most recent 30 from http://mathoverflow.net 2013-05-24T04:14:38Z http://mathoverflow.net/feeds/question/27075 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics coudy 2010-06-04T18:30:16Z 2011-05-29T21:08:24Z

<p>What is the oldest open problem in mathematics ? By old, I am refering to the date the problem was stated.</p> <p>Browsing wikipedia list of open problems, it seems that the <em>Goldbach conjecture</em> (1742, every even integer greater than 2 is the sum of two primes) is a good candidate. </p> <p>The <em>Kepler conjecture</em> about sphere packing is from 1611 but I think this is finally solved (anybody confirms ?). There may still be some open problem stated at that time on the same subject, that is not solved. Also there are problems about cuboids that Euler may have stated and are not yet solved, but I am not sure about that.</p> <p>A related question: can we say that we have solved all problems handed down by the mathematicians from Antiquity ?</p>

http://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics/27080#27080 Noah Snyder 2010-06-04T18:51:10Z 2010-06-04T19:51:42Z

<p>Existence or nonexistence of odd perfect numbers. </p> <p>Update: Goes back at least to Nicomachus of Gerasa around 100 AD, according to <a href="http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Perfect_numbers.html" rel="nofollow">http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Perfect_numbers.html</a> Nichomachus also asked about infinitude of perfect numbers.</p> <p><strike>(Goes back at least to Descartes 1638 <a href="http://mathworld.wolfram.com/OddPerfectNumber.html" rel="nofollow">http://mathworld.wolfram.com/OddPerfectNumber.html</a> and arguably all the way back to Euclid.)</strike></p>

http://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics/27084#27084 TonyK 2010-06-04T19:10:45Z 2010-06-04T19:10:45Z

<p>The Congruent Number problem (Which integers are the areas of right triangles with rational sides?) dates back to an Arab manuscript written before 972 AD, according to <a href="http://www.jstor.org/pss/2320381" rel="nofollow">http://www.jstor.org/pss/2320381</a>.</p>

http://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics/27112#27112 John Stillwell 2010-06-04T22:09:17Z 2010-06-05T01:30:13Z

<p>Another unsolved problem from ancient Greek times is: which regular $n$-gons are constructible by ruler and compass? We know, since Gauss, that this problem reduces to finding all the Fermat primes, but we don't know that we have found them all yet.</p>

http://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics/27119#27119 rpotrie 2010-06-04T23:58:14Z 2010-09-15T09:35:09Z

<p>This is not older than the rest, but old enough I believe: In 1775 Fagnano constructed periodic orbits for acutangular triangular billiards. The question about the existence of periodic oribits in general triangular (or poligonal) billiards (in the case of irrational angles) remains open. ( <a href="http://iml.univ-mrs.fr/editions/preprint2007/files/troubetzkoy_fagnano.pdf" rel="nofollow">http://iml.univ-mrs.fr/editions/preprint2007/files/troubetzkoy_fagnano.pdf</a> ).</p>

http://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics/27124#27124 Igor Pak 2010-06-05T02:03:46Z 2010-06-05T02:03:46Z

<p>Albrecht Dürer's conjecture states that every convex polytope has a non-overlapping edge unfolding (see <a href="http://plus.maths.org/issue27/features/mathart/index.html" rel="nofollow">here</a> for the intro). This problem was raised in 1525, revived by Shephard in 1975, and remains wide open. </p>

http://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics/40856#40856 Łukasz Grabowski 2010-10-02T17:28:26Z 2010-10-02T17:28:26Z

<p>According to <a href="http://www.britannica.com/EBchecked/topic/1556762/twin-prime-conjecture" rel="nofollow">Encyclopaedia Britannica</a>, "Greek mathematician Euclid (flourished c. 300 bce) gave the oldest known proof that there exist an infinite number of primes, and he conjectured that there are an infinite number of twin primes," which makes the twin prime conjecture remarkably old.</p>

http://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics/40886#40886 Richard Stanley 2010-10-03T00:37:52Z 2011-05-29T21:08:24Z

<p>Not exactly what you are asking for, but a candidate for the longest time elapsing between the proposal and the solution of a problem: the Archimedes cattle problem, proposed by Archimedes and solved by A. Amthor in 1880. See <a href="http://en.wikipedia.org/wiki/Archimedes%27_cattle_problem" rel="nofollow">http://en.wikipedia.org/wiki/Archimedes%27_cattle_problem</a>. </p>