The World Record for the Shortest Math Article: 2 Words

shortest math paper

On Mon­day, on a lark, we post­ed what we thought was The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal. Two suc­cinct sen­tences.

But then today, an OC read­er gave us a heads-up on a more extreme dis­play of brevi­ty. In 2004, John Con­way and Alexan­der Soifer, both work­ing on math­e­mat­ics at Prince­ton Uni­ver­si­ty, sub­mit­ted to the Amer­i­can Math­e­mat­i­cal Month­ly what they believed was “a new world record in the num­ber of words in a [math] paper.”

Soifer explains: “On April 28, 2004 … I sub­mit­ted our paper that includ­ed just two words, ‘n2 + 2 can’ and our two draw­ings. [See one of them above.]” The sto­ry then con­tin­ues: “The Amer­i­can Math­e­mat­i­cal Month­ly was sur­prised, and did not know what to do about our new world record of a 2‑word arti­cle. Two days lat­er, on April 30, 2004, the Edi­to­r­i­al Assis­tant Mrs. Mar­garet Combs acknowl­edged the receipt of the paper”:

The Month­ly pub­lish­es expo­si­tion of math­e­mat­ics at many lev­els, and it con­tains arti­cles both long and short. Your arti­cle, how­ev­er, is a bit too short to be a good Month­ly arti­cle… A line or two of expla­na­tion would real­ly help.

Soifer writ­ers: “The same day at the cof­fee hour I asked John [Con­way], ‘What do you think?’ His answer was con­cise, ‘Do not give up too eas­i­ly.’ Accord­ing­ly, I replied [to] The Month­ly the same day”:

I respect­ful­ly dis­agree that a short paper in general—and this paper in particular—merely due to its size must be “a bit too short to be a good Month­ly arti­cle.” Is there a con­nec­tion between quan­ti­ty and qual­i­ty?… We have posed a fine (in our opin­ion) open prob­lem and report­ed two dis­tinct “behold-style” proofs of our advance on this prob­lem. What else is there to explain?

Soifer adds: “The Month­ly, appar­ent­ly felt out­gunned, for on May 4, 2004, the reply came from The Monthly’s top gun, Edi­tor-in-Chief Bruce Pal­ka”:

The Month­ly pub­lish­es two types of papers: “arti­cles,” which are sub­stan­tive expos­i­to­ry papers rang­ing in length from about six to twen­ty-five pages, and “notes,” which are short­er, fre­quent­ly some­what more tech­ni­cal pieces (typ­i­cal­ly in the one-to-five page range). I can send your paper to the notes edi­tor if you wish, but I expect that he’ll not be inter­est­ed in it either because of its length and lack of any sub­stan­tial accom­pa­ny­ing text. The stan­dard way in which we use such short papers these days is as “boxed filler” on pages that would oth­er­wise con­tain a lot of the blank space that pub­lish­ers abhor. If you’d allow us to use your paper in that way, I’d be hap­py to pub­lish it.

Soifer con­cludes: “John Con­way and I accept­ed the ‘filler’, and in the Jan­u­ary 2005 issue our paper was pub­lished.” Vic­to­ry!

Get more of the back­sto­ry here.

Relat­ed Con­tent:

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

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Comments (6)
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  • Keith Brown says:

    It may be help­ful to note that the title of the paper was “Can $n^2 + 1$ unit equi­lat­er­al tri­an­gles cov­er an equi­lat­er­al tri­an­gle of side $>n$, say $n+\varepsilon$?

  • Ed Lewis says:

    Nah. That did­n’t help me.

  • Rahul Siddharthan says:

    @Ed (and any­one else who’s con­fused) — it’s sim­ple. If you divide an equi­lat­er­al tri­an­gle of side n into equi­lat­er­al tri­an­gles of side 1, you will get n^2 such tri­an­gles. (Look at all rows in the fig­ure except the last, which has over­laps and two extra tri­an­gles). So if your big tri­an­gle’s side is a lit­tle big­ger than n, you can­not cov­er it with n^2 tri­an­gles. They show, how­ev­er, that you can cov­er it with n^2+2 tri­an­gles, by adding two tri­an­gles to the last row and doing this over­lap­ping trick. The title asks (and the paper does­n’t answer): can you do it with n^2+1 tri­an­gles?

  • Rahul Siddharthan says:

    And accord­ing to the linked arti­cle by Soifer, the AMM edi­tors pushed the authors’ title (com­ment #1 above) into the body of the paper and put in their own title instead. So the paper was a bit longer than two words.

    Also, there’s that pic­ture, which, though per­haps not worth a thou­sand words, would prob­a­bly need at least a cou­ple hun­dred words to describe clear­ly. And there was anoth­er pic­ture with an alter­na­tive cov­er­ing.

  • WM BICKHAM says:

    Thought-pro­vok­ing piece . I was enlight­ened by the infor­ma­tion — Does some­one know where my assis­tant could grab a sam­ple a form exam­ple to fill in ?

  • Tim Thornton says:

    Does any­one else think that pos­si­bly, just POSSIBLY, the MAIN rea­son this got pub­lished more-or-less as sub­mit­ted, was because JOHN CONWAY was involved? Just curious–I know noth­ing about the top­ic (go ahead, pile right on me, lol).

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