# What is the shortest paper in the history of mathematics?

Now-a-days a research paper can have many pages (the paper claiming the proof of abc conjecture is of $500$ pages long!). But is there any paper in the history of mathematics which we can say as the shortest paper ever published in a well-known journal which has a remarkable impact?

## 4 Answers

There are many research announcements, sometimes containing few lines, so the question is not very meaningful. French Comptes rendus and old issues of AMS Bulletin have many papers of one page length or less. So they can be only compared by counting letters, and I do not think this counting is a reasnoable occupation.

But if we are talking of serious papers, with complete proofs, and containing great discoveries, then this one is hard to beat:

J. Milnor, Eigenvalues of the Laplace operator on certain manifolds, Proc. Nat. Acad. Sci. 51 N4, 1964, p. 542.

It occupies substantially less than one page, including title, author and reference list. And it is really a great discovery, and frequently cited.

• One might try to maximize the ratio of citations to words, if one really had nothing better to do with one's time. – Jack M Nov 26 '15 at 19:02
• @JackM Watch out for papers with $0$ words. – PyRulez Jul 1 '16 at 16:34

After few searching I found this paper by L. J. Lander and T. R. Parkin on counterexample to Euler's conjecture on the sum of like powers. May be this is the shortest paper?

• if your answer covered just how short the paper is (to save having to click the link) it would be a better answer – Kate Gregory Dec 16 '15 at 14:28

If you see at the bottom of the contents of American Mathematical Monthly it has a section called "Mathbits".
These are papers less than a page in length.
Maybe there you can find many short papers.

"The shortest paper ever published in a serious math journal":

J. H. Conway and A. Soifer, Can n² + 1 unit equilateral triangles cover an equilateral triangle of side > n, say n + ε?