Who are the youngest mathematicians that published an original research article in a peer-reviewed journal?

Question

There is a lot of interesting information about young mathematicians, but I cannot find any information about the youngest mathematician that published an original research article in a peer-reviewed journal.

Does anyone have this information? Thanks a lot.

Answer 1

George Bergman, "A number system with an irrational base," Mathematics Magazine, Vol. 31, No. 2, Nov.-Dec. 1957, pp. 98-110.

George Mark Bergman is an American mathematician who was born on July 22, 1943 in Brooklyn, New York. He was 14 years old at the time of publication. The paper is referenced in Knuth's TAOCP. According to the journal's publisher, the Mathematical Association of America (bolding mine):

Mathematics Magazine is an Open Select, international, peer-reviewed journal publishing high-quality, lively, readable, and appealing exposition on a wide range of mathematical topics, including original mathematics, historical content, and connections among mathematics and other disciplines.

G. L. Alexanderson (ed.), Harmony of the World: 75 Years of Mathematics Magazine, Mathematical Association of America 2007, is a collection of selected papers from the journal's history. Bergman's paper appears on pp. 99-106. According to the editor's note:

This article was written by the author when he was a 12-year old student at Junior High School 246 in Brooklyn, New York. Here he explores using the golden mean, which he calls τ, more commonly now called ϕ, as the base of a number system. Bergman later went on to get a PhD at Harvard under the direction of John Tate and has had a distinguished career as a mathematician at the University of California, Berkeley.

Pr$\infty$fWiki lists the publication in their article stub on Bergman.

Answer 2

Arthur Leonard Rubin submitted the following paper at age 12.5 -- he was born in Feb 1956 and the paper was submitted in Nov 1968:

Arthur L. Rubin and Jean E. Rubin, Extended operations and relations on the class of ordinal numbers, Fundamenta Mathematicae 69 #2 (1969), 227-242.

Aficionados (i.e. fans) of large numbers (e.g. see here and this search) and large countable ordinals (e.g. see Baez's Part 1 & Part 2 & Part 3) and hyperoperations (i.e. iteratively iterating from tetration) might have encountered this paper.

(ADDED ABOUT 4 MONTHS LATER)

The Notices of the American Mathematical Society "Preliminary report" for this paper appears on pp. 196-197 of the 15 #1 (January 1968) issue, and the published abstract's received date is 20 October 1967 (age 11.5).

Answer 3

Daniel Larsen published his "Bertrand's Postulate for Carmichael Numbers" in International Mathematics Research Notices at age 19.

Answer 4

John von Neumann published his first co-authored paper ''On the position of zeroes of certain minimum polynomials'' with Michael Fekete at the age of 18.

His first solo paper ''On the introduction of transfinite numbers'' was published at age 19.

Maryam Mirzakhani also published her first paper (''A small non-4-choosable planar graph'') aged 19.

Answer 5

• It's well known that Blaise Pascal published his Essai pour les coniques in February of 1640 at the age of 16.
• Galois' Démonstration d’un théorème sur les fractions continues périodiques paper was published in the Annales de mathématiques pures et appliquées in April 1829 at the age of 17.
• At age 18, Erdős proved Bertrand's postulate and had it published the next year at age 19 in the article Beweis eines Satzes von Tschebyschef in Acta Litterarum ac Scientiarum (1932).

Answer 6

Katherine Knox recently published Billiard circuits in quadrilaterals in the American Mathematical Monthly, and the paper contains original research results. I'm not sure of her exact age, but she is a seventh grader.

Answer 7

Certainly not as young as Arthur Rubin, but Carl Størmer was also very precocious.

Størmer entered the University of Christiana (Oslo) in 1892 and in the same year, at the age of 18, he published his first work, Summation af nogle trigonometriske rækker (Summation of some trigonometric series), and then published six more articles before the end of his studies.

Answer 8

Lajos Posa wrote one 1 with Erdos and was submitted for publication in September 1961. At the time of submission Posa was not 14 yet.
[1] Erdos and Posa : On the maximal number of disjoint circuits of a graph, http://combinatorica.hu/~p_erdos/1962-13.pdf

Answer 9

Other examples of articles published by mathematicians at an early age:

• High-schooler Britney Gallivan was born in 1985 and published a paper early 2002 in which she established a formula for the "loss function" of folding paper in half. So she was either 16 or 17 at the time of publication. By means of her new folding techniques, she managed to fold a large piece of toilet paper 12 times, even though the commonly held belief at the time was that paper could be folded in half only 8 times.
• Werner Boy (1879 - 1914) published on what later would become known as "Boy's Surface" in 1901 (age 21/22). A link to the paper can be found here.
• At age 16, Dmitriy Zakharov posted an article on the ArXiv entitled "Acute Sets", in which he proved a new bound for a 1962 problem - improving a result of Erdős.
• There is also Norbert Wiener who published the main findings of his dissertation on mathematical logic when he was either 19 or 20 years (!) of age. The paper is called A simplification in the logic of relations and was published in 1914.