Misnamed Theorems And The Reasons Behind It

While many distinguished mathematicians managed to give name to their discoveries, some were misnamed in the detriment of their original discoverer. Here are just a few of them.

Benford’s Law

This was first stated in 1881 by Simon Newcomb, and rediscovered in 1938 by Frank Benford. The first rigorous formulation and proof seems to be due to Ted Hill in 1988.

The discovery of Benford’s law goes back to 1881, when the American astronomer Simon Newcomb noticed that in logarithm tables (used at that time to perform calculations) the earlier pages (which contained numbers that started with 1) were much more worn than the other pages. Newcomb’s published result is the first known instance of this observation and includes a distribution on the second digit, as well. Newcomb proposed a law that the probability of a single number N being the first digit of a number was equal to log(N + 1) − log(N).

The phenomenon was again noted in 1938 by the physicist Frank Benford, who tested it on data from 20 different domains and was credited for it. His data set included the surface areas of 335 rivers, the sizes of 3259 US populations, 104 physical constants, 1800 molecular weights, 5000 entries from a mathematical handbook, 308 numbers contained in an issue of Readers’ Digest, the street addresses of the first 342 persons listed in American Men of Science and 418 death rates. The total number of observations used in the paper was 20,229. This discovery was later named after Benford making it an example of Stigler’s law.

L’Hôpital’s rule

This rule first appeared in l’Hôpital’s book L’Analyse des Infiniment Petits pour l’Intelligence des Lignes Courbes in 1696. The rule is believed to be the work of Johann Bernoulli since l’Hôpital, a nobleman, paid Bernoulli a retainer of 300 francs per year to keep him updated on developments in calculus and to solve problems he had.

Cramer’s paradox

This was first noted by Colin Maclaurin in 1720, and then rediscovered by Leonhard Euler in 1748 (whose paper was not published for another two years, as Euler wrote his papers faster than his printers could print them). It was also discussed by Gabriel Cramer in 1750, who independently suggested the essential idea needed for the resolution, although providing a rigorous proof remained an outstanding open problem for much of the 19th century. Even though Cramer had cited Maclaurin, the paradox became known after Cramer rather than Maclaurin. Halphen, Arthur Cayley, and several other luminaries contributed to the earliest more or less correct proof.

Heine–Borel theorem

This theorem was proved in 1872 by Émile Borel, not by Eduard Heine. Borel used techniques similar to those that Heine used to prove that continuous functions on closed intervals are uniformly continuous. Heine’s name was attached because Schönflies noticed the similarity in Heine’s and Borel’s approaches. In fact, the theorem was first proved in 1852 by Peter Dirichlet, but Dirichlet’s lecture notes were not published until 1904.

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