Mathematics: "the handmaiden of the sciences"

I know I’ve heard and read this turn of phrase before. So has my wife, who is a research mathematician, who finds it irritating (and thus increases my occasional use of it). But where does it come from?

A Google search turns it up as the title of a 1937 book or article by E. T. Bell, which is also referenced a few other times by other writers, yet that seems way too recent an etymology. The very word “handmaiden” seems archaic to me.

Any ideas how to proceed? Or is that really it?

Try googling “Queen of Sciences”. (Oddly, some entries gave that honor to theology).

Here Gauss is quoted as saying that, “Mathematics is the queen of sciences and arithmetic is the queen of mathematics”.

I’ll note that mathematics is a nonempirical discipline and thus cannot be said to be a science. Thus, “Handmaiden” seems appropriate, if a little dated.

Many do use the word “science” in your way, but not all. Even so, however, “handmaiden” makes it sound as if math exists only to serve science, in a subordinate position.

Exactly, which is why my wife finds it irritating. Googling also turns up quotes that “if mathematics is the handmaiden of the sciences, statistics is its whore”.

And knot theory its dominatrix?

You’re apparently not familiar with E. T. Bell if you don’t associate him and archaic.

You’re apparently not familiar with E. T. Bell if you don’t associate him and archaic.

Engineers can sometimes get mathematics to do some pretty wonderful things. That doesn’t mean that your ordinary engineer will necessarily fully understand mathematics.

Or am I taking this metaphor much too far?

Arithmetic and mathematics are not the same thing?

Arithmetic is part of mathematics, just as (in Gauss’s view), mathematics is part of the sciences.

Ok, but if a discipline is not empirical it might be a science to some, but it does not use the scientific method.

Here’s the dictionary definition. Contrary to popular belief, the first listed definition isn’t intended to be the most common, but rather on the basis of etymology. Be that as it may, it seems to support Indistinguishable’s characterization

1. a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws: the mathematical sciences.
2. systematic knowledge of the physical or material world gained through observation and experimentation.
3. any of the branches of natural or physical science.
4. systematized knowledge in general.

Re: the OP.

Theology and philosophy[sup]1[/sup] are apparently also handmaidens of science, as is Fact and the Tablet PC. Melody too:

From Huneker, James, 1860-1921, Chopin : the Man and His Music, http://www.gutenberg.org/catalog/world/fulltext-context?fulltext="handmaiden+of+science"&fk_files[]=9283

It would appear that science is quite the stud.
[sup]1[/sup]See David C. Lindberg, “The Medieval Church Encounters the Classical Tradition: Saint Augustine, Roger Bacon, and the Handmaiden Metaphor”, in David C. Lindberg and Ronald L. Numbers, ed. When Science & Christianity Meet, (Chicago: University of Chicago Pr., 2003), p.8

Speaking of archaic…

“Arithmetic” (or, sometimes, “higher arithmetic”) is the old-fashioned word for what modern mathematicians usually refer to as number theory. I’m pretty sure that’s what was meant in the Gauss quote.

Besides arithmetic, mathematics also includes Euclidean geometry, differential geometry, fractal geometry, topology, set theory, trigonometry, calculus, vector calculus, abstract algebra, linear algebra, matrix algebra, number theory, statistics, differential equations, chaos theory, etc.

Google turned up the following quote from Francis Bacon: (mmm, bacon…)

Arithmetic is what you do in elementary school.

Mathematics is what you do in college.

(Sleep is apparently what most people do in high school when the subject comes up.)

I’m not sure what you intended to mean by this, but it’s simply wrong as stated.

Each dictionary uses its own preferred method to list definitions. Your very own link clearly shows that the American Heritage dictionary quote on that same page uses a different ranking that is non-etymological. I see no evidence at all that The Random House dictionary listing that is in your quote uses an etymological ordering.

In fact, I can guarantee that it doesn’t, since unlike you I own the Random House unabridged and took the trouble to look up how it orders its definitions.

Looks like popular belief wins this one.

And here I see that the word that was translated “arithmetic” in Measure for Measure’s link is “Zahlentheorie,” which does indeed mean “number theory.”

I think what Gauss meant is that number theory is the purest of pure mathematics, studied for its own sake and not to serve some other purpose.

Almost entirely so for millenia, till those damn cryptographers discovered uses for primes.

You got me. I carelessly assumed that my dictionary (Webster’s New World, 2nd college edition, 1980) reflected standard practice. It turns out there is no standard practice.

For reference purposes, I’ll quote from them: “The senses of an entry have, wherever possible, been arranged in semantic order from the etymology to the most recent sense so that there is a logical, progressive flow showing the development of the word and the relationship of its senses to one another (see for example stock and common). In longer entries, where the treatment would not greatly disturb the semantic flow, technical senses have been entered…”

But obsolete senses, “…are generally preceded by “originally” or “formerly” rather than by a formal usage label.”

I detail all of this because on occasion, dictionary definitions are introduced at the SDMB to settle debates. Obviously confusing an etymological ordering with the other kind can lead to difficulties.

(Thanks for the correction, btw.)

Re: The OP.

“Handmaiden of science” appears to be an old cliche, applying to any number of fields. The Lindberg reference above might provide some detail.

From Dictionary.com:

1. something that is necessarily subservient or subordinate to another: Ceremony is but the handmaid of worship.
2. a female servant or attendant.

(Random House Unabridged ordering!)

Interesting discussion so far.

Has the “handmaiden” quote been traced to anyone other than Bell and possibly Bacon?

I intend to use the distinction between “handmaiden” and “queen” to highlight the differences in emphasis in both the content and teaching of mathematics in high school and university respectively.

What I found unsettling was that E T Bell also wrote another book using the “queen” metaphor in its title. So, perhaps he could not make up his mind?!