Why Is Everything Named After Gauss?
The Matthew Effect
Robert Merton is not a theorist, but was a sociologist. He created terms that seem to have been always with us, including “unintended consequences,” “role model,” and “self-fulfilling prophecy.” For this and other seminal work he was awarded the National Medal of Science in 1994, among many other awards and honors.
Today I want to talk about the Matthew Effect, or: why is everything named after Gauss? The Matthew Effect is:
“the rich get richer and the poor get poorer.”
Those who possess power often can use it to get more power, and on and on. Merton named his concept after a verse in the Gospel of Matthew:
For to all those who have, more will be given, and they will have an abundance; but from those who have nothing, even what they have will be taken away. —Matthew 25:29, New Revised Standard Version.
A related phenomenon is Stigler’s Law of naming stated first by professor Stephen Stigler in 1980, which says: No scientific discovery is named after its original discoverer. Stigler named Merton as the discoverer of “Stigler’s Law,” thus creating a diagonal type statement that complexity theory uses all the time.
Another related phenomenon is Graham’s Law stated years ago to me by Ron Graham: If you win awards, then you will win at least .
A Hadamard Matrix: Such a matrix was invented by James Sylvester in 1867, who called it the wonderfully complex name, an “anallagmatic pavement”—here “anallagmatic” refers to the matrix being virtually its own inverse. Almost thirty years later it was discovered by Jacques Hadamard. The defining property is that it is a matrix of ‘s and satisfies
A bit more precisely Sylvester discovered the recursive family of Hadamard matrices that are of great importance today. Let be
Then the given an , the following matrix is a Hadamard matrix of twice the size.
An important open problem is, are there Hadamard matrices of all orders ? This is usually called the Hadamard conjecture. It probably should be named after Raymond Paley, who in 1933 found another general method to create Hadamard matrices that works (for example) when is a prime power. Oh well.
Carl Friedrich Gauss is so famous that he probably is one the best examples of the Matthew effect in action.
The famous Gaussian distribution is named after Gauss, of course. Many believe that it should be credited to Abraham de Moivre, who in 1738 published the second edition of his “The Doctrine of Chances.” Probably—no pun—it is at best unclear, de Moivre did not seem to completely understand what he had. The biggest problem was he lacked a formal notion of a probability density function.
The famous method of Gaussian elimination for solving linear systems is perhaps one of the single most important algorithms in the world. It was known to the Chinese mathematicians as early as 150 BCE; it was commented on by Liu Hui in the 3rd century. Issac Newton in 1670 supplied essentially this method. Apparently the naming of the method after Gauss only happened in the 1950’s after confusion over the history.
In the 1800’s hyperbolic geometry was discovered by János Bolyai and Nikolai Ivanovich Lobachevsky, after whom it sometimes is named. Gauss knew about it a few years before, but never published his discovery. At least the name is joint and not just due to Gauss.
The mathematician of recent memory with the widest Gauss-like sweep of results is undoubtedly Paul Erdős. Surely if we wish to observe the “Matthew Effect” in action, he is the best single person to track. Yet we cannot think of a single instance of his receiving undue credit for a theorem, or even a definition, and his single credit for the “Probabilistic Method” seems merited—although others used a similar method around the same time he first did. Perhaps this owes to his generosity in being the most prolific co-author in history.
However, we can point to the effect with “his” maxim: A mathematician is a device for turning coffee into theorems. Erdős repeated this phrase often, but according to several sources, and as echoed in Wikipedia’s biography of Alfréd Rényi, the phrase originated with Rényi.
Erdős may instead be exemplifying the “Lazarus Effect': according to this list he has published 34 papers since 1999. Allowing 2–3 years as a typical upper bound on gestation for a journal paper, this would seem to indicate a fair bit of effort since his death in 1996. It appears not to be true that he got a paper with Adam Tauman Kalai, Ankur Moitra, and Gregory Valiant into STOC 2010 (about learning Gaussians), even though they suggested that was the case.
How It Happens
Let’s call the first discover the finder and the person who later gets it named after them the namee. Note there are several ways finders do not become namees.
Sometimes the finder does not publish it, or does so in an odd place. Perhaps this will become less of an issue in the future, but it has happened many times this way.
Sometimes the finder does not have a correct proof of the result and the namee does.
Sometimes the finder does not really know what they have. The namee does, and so perhaps they really should get the credit.
Most often it seems that it is the Matthew Effect at work: the namee is the more famous person and gets the credit.
Here is a partial list of misnamed theorems from our friends at Wikipedia. See it for the details—I will just give the finder and the namee.
Benford’s Law. The finder is Simon Newcomb in 1881 and the namee is Frank Benford in 1938.
Bézout’s Theorem. The finder is Isaac Newton in 1665, who only stated it. The proof was found much later by several mathematicians including Leonhard Euler as well as Etienne Bézout. This is one case where the namee beat out a more famous person, Euler. There is hope. At least in some cases the “Matthew Effect” is reversed.
Burnside’s Lemma. The finder was Georg Frobenius and the namee was William Burnside, who perhaps won because he included it in his textbook.
Frobenius’ Theorem. The finder was Feodor Deahna in 1840, who stated it and proved it. Frobenius cited the earlier work, but still became the namee in 1875.
Morrie’s Law. The finder was Richard Feynman. He named it explicitly after a childhood friend, Morrie Jacobs—he said that he learned it from Morrie.
Pell’s Equation. The finder was probably Brahmagupta in 628. Fermat made it a challenge problem to others in 1657. In those days it was common for a mathematician to prove something, and then challenge colleagues to try and solve it. The namee was believed to be created by Euler who confused John Pell with another, William Brouncker. Thus we have multiple errors, an example of misnaming due to cultural barriers and lack of the ability to find information easily.
Stokes’ Theorem. The finder appears to be William Thompson, Lord Kelvin. The namee is George Stokes who probably got the credit since he included it often on his analysis examinations.
What are your favorite examples of this phenomenon?