzen You probably mean the story about Dantzig: Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.
$endgroup$
– Martin Sleziak
Jun 9 '14 at 12:19
$begingroup$
@HagenvonEitzen You probably mean the story about Dantzig: Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.
$endgroup$
– Martin Sleziak
Jun 9 '14 at 12:19
|
show 7 more comments
1 Answer
1
active
oldest
votes
$begingroup$
J. von Neumann studied at Zürich during in Ph.D. and got Ph.D at the age of 22, in 1925. Before that year, Neumann published four papers (see here).
The first one, published in 1922, is about roots of polynomials. The paper does not mention Polyá, but Polyá is known to have worked on ths subject.
The second paper is about the ordinals, the third about set theory which seems less likely. The fourth (in hungarian) is about sequences and could contain the theorem, but I have not been able to access this [article](http://real-j.mtak.hu/7301/1/MTA_MatematikaiEsPhysikaiLapok_32.pdf
).
Of course, there is the possibility that von Neumann never wrote a paper about this theorem.
edited Feb 1 at 7:03
mathfossil
33
answered Sep 9 '14 at 10:15
Tom-TomTom-Tom
6,09011140
$endgroup$
add a comment |
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oldest
votes
$begingroup$
J. von Neumann studied at Zürich during in Ph.D. and got Ph.D at the age of 22, in 1925. Before that year, Neumann published four papers (see here).
The first one, published in 1922, is about roots of polynomials. The paper does not mention Polyá, but Polyá is known to have worked on ths subject.
The second paper is about the ordinals, the third about set theory which seems less likely. The fourth (in hungarian) is about sequences and could contain the theorem, but I have not been able to access this [article](http://real-j.mtak.hu/7301/1/MTA_MatematikaiEsPhysikaiLapok_32.pdf
).
Of course, there is the possibility that von Neumann never wrote a paper about this theorem.
edited Feb 1 at 7:03
mathfossil
33
answered Sep 9 '14 at 10:15
Tom-TomTom-Tom
6,09011140
$endgroup$
add a comment |
$begingroup$
J. von Neumann studied at Zürich during in Ph.D. and got Ph.D at the age of 22, in 1925. Before that year, Neumann published four papers (see here).
The first one, published in 1922, is about roots of polynomials. The paper does not mention Polyá, but Polyá is known to have worked on ths subject.
The second paper is about the ordinals, the third about set theory which seems less likely. The fourth (in hungarian) is about sequences and could contain the theorem, but I have not been able to access this [article](http://real-j.mtak.hu/7301/1/MTA_MatematikaiEsPhysikaiLapok_32.pdf
).
Of course, there is the possibility that von Neumann never wrote a paper about this theorem.
edited Feb 1 at 7:03
mathfossil
33
answered Sep 9 '14 at 10:15
Tom-TomTom-Tom
6,09011140
$endgroup$
add a comment |
$begingroup$
J. von Neumann studied at Zürich during in Ph.D. and got Ph.D at the age of 22, in 1925. Before that year, Neumann published four papers (see here).
The first one, published in 1922, is about roots of polynomials. The paper does not mention Polyá, but Polyá is known to have worked on ths subject.
The second paper is about the ordinals, the third about set theory which seems less likely. The fourth (in hungarian) is about sequences and could contain the theorem, but I have not been able to access this [article](http://real-j.mtak.hu/7301/1/MTA_MatematikaiEsPhysikaiLapok_32.pdf
).
Of course, there is the possibility that von Neumann never wrote a paper about this theorem.
edited Feb 1 at 7:03
mathfossil
33
answered Sep 9 '14 at 10:15
Tom-TomTom-Tom
6,09011140
$endgroup$
J. von Neumann studied at Zürich during in Ph.D. and got Ph.D at the age of 22, in 1925. Before that year, Neumann published four papers (see here).
The first one, published in 1922, is about roots of polynomials. The paper does not mention Polyá, but Polyá is known to have worked on ths subject.
The second paper is about the ordinals, the third about set theory which seems less likely. The fourth (in hungarian) is about sequences and could contain the theorem, but I have not been able to access this [article](http://real-j.mtak.hu/7301/1/MTA_MatematikaiEsPhysikaiLapok_32.pdf
).
Of course, there is the possibility that von Neumann never wrote a paper about this theorem.
edited Feb 1 at 7:03
mathfossil
33
answered Sep 9 '14 at 10:15
Tom-TomTom-Tom
6,09011140
edited Feb 1 at 7:03
mathfossil
33
edited Feb 1 at 7:03
mathfossil
33
edited Feb 1 at 7:03
mathfossil
33
33
answered Sep 9 '14 at 10:15
Tom-TomTom-Tom
6,09011140
answered Sep 9 '14 at 10:15
Tom-TomTom-Tom
6,09011140
answered Sep 9 '14 at 10:15
Tom-TomTom-Tom
6,09011140
6,09011140
add a comment |
add a comment |
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2
$begingroup$
The fly infinite sum?
$endgroup$
– CAGT
Feb 1 '14 at 3:31
13
$begingroup$
@CAGT That's not a "theorem" that "is not proved" and "may be difficult". Polya is probably referring to an open problem here, since he says in other places that when he mentioned open problems in class that Von Neumman would often present him with the solution after class.
$endgroup$
– Bill Dubuque
Feb 1 '14 at 3:52
3
$begingroup$
Is thi srelated to the anecdote about a student coming late to class, copyiing what he thinks is a problem from the blackboard, handing in a solution next time saying "todays homework was quite tricky" - not having noticed that the "homework problem" was in fact an open problem?
$endgroup$
– Hagen von Eitzen
Apr 12 '14 at 20:13
4
$begingroup$
In the book Famous Puzzles of Great Mathematicians it says that George Pólya said "Johnny was the only student I was ever afraid of. If in the course of a lecture I stated an unsolved problem, the chances were he'd come to me at the end of the lecture with the complete solution scribbled on a slip of paper."
$endgroup$
– Euna Ko
Apr 17 '14 at 5:44
8
$begingroup$
@HagenvonEitzen You probably mean the story about Dantzig: Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.
$endgroup$
– Martin Sleziak
Jun 9 '14 at 12:19