The Shortest-Known Paper Published in a Serious Math Journal: 2 Succinct Sentences

Euler’s con­jec­ture, a the­o­ry pro­posed by Leon­hard Euler in 1769, hung in there for 200 years. Then L.J. Lan­der and T.R. Parkin came along in 1966, and debunked the con­jec­ture in two swift sen­tences. Their arti­cle — which is now open access and can be down­loaded here — appeared in the Bul­letin of the Amer­i­can Math­e­mat­i­cal Soci­ety. If you’re won­der­ing what the con­jec­ture and its refu­ta­tion are all about, you might want to ask Cliff Pick­over, the author of 45 books on math and sci­ence. He brought this curi­ous doc­u­ment to the web a cou­ple of years back…

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Note: An ear­li­er ver­sion of this post appeared on our site in April, 2015.

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  • Antonio says:

    A small note, in the spir­it of con­struc­tive crit­i­cism:

    >Euler’s con­jec­ture, a the­o­ry pro­posed by (…)

    A con­jec­ture is not a the­o­ry, it is a con­jec­ture; leave it at that. It’s some­thing that you guess is true but don’t know how to prove.

    >and debunked the con­jec­ture

    “debunk” is harsh. You “debunk” a hoax, maybe. You *dis­prove* a con­jec­ture, or, more causal­ly, you “show it to be false”.

    > If you’re won­der­ing what the con­jec­ture and its refu­ta­tion are all about, you might want to ask

    What the con­jec­ture is, is writ­ten right there, on the last line of those “two swift sen­tences”. But ok, I sup­pose many of your read­ers may appre­ci­ate a bit of hand-hold­ing — although it’s pret­ty read­able, as long as you remem­ber what an “nth pow­er” is.

    Any­way, I don’t mean to be harsh, hope you take this in the way I meant it.

  • Albert S. Franzen says:

    I would like to show thanks to you just for bail­ing me out of this this par­tic­u­lar trou­ble. As a result of check­ing through the net and meet­ing tech­niques that was not pro­duc­tive, I released my life was done.

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