I Have a Threem

And now I have another. My first “threem”, or “three-M”, for this bijou bloguette was the alliterative three-word Latin phrase Mathematica Magistra Mundi, meaning “Mathematics Mistress of the World”. I also use it in the form Mathematica Machina Mundi, which has a variety of translations. In both Latin phrases, the words have five, three and two syllables, respectively. That’s the first three prime numbers in reverse and also part of the Fibonacci sequence in reverse.

You can find the same alliteration in languages derived from Latin, like the French La Mathématique, Maîtresse du Monde, but you don’t get the same syllable-count. So how likely was it that everything – the same alliteration and the same syllable-count – would appear in a language unrelated to Latin? But it does. Here’s a Georgian translation of the threem:

მათემატიკა მსოფლიოს მეფე

Matemat’ik’a Msoplios Mepe

“Mathematics the World’s King”

Msoplios isn’t a typo: Georgian is famous for its exotic consonant clusters and მს- / ms- isn’t a particularly unusual example. But it’s one I particularly like.

On the M3!

6 = 2 x 3. And 6 = 1 + 2 + 3. But 6 also equals 3!. That is, 6 = 3 x 2 x 1, or factorial three. If you have three different items, you can arrange them in six different ways. There are three posibilities for the first item, two for the second and one for the third.

You can illustrate this linguistically. All languages are governed by mathematics, but maths manifests itself in different ways. Emphasis is an important part of language, for example, but there are different ways to achieve it. English usually does it with stress or by adding an emphatic word. Other languages can do it by varying the order of words. Latin, for example:

  • Mathematica Magistra Mundi
    — Mathematics is Mistress of the World.
  • Mathematica Mundi Magistra
    — Mathematics of the World is Mistress.
  • Magistra Mathematica Mundi
    — Mistress is Mathematics of the World
  • Magistra Mundi Mathematica
    — Mistress of the World is Mathematics.
  • Mundi Mathematica Magistra
    — Of the World Mathematics is Mistress.
  • Mundi Magistra Mathematica
    — Of the World the Mistress is Mathematics.

Elsewhere other-posted:

Mathematica Magistra Mundi — more on the motto
Moto-Motto — a variant on the motto

He Say, He Sigh, He Sow #19

“The study of mathematics is the indispensable basis for all intellectual and spiritual progress.” — F.M. Cornford (1874-1943) quoted in The Sacred in Music (see also Pythagoreanism).

Poulet’s Propeller

The Penguin Dictionary of Curious and Interesting Numbers (1986) is one of my favourite books. It’s a fascinating mixture of math, mathecdote and math-joke:

2·618 0333…

The square of φ, the golden ratio, and the only positive number such that √n = n-1. (pg. 45)


Kepler discussed the 6-fold symmetry of snowflakes, and attempted to explain it by considering the close packing of spheres in a hexagonal array. (pg. 69)


This appears to be the first uninteresting number, which of course makes it an especially interesting number, because it is the smallest number to have the property of being uninteresting.

It is therefore also the first number to be simultaneously interesting and uninteresting. (pg. 120)

David Wells, who wrote the Dictionary, “had the rare distinction of being a Cambridge scholar in mathematics and failing his degree”. He must be the mathematical equivalent of the astronomer Patrick Moore: a popularizer responsible for opening many minds and inspiring many careers. He’s also written books on geometry and mathematical puzzles. But not everyone appreciates his efforts. This is a sideswipe in a review of William Hartston’s The Book of Numbers:

Thankfully, this book is more concerned with facts than mathematics. Anyone wanting to learn more about [π] or the Fibonacci sequence should turn to the Penguin Dictionary of Curious and Interesting Numbers, a volume which none but propeller-heads will find either curious or interesting. (Review in The Independent, 18th December 1997)

Continue reading: Poulet’s Propeller