# Mathematics: "the handmaiden of the sciences" **URL:** \ **Category:** Factual Questions\ **Created:** [April 10, 2008, 11:16pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819 "2008-04-10T23:16:44Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![BlinkingDuck](https://avatars.discourse-cdn.com/v4/letter/b/eada6e/32.png) [@BlinkingDuck](https://boards.straightdope.com/u/BlinkingDuck)\ **Post date:** [October 14, 2011, 3:41pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/21 "2011-10-14T15:41:27Z")
Math is not science! It is much better than that 🙂 Edit - should have said +1 to Mr Door. ---
**Author:** ![Tom\_Tildrum](https://avatars.discourse-cdn.com/v4/letter/t/e95f7d/32.png) [@Tom\_Tildrum](https://boards.straightdope.com/u/Tom_Tildrum)\ **Post date:** [October 14, 2011, 3:42pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/22 "2011-10-14T15:42:43Z")
[Here](http://www.smbc-comics.com/index.php?db=comics&id=2396#comic) is a recent cartoon on this topic. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [October 14, 2011, 4:12pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/23 "2011-10-14T16:12:36Z")
I always thought it was an appropriation of Thomas Aquinas’ idea of philosophy as the handmaiden of theology (see [here](http://en.wikipedia.org/wiki/Medieval_philosophy#Character_of_medieval_philosophy)). ---
**Author:** ![thelabdude](https://avatars.discourse-cdn.com/v4/letter/t/dc4da7/32.png) [@thelabdude](https://boards.straightdope.com/u/thelabdude)\ **Post date:** [October 14, 2011, 4:31pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/24 "2011-10-14T16:31:11Z")
> [@Thudlow\_Boink](#): > > Google turned up the following quote from [Francis Bacon](http://books.google.com/books?id=XQF-bwn5hXIC&pg=PA395&lpg=PA395&dq=mathematics+handmaid&source=web&ots=kX3YaQwW0e&sig=XTDcXu1Pwu5EnIIZRaZW-JOHK-M&hl=en): (mmm, bacon…) 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. Reply With Quote 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. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [October 14, 2011, 5:04pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/25 "2011-10-14T17:04:34Z")
[Another](http://xkcd.com/435/) relevant comic. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 14, 2011, 5:43pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/26 "2011-10-14T17:43:36Z")
Since nobody else has mentioned it, the implication of the “queen of the sciences” quote is that a queen is beautiful, elegant, and useless. ---
**Author:** ![Acsenray](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/acsenray/32/4519_2.png) [@Acsenray](https://boards.straightdope.com/u/Acsenray)\ **Post date:** [October 14, 2011, 5:48pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/27 "2011-10-14T17:48:02Z")
Useless? Or highly necessary in her ability to produce legitimate heirs? Ask Prince Physics and Princess Astronomy how useless the queen was. ---
**Author:** ![Kimstu](https://avatars.discourse-cdn.com/v4/letter/k/ecd19e/32.png) [@Kimstu](https://boards.straightdope.com/u/Kimstu)\ **Post date:** [October 14, 2011, 9:15pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/28 "2011-10-14T21:15:11Z")
> [@ganita](#): > > 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?! 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. ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [October 15, 2011, 5:56am UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/29 "2011-10-15T05:56:33Z")
> [@](#): > > I always thought it was an appropriation of Thomas Aquinas’ idea of philosophy as the handmaiden of theology (see here). 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](http://books.google.com/books?hl=en&lr=&id=weOOCfiDhDcC&oi=fnd&pg=PA57&dq=mathematics+handmaiden+of+science+medieval&ots=EOXZYnYm6W&sig=c6ejSz5hR4OF1ALid_YkU9gsOXE#v=onepage&q=handmaiden&f=false) 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](http://books.google.com/books?id=9JcXAAAAYAAJ&pg=PA41&dq=handmaiden+of+science&hl=en&ei=4RuZTruIMJTViALB8ZHNDQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC4Q6AEwAA#v=onepage&q=handmaiden%20of%20science&f=false) 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 ---
**Author:** ![psychonaut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/psychonaut/32/4655_2.png) [@psychonaut](https://boards.straightdope.com/u/psychonaut)\ **Post date:** [October 15, 2011, 6:51am UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/30 "2011-10-15T06:51:34Z")
> [@Measure\_for\_Measure](#): > > 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. 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. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [October 15, 2011, 2:19pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/31 "2011-10-15T14:19:59Z")
> [@astro](#): > > Arithmetic and mathematics are not the same thing? 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. ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [October 15, 2011, 3:32pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/32 "2011-10-15T15:32:24Z")
> [@thelabdude](#): > > Good find. Since Francis Bacon was there at the dawn of science, that may be the first reference. 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. > [@Measure\_for\_Measure](#): > > > [@](#): > > > > I always thought it was an appropriation of Thomas Aquinas’ idea of philosophy as the handmaiden of theology (see here). > > During medieval times, science was also a handmaiden to theology. During medieval times, what we now call “science” was considered a part of philosophy. ---
**Author:** ![thelabdude](https://avatars.discourse-cdn.com/v4/letter/t/dc4da7/32.png) [@thelabdude](https://boards.straightdope.com/u/thelabdude)\ **Post date:** [October 15, 2011, 5:02pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/33 "2011-10-15T17:02:12Z")
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. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [October 15, 2011, 5:28pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/34 "2011-10-15T17:28:08Z")
> [@Hari\_Seldon](#): > > 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. 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? ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [October 15, 2011, 5:31pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/35 "2011-10-15T17:31:27Z")
> [@thelabdude](#): > > 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. 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. ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [October 15, 2011, 6:06pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/36 "2011-10-15T18:06:26Z")
> [@astro](#): > > Arithmetic and mathematics are not the same thing? 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. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [October 15, 2011, 6:55pm UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/37 "2011-10-15T18:55:56Z")
> [@Frylock](#): > > 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? 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). ---
**Author:** ![thelabdude](https://avatars.discourse-cdn.com/v4/letter/t/dc4da7/32.png) [@thelabdude](https://boards.straightdope.com/u/thelabdude)\ **Post date:** [October 16, 2011, 1:48am UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/38 "2011-10-16T01:48:35Z")
> [@njtt](#): > > , outside of undergraduate textbooks). 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. ---
**Author:** ![robardin](https://avatars.discourse-cdn.com/v4/letter/r/43a26b/32.png) [@robardin](https://boards.straightdope.com/u/robardin)\ **Post date:** [October 16, 2011, 2:18am UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/39 "2011-10-16T02:18:00Z")
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](http://www.youtube.com/watch?v=mJgFU3U4X_Y).) ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [October 16, 2011, 2:29am UTC](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819/40 "2011-10-16T02:29:04Z")
> [@thelabdude](#): > > 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. 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. [Previous page](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819.md?page=1) [Next page](https://boards.straightdope.com/t/mathematics-the-handmaiden-of-the-sciences/444819.md?page=3)