Re: [math-fun] Database of math problems
Veit Elser <ve10@cornell.edu> wrote:
There must be a better example. For this problem I would generate a list of even perfect numbers and get lots of hits on that. Somewhere in all that material there surely will be mention of the odd perfect number problem.
Fair enough. How about the problem of whether every even number greater than 2 is the sum of two primes? If I didn't know that was called the Goldbach conjecture, how would I find it? Well, okay, Googling "sum of two primes" finds it. Never mind.
I imagine that most interesting problems can be perturbed in some way so that their solutions generate a searchable signature of large integers.
Meta-problem: Find a problem that doesn't generate anything searchable. Not sequences, not large integers, not unusual real numbers, not even unusual keywords. Bonus points if it's not obvious what, if any, existing branch of math it belongs to.
I've worked on at least two problems in the past five years that I couldn't find anything about previous work on, even when I used to have access to the MathSciNet database. I did eventually conclude that they hadn't been addressed before by asking several experts in the areas they fell in. (In these cases, they didn't straddle several areas.) —Dan
On Apr 2, 2016, at 2:46 PM, Keith F. Lynch <kfl@KeithLynch.net> wrote:
Meta-problem: Find a problem that doesn't generate anything searchable. Not sequences, not large integers, not unusual real numbers, not even unusual keywords. Bonus points if it's not obvious what, if any, existing branch of math it belongs to.
For instance when I discovered that 8022581057533823761829436662099 was a palindrome in both binary and ternary, a Google search assured me that (probably) nobody had ever noticed this fact before.
It has been in the OEIS for ever: did you try searching there? Just enter 8022581057533823761829436662099 in the search window and you get https://oeis.org/A060792 Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sat, Apr 2, 2016 at 6:03 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I've worked on at least two problems in the past five years that I couldn't find anything about previous work on, even when I used to have access to the MathSciNet database. I did eventually conclude that they hadn't been addressed before by asking several experts in the areas they fell in. (In these cases, they didn't straddle several areas.)
—Dan
On Apr 2, 2016, at 2:46 PM, Keith F. Lynch <kfl@KeithLynch.net> wrote:
Meta-problem: Find a problem that doesn't generate anything searchable. Not sequences, not large integers, not unusual real numbers, not even unusual keywords. Bonus points if it's not obvious what, if any, existing branch of math it belongs to.
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Well, not "for ever" but since January 2014 (edit #26) which is when Keith discovered it. If you Google the number *now* you will also get hits.
On Apr 2, 2016, at 6:23 PM, Neil Sloane <njasloane@gmail.com> wrote:
For instance when I discovered that 8022581057533823761829436662099 was a palindrome in both binary and ternary, a Google search assured me that (probably) nobody had ever noticed this fact before.
It has been in the OEIS for ever: did you try searching there? Just enter 8022581057533823761829436662099 in the search window and you get https://oeis.org/A060792
I mistakenly said: "It has been in the OEIS for ever: did you try searching there? Just enter 8022581057533823761829436662099 in the search window and you get https://oeis.org/A060792". I was wrong - although the sequence has been in the OEIS since about 2003, the term 8022581057533823761829436662099 wasn't there until Keith added it in January 2014! Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Sat, Apr 2, 2016 at 6:23 PM, Neil Sloane <njasloane@gmail.com> wrote:
For instance when I discovered that 8022581057533823761829436662099 was a palindrome in both binary and ternary, a Google search assured me that (probably) nobody had ever noticed this fact before.
It has been in the OEIS for ever: did you try searching there? Just enter 8022581057533823761829436662099 in the search window and you get https://oeis.org/A060792
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Sat, Apr 2, 2016 at 6:03 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I've worked on at least two problems in the past five years that I couldn't find anything about previous work on, even when I used to have access to the MathSciNet database. I did eventually conclude that they hadn't been addressed before by asking several experts in the areas they fell in. (In these cases, they didn't straddle several areas.)
—Dan
On Apr 2, 2016, at 2:46 PM, Keith F. Lynch <kfl@KeithLynch.net> wrote:
Meta-problem: Find a problem that doesn't generate anything searchable. Not sequences, not large integers, not unusual real numbers, not even unusual keywords. Bonus points if it's not obvious what, if any, existing branch of math it belongs to.
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I would welcome something close to a database of problems / theorems across all mathematics, but there at least two things that already exist and have not been mentioned yet. - It is a tradition of several great conferences (such as the British Combinatorial Conference) to take advantage of the gathering of many experts and make a list of open problems and conjectures (as well as survey papers), publish it. They usually end up on the web and can be commented and updated. Talking of surveys, one of the features of the EJC (Electronic Journal of Combinatorics) was "dynamic surveys", meaning articles regularly updated by their authors on a given topic. That's something that could be carried further with computer support tools. Of course this does not cover the multi-field case. - We have new (a few years ago), quite open, virtual discussion places for scientists, such as MathOverflow with a very diverse expertise. One advantage of M.O. for short is that almost everything is archived and searchable (there are situations where questions are deleted or closed, but that's more a problem for other forums of the same kind for more practical subjects) And we may hope that the trend toward computer assisted proofs push for a large repository of more formalised mathematical knowledge and questions. Olivier On Sun, Apr 3, 2016 at 2:29 AM, Neil Sloane <njasloane@gmail.com> wrote:
I mistakenly said: "It has been in the OEIS for ever: did you try searching there? Just enter 8022581057533823761829436662099 in the search window and you get https://oeis.org/A060792".
I was wrong - although the sequence has been in the OEIS since about 2003, the term 8022581057533823761829436662099 wasn't there until Keith added it in January 2014!
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Sat, Apr 2, 2016 at 6:23 PM, Neil Sloane <njasloane@gmail.com> wrote:
For instance when I discovered that 8022581057533823761829436662099 was a palindrome in both binary and ternary, a Google search assured me that (probably) nobody had ever noticed this fact before.
It has been in the OEIS for ever: did you try searching there? Just enter 8022581057533823761829436662099 in the search window and you get https://oeis.org/A060792
Best regards Neil
Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Sat, Apr 2, 2016 at 6:03 PM, Dan Asimov <dasimov@earthlink.net> wrote:
I've worked on at least two problems in the past five years that I couldn't find anything about previous work on, even when I used to have access to the MathSciNet database. I did eventually conclude that they hadn't been addressed before by asking several experts in the areas they fell in. (In these cases, they didn't straddle several areas.)
—Dan
On Apr 2, 2016, at 2:46 PM, Keith F. Lynch <kfl@KeithLynch.net> wrote:
Meta-problem: Find a problem that doesn't generate anything searchable. Not sequences, not large integers, not unusual real numbers, not even unusual keywords. Bonus points if it's not obvious what, if any, existing branch of math it belongs to.
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_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Fair enough. How about the problem of whether every even number greater than 2 is the sum of two primes? If I didn't know that was called the Goldbach conjecture, how would I find it?
Well, okay, Googling "sum of two primes" finds it. Never mind.
Or, compute the number of ways to write 4, 6, 8, ..., 20 as a sum of two primes, and enter this sequence into oeis.org. Jim Propp
How about the problem of whether every even number greater than 2 is the sum of two primes? If I didn't know that was called the Goldbach conjecture, how would I find it?
As you pointed out, Google works for this one, but the general approach I use for questions like this is to search the OEIS for the number of ways that 2n (or n) can be represented as the sum of two primes. These lead to A045917 and A061358 which both lead to material on the Goldbach conjecture. Charles Greathouse Analyst/Programmer Case Western Reserve University On Sat, Apr 2, 2016 at 5:46 PM, Keith F. Lynch <kfl@keithlynch.net> wrote:
Veit Elser <ve10@cornell.edu> wrote:
There must be a better example. For this problem I would generate a list of even perfect numbers and get lots of hits on that. Somewhere in all that material there surely will be mention of the odd perfect number problem.
Fair enough. How about the problem of whether every even number greater than 2 is the sum of two primes? If I didn't know that was called the Goldbach conjecture, how would I find it?
Well, okay, Googling "sum of two primes" finds it. Never mind.
I imagine that most interesting problems can be perturbed in some way so that their solutions generate a searchable signature of large integers.
Meta-problem: Find a problem that doesn't generate anything searchable. Not sequences, not large integers, not unusual real numbers, not even unusual keywords. Bonus points if it's not obvious what, if any, existing branch of math it belongs to.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (7)
-
Charles Greathouse -
Dan Asimov -
Hans Havermann -
James Propp -
Keith F. Lynch -
Neil Sloane -
Olivier Gerard