Math is not science!
It is much better than that 
Edit - should have said +1 to Mr Door.
I always thought it was an appropriation of Thomas Aquinas’ idea of philosophy as the handmaiden of theology (see here).
Quote:
Of all these arts those which belong to the eye and ear are esteemed the most liberal; for these two senses are the purest; and the sciences thereof are the most learned, as having mathematics like a handmaid in their train.
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Good find. Since Francis Bacon was there at the dawn of science, that may be the first reference.
I think mathematics as a discipline existed long before the sciences. I once had a physics professor that insisted that if it wasn’t mathematical, it wasn’t science. Even sciences where you don’t do a lot of calculating within the science, statistics helps sort out data.
I can well understand a mathematician objecting to mathematics as only being a servant to the sciences.
I also can understand statistics being called a whore.
Since nobody else has mentioned it, the implication of the “queen of the sciences” quote is that a queen is beautiful, elegant, and useless.
Useless? Or highly necessary in her ability to produce legitimate heirs? Ask Prince Physics and Princess Astronomy how useless the queen was.
Namaste ganita, I can see why you would take this personally!
Actually, if you’re thinking of Bell’s 1951 book Mathematics: Queen and Servant of Science, then I think he was very deliberately asserting that mathematics is important in both roles: namely, as the paradigmatic ideal of rational certainty that other sciences aspire to, and as the useful functionary who provides necessary services and tools for other sciences to work with.
During medieval times, science was also a handmaiden to theology. See Science and religion: a historical introduction by Gary B. Ferngren, p. 324 Science and Religion: A Historical Introduction - Google Books Then again, science was known as natural philosophy back then.
Sort of odd and offensive, but…
… if she has any role at all, must, whatever else she is, also be the handmaiden of science … If not, she will remain a prostitute science: available to others, when all else fails, for instant…
“Mathematics Governess or Handmaiden?” by Stephen Senn Journal of the Royal Statistical Society: Series D (The Statistician), Volume 47, Issue 2, pages 251–259, July 1998
Fishing, btw, was also a handmaiden of science, at least in 1899: Lochs and Loch Fishing - Hamish Stuart - Google Books
See also the title: “The Rise of Modern Science and the Decline of Theology as the ‘Queen of Sciences’ in the Early Modern Era” by Avihu Zakai
If this were true, we would have to discard some seventy years of research in computational lexical semantics. Fortunately, it is not; most dictionaries do indeed place the most common definition first. In any case, all the senses you list share the same etymology; this is the true for the vast majority of words.
You’re joking, I hope. Actually, what Gauss meant by arithmetic is what we now call number theory. I don’t know if an English translation of Disquisitiones Arithmeticae is in the public domain, but you would be amazed at what Gauss called arithmetic. A standard (albeit unsolved) problem is to describe the rate of growth of the function, I think it’s called M, for which M(x) is the difference between the number of square-free numbers less than x (assumed positive) for the which the number of prime divisors is even and the number of them for which that number is odd. Solve that and win $1,000,000. Really.
Arguably, Bacon was around near the dawn of what we now call science, but the word science, meaning organized, reliable knowledge is very much older,and is pretty much a straightforward appropriation of the Latin scientia. Still, Bacon may well be teh source of the saying referenced in the OP. He was once very widely read.
During medieval times, what we now call “science” was considered a part of philosophy.
Ah, but Bacon was an early adopter of what we know as science where speculation leads to physical testing to confirm hypotheses. A good example is the story of Galileo dropping the balls off the tower of Pisa. Perhaps that has the veracity of Washington and the cherry tree, but it shows how methods of determining the truth were changing.
Plenty of cites for Galileo doing it, but mostly Wikipedia.
Bit of trouble parsing this.
Are you saying that’s a problem Gauss put forth in the work you mentioned, which he called arithmetic, which most of us would not, and which remains unsolved, and which one can win $1,000,000 for solving?
Also, who’s offering the prize?
Bacon was in favor of experiment and observation of nature, but the methodology he suggested was not the method of hypothesis testing (not that modern science always uses that method either, outside of undergraduate textbooks).
Furthermore, people have been testing hypotheses since time immemorial. Babies do it, even animals do it. This was not some new method of discovery that was invented at the time of the scientific revolution.
Examples that are completely fictional do not “show” anything. Nowhere in his own writings does Galileo claim to have done such an experiment, and no-one around at the time ever claimed to have seen him do so. There is also good reason to think that if he had done it, it would have failed.
Despite some hedging and waffling, Wikipedia actually (currently) says that it is “generally accepted” that no such experiment took place.
In fact, Galileo proved that objects of different weights fall at the same rate (in a vacuum), through an ingenious thought experiment, which showed that the hypothesis that they fall at different rates leads to a contradiction. This was a brilliant and seminal contribution to science, despite the fact that it did not conform to the methodology of empirical hypothesis testing.
Arithmetic is the method of computation with numbers; e.g. operations with addition, division, multiplication, and division mainly. It’s the most elementary branch of mathematics.
Mathematics expands on that, including algebra (symbolic manipulations other than numbers; variables), functions, properties of real and imaginary numbers, and concepts like infinity and infinitesimals.
I believe he’s saying two separate things: A) Gauss used the word translated as “arithmetic” to describe what we now call “number theory”, B) A problem in number theory (not due to Gauss) for which one can win $1,000,000 is to describe the rate of growth of the Mertens function M(x). Because establishing that the rate of growth of M(x) is on the order of sqrt(x) [in the sense that for every epsilon > 0, there is a constant K such that M(x) is always less than K * x^(1/2 + epsilon)] is equivalent to the Riemann Hypothesis. You are likely already familiar with the fact that the Riemann Hypothesis is one of the Millenium Problems the Clay institute will offer million dollar prizes for solving (proving the Poincare Conjecture being the only one completed so far).
Sorry about that, but I it did daily for 12 years before moving into mangement. Even there I did some of it, just bigger batch sizes.
Wow, a zombie thread started by me over 3 years ago 
Funny because not long ago, this phrase came up again with my wife, in the context of her giving a math talk to an audience mostly of physicists, one of who trotted out the phrase again that mathematics was like a “handmaiden” to Physics.
It didn’t help her mood when I told her that from my POV it could only get worse: if mathematics was the handmaiden to the sciences, she really didn’t want to know what it was to engineers and computer programmers. (I then started to sing the refrain from the 1990s classic O.P.P.)
I don’t doubt it. I did not say nobody in science ever does the hypothesis and test thing. I am sure a lot of it goes on. What I am saying is that there is also a lot of scientific research, real science, good science, even brilliant science (such as the way Galileo actually refuted Aristotle’s theory about falling bodies) that does not fit that mold. Thus it provides a very poor, and even dangerous, way to define science. Much of the best science would be stigmatized as not really science at all under that definition. Furthermore, the scientific revolution of the 17th century was not the result of the sudden discovery or invention of the hypothesis and test methodology.