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I'm thinking people in Westeros and Essos know or ought to know maths such as basic geometry and probability and maybe some basics of finance, economics, physics, engineering, technology, medicine or statistics

In a scene from S02E04 Littlefinger says to Margaery Tyrell:

If war were arithmetic, the mathematicians would rule the world

However, I find the profession of theoretical mathematician to be kind of useless in a place like Westeros (or Essos, Wall Maria, Alexandria Safe-Zone).

Theoretical mathematicians today study things like algebraic geometry, number theory, probability theory, functional analysis, harmonic analysis, etc.

There are of course statisticians and applied mathematicians whose research are used in finance, economics, physics, engineering, technology, medicine, statistics and the like.

My guess is that 'mathematician' is a broad term used to encompass experts in finance, economics, physics, engineering, technology, medicine or statistics much like a 'philosopher' in ancient times studied a lot of things including maths, physics and economics.

Perhaps Littlefinger in that scene means 'statistician'.

Any other mention of maths as a study or the profession of 'mathematician' in the books or series? Any word from GRRM or Benioff & Weiss on what it means for a Westerosi (or Essosi) to be a 'mathematician' ?

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    They had philosophers... "What happens when the nonexistent bumps against the decrepit? A question for the philosophers" (TV show, Olena to Varys) And The Citadel is basically a university, with economics (yellow gold links) as one of it's subjects. Presumably other practical branches of mathematics have their own links (they're not all known). I'm not quite making sense of this question though, it's a bit stream of consciousness right now. Dec 4, 2015 at 17:01
  • There are numerous occasions where adults tell the children to "learn their numbers"; this refers to simple mathematics.
    – Möoz
    Dec 7, 2015 at 20:34

3 Answers 3

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Noble-born girls were educated in mathematics, but apparently only to the proficiency required for running the accounts of a household. See the following quote (emphasis mine):

It hurt that the one thing Arya could do better than her sister was ride a horse. Well, that and manage a household. Sansa had never had much of a head for figures. If she did marry Prince Joff, Arya hoped for his sake that he had a good steward.
-- A Game of Thrones (book), Chapter 7, Arya

The place for the study of abstract mathematics would surely be the Citadel, where maesters are educated. But so far we have seen very little of what goes on in the Citadel in either the books or the TV show (this may be updated in the future). As far as we know currently, maesters can earn the following types of links in their chain:

  • Black iron (ravenry)
  • Brass
  • Bronze (astronomy)
  • Copper (history)
  • Electrum (astrology)
  • Yellow Gold (economics)
  • Iron (warcraft)
  • Lead
  • Pale steel (smithing)
  • Pewter
  • Platinum
  • Red gold
  • Silver (medicine and healing)
  • Steel
  • Tin
  • Valyrian steel (magic and the occult)
    source

Note that we do not know the type of study associated with all these metals, and that there may well be other types of metal links not included in this list. It's quite plausible that the maesters in the Citadel, who are essentially cloistered academics, have taken the study of mathematics far beyond what is required for accountancy, land surveying, war, etc. - but this is currently unknown in book/TV canon.

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    +1. It could be noted that in real life, until recently, maths and astronomy (and actually astrology and alchemy and philosophy) were not as separated as they are now.
    – Taladris
    Dec 4, 2015 at 23:56
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    @Taladris Indeed: astronomy grew out of astrology and chemistry grew out of alchemy. Gauss, one of the greatest mathematicians of all time, is sometimes said to have been primarily an astronomer. 'Pure' mathematics as a profession, rather than a hobby, has appeared only in the last 100-200 years.
    – Rand al'Thor
    Dec 5, 2015 at 0:00
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The words "math, maths, or mathematics" do not appear in the books. I did a text search on my e-books to confirm this and other mentions as noted below.

Most of the time when referring to maths (what we probably consider arithmetic) is called "sums". I'l list a couple examples below, but there are dozens of them scattered throughout all the novels.

  • Jon glanced warily at Chett, standing beside the door, his boils red and angry. "He could help you," he said quickly. "He can do sums, and he knows how to read and write.

    A Game of Thrones - Jon V

  • Every time you learn something you get another link. Black iron is for ravenry, silver for healing, gold for sums and numbers. I don't remember them all."

    A Clash of Kings - Bran IV

Eventually we do see the some more advanced mathematics are known, namely geometry.

Geometry followed languages. There the boy was less adroit, but Haldon was a patient teacher, and Tyrion was able to make himself of use as well. He had learned the mysteries of squares and circles and triangles from his father's maesters at Casterly Rock, and they came back more quickly than he would have thought.

A Dance with Dragons - Tyrion IV

Geometry is only mentioned this one time, and I have no other mentions of advanced mathematics.

In conclusion, most high-born children are taught basic maths by their Maesters. The Maesters themselves are the ones who seem to hold the knowledge, so one must assume there are some books written on the subjects in the library at the Citadel and possibly other prominent castles.

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Not exactly an answer, but too long for a comment...

Our own knowledge of mathematics grew largely out of need. Here is a quote from Mathematical Thought from Ancient to Modern Times (M. Kline, chapter 2, section 4):

The Egyptians used mathematics in the administration of the affairs of the state and church, to determine wages of paid laborers, to find the volumes of granaries and the areas of fields, to collect taxes assessed according to the land area, to convert from one system of measures to another and to calculate the number of bricks needed for the construction of buildings and ramps.

Later, the ancient Greeks studied some quite advanced geometry, which can appear abstract, but they needed it for astronomy, which in turn was needed for correct prediction of the seasons. As technology improved, we have come to rely on more and more advanced mathematics.

Given the primitive level of technology in Westeros, Essos, etc. we can speculate that knowledge of mathematics there is probably at a similar level of development. More sophisticated topics such as group theory would come later (assuming the civilisations survive in some form).

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