As we know Erdos has proposed a considerable number of problems in the "American Mathematical Monthly" journal. Is there any published summary of Erdos's published problems in the American Mathematical Monthly journal?
Thank you!
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3$\begingroup$ You may try contacting Ronald Graham and Alexander Soifer. They each were trying to compile complete lists of his open problems. $\endgroup$– Andrés E. CaicedoCommented Sep 1, 2017 at 12:20
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$\begingroup$ Related: mathoverflow.net/questions/27716/… $\endgroup$– Timothy ChowCommented Sep 1, 2017 at 17:04
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$\begingroup$ Also related: mathoverflow.net/questions/27271/… $\endgroup$– Timothy ChowCommented Sep 1, 2017 at 17:04
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1$\begingroup$ Tag open-problems-list seems relevant $\endgroup$– Alexander ChervovCommented Sep 1, 2017 at 17:09
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1$\begingroup$ @AlexanderChervov : Most of the Monthly problems are not open problems (unless Erdos is an exception?). $\endgroup$– Timothy ChowCommented Sep 1, 2017 at 17:12
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2 Answers
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I do not know of such a summary. But JSTOR has spent considerable time indexing the Monthly, including the "Problems and Solutions" sections. So if your library has a JSTOR subscription you can search for these. (Access it on-line through your library. Or in person on a terminal at your library.)
Searching Author Erdos and Publication Title American Mathematical Monthly, I got 304 matches. Some of those may be actual articles by Erdos, but most of them are solutions in the Problems and Solutions section. If Erdos was the proposer, it should be indexed in this way.
For example, May 1961:
answered Sep 1, 2017 at 12:14
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I do not think that anyone ever made an effort to collect ALL problems of Erdos. In the later part of his life he liked to give talks on various conferences under the title "My favorite unsolved problems" (I recomend typing this on Google, there are many versions). But usually these collections were selected according to the topic of the conference.
EDIT. In general, his problems are widely scattered. In the last years of his life he was mostly interested in graphs and combinatorics. But I know, for example, a collection of Erdos's problems in complex analysis dated 1964, and included in the book of W. Hayman "Research Problems in Function theory". This example shows that it would be very difficult to collect them all. A person searching for "Erdos problems" is unlikely to find a book like this.
answered Sep 1, 2017 at 17:48
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$\begingroup$ Soifer has tried. He has written extensively, in his usual fashion, of this project. $\endgroup$ Commented Sep 1, 2017 at 18:05
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1$\begingroup$ Not yet. It was meant to appear last month, I believe; it was advertised in Springer catalogues, but there seem to be some delays and the ad disappeared. $\endgroup$ Commented Sep 1, 2017 at 18:15
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1$\begingroup$ It seems he is changing the scope of the project, though. This is from a recent interview: "His current work includes “Problems of pgom Erdös,” a book about “the greatest problem creator of all time, and also friend, coauthor, and mentor,” Paul Erdös, who personally selected his favorite open problems for the upcoming publication." See here. $\endgroup$ Commented Sep 1, 2017 at 18:21
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2$\begingroup$ @Todd Not really. It is a joke. Erdős used to complain for comedic effect about his old age. At some point in his 50s he started to add at the end of his signature the acronym P.G.O.M., meaning "Poor great old man". From then on he would add further acronyms every few years. $\endgroup$ Commented Sep 2, 2017 at 0:12
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2$\begingroup$ Here is Paul Erdös PGOM LD AD LD CD: youtube.com/watch?v=OJCQP1DTAOM (see the first few minutes). $\endgroup$ Commented Sep 2, 2017 at 12:59