Mathematicians
don’t always get their history correct. Maybe that’s why they went into math.
Because of this, there are numerous examples of results that have gone by the
name of someone other than the original discoverer. Stephen Stigler, author
of several books on the often neglected topic of the history of statistics has gone so far as to
suggest (with his tongue firmly planted in his cheek) “Stigler’s Law of
Eponymy”: “No scientific discovery is named after its original discoverer.”

Incidentally,
Stigler’s Law was first postulated by Robert Merton.

Famous example

The
Pythagorean theorem is perhaps the most well known mathematical misnomer.
Although is it likely that Pythagoras first proved the theorem, the theorem
was known by the Babylonians long before Pythagoras. There is a tablet from
Mesopotamia that lists fifteen different Pythagorean triplets. This tablet
was inscribed at least a millennia before the birth of Pythagoras.

Pascal’s
triangle is yet another case where the proper person has not received full
credit. Chu ShihChieh tabulated the triangle to show the binomial
coefficients in 1303. Pascal got a triangle and a programming language named
after him. Contrary to popular belief, Chu ShihChieh did not have a dog
breed named after him.
This
triangle appeared in print in Europe in the Rechnung by Peter Apian in 1527, nearly a hundred years before
Pascal’s birth. Peter Apian was a bit luckier than Chu ShihChieh. A crater
on the moon and a minor planet were named after him. Although Apian was into
maps and astronomy and all that, he paid little attention to either his
crater or his planet. To the best of my knowledge, he never planned a summer
holiday to either.

Our
number system (that is, the way we write numbers) has commonly been referred
to as the Arabic number system. The Encarta encyclopedia calls our number
system the Arabic numbers. Rouse Ball^{1} refers to our number system
as Arabic. This is unfortunately a misnomer.

The
number system we use today did make it to Europe from Arabia, but the
concepts and symbols are entirely due to the Hindus. Hence it is more
appropriate to call our numbers the Hindu system of numerals. It was first
introduced to Europe through the translation of a book by Mohammed ibnMusa
alKwarizmi, and from him has become known as the Arabic system.

The
hapless De Moivre

Ah, poor DeMoivre. So often misunderstood.

A
statistician calls the curve the “normal curve”, a teacher calls it the “bell
curve”, and a mathematician refers to it as the “Gaussian”. The discovery of
this curve rightfully belongs to De Moivre, however. It was De Moivre who
first described this as a probability distribution.

De
Moivre was also cheated out of recognition for a formula to approximate the
factorial. The formula
is
known as Stirling’s formula, although De Moivre discovered it earlier. This
formula isn’t that well known under either name. I was rather taken by it
when I was in high school. I found it in a book somewhere. Perhaps if this
formula became part of the normal high school curricula, there would be more
people like me?

Ironically,
the one relation that bears De Moivre’s name is one that he never explicitly
stated. The famous De Moivre’s theorem states that
From
reviewing his work, it is certain that De Moivre was aware of this magical
result. I, personally, am not aware of any historian that came right out an
asked the guy, "Hey Abraham, you ever hear of De Moivre's theorem?"
I am guessing that this is yet another historical event that will never be
completely resolved.

Cauchy

The
Cauchy distribution and its odd properties as a statistical distribution were
first written about by Poisson, almost thirty years before Cauchy did any
work with this function.

The
Cauchy distribution, itself a misnomer, is another name for the mathematical
curve known as the witch of Agnesi. A more proper name for this might be the
“curve of Grandi”. I will write more about the multiple times this was
invented in a future blogpost.

Cauchy
did a great deal to make other mathematicians aware the danger of a divergent
series. He certainly popularized the ratio test for convergence of a series.
Laplace immediately rushed home to recheck his series in Mécanique Céleste after hearing Cauchy give a paper.

Reading
Boyer^{2} however, it is rather difficult to say just who deserves
the credit for discovery of what:

“… the familiar ratio test … more
frequently is known as Cauchy’s test, despite the fact that it had given by
Waring as early as 1776.” [p. 458]

"Gauss as early as 1812, for example, used
the ratio test to show [convergence of a hypergeometric series]… This test
seems to have been first used long before, in England, by Edward Waring
although it generally bears the name d’Alembert or, more occasionally, that
of Cauchy.

"[Another convergence test] has come to be
known as Cauchy’s criterion, but it was known earlier by Bolzano (and
possibly still earlier by Euler). [p. 517]"

Cauchy
first used the matrix of partial derivatives that has come to be known as the
Jacobian.

Various other misnomers

“Euler’s
formula” is the name given to the beautiful relation v + f = e + 2, where v
is the number of vertices in a polyhedra, f
is the number of faces, and e is
the number of edges. As prolific as Euler was, he did not invent the formula.
René Descartes first discovered this relationship in 1619. Euler was not born
until 1707.

Cartesian
coordinates were named after Rene Descartes, but were first used by Nicole
Oresme, who lived in the 14^{th} century. Oresme did have a crater on
the moon named after him, though. Any guess as to whether he discovered the crater?

Pell's
equation, y = ax^{2} + 1, where a
is a nonsquare integer, was first studied by Brahmagupta and Bhaskara.
Its complete theory was worked out by Lagrange, not Pell.

I
am still looking for an unnamed discovery to put my name on. Any suggestions?

1)
Rouse Ball,
W. W., A Sort Account of the History of Mathematics, 1960, Dover
Publications, (unabridged and unaltered republication of the 1908 4^{th}
edition)
2)
Boyer, Carl B., A History of Mathematics,
2^{nd} Edition, 1991, John Wiley and Sons

Wednesday, June 27, 2012
Mathematical misnomers
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How about tropical algebra? Fuzzy numbers (not numbers but functions)
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