# Abstract Math Names

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MATHEMATICAL ENGLISH: NAMES
The name of a mathematical object is a word or phrase in math English used to identify
an object. Names play the same role in math English that symbolic terms play in the symbolic
language.

Contents

Sources of names ......................................................................................................................................... 1
Suggestive names ....................................................................................................................................................1
Names coined from other languages ........................................................................................................................1
Person’s name .........................................................................................................................................................1
Named after symbol .................................................................................................................................................2
Synecdoche..............................................................................................................................................................2
Names from other languages ........................................................................................................................ 2
No suggestion of the meaning ..................................................................................................................................2
Pronunciation ...........................................................................................................................................................3
German spelling and pronunciation ..........................................................................................................................3
Transliterations from Cyrillic .....................................................................................................................................3
Plurals ......................................................................................................................................................................4

Sources of names
Suggestive names
A suggestive name is a a common English word or phrase, chosen to suggest its meaning. Thus it
is a metaphor.
Examples
 Slope (of a curve at a point).
 Connected subspace (of a topological space).
Suggestive names cause problems. See semantic contamination.

Names coined from other languages
A name may be a new word coined from (usually) Greek or Latin roots. Such an identifier is also
called a learned name (“learned” is two syllables).
Examples
Homomorphism, parabola, matrix. More

Person’s name
A concept may be named after a person.
Examples
L'Hôpital's Rule, Hausdorff space, Gaussian function.

Named after symbol
A mathematical object may be named by the typographical symbol(s) used to denote it. This is used
both formally and in on-the-fly references.
Examples
Many objects have standard names that are Greek letters, such as p and G. Punctuation marks
are used, too: Bracket, comma category.

Synecdoche                                                                                The Tocharians appear to have called a
A synecdoche is a name of part of something that is used as a name for the            cart by their word for wheel around 1100
years ago (possibly much more). See
whole thing.                                                                              the blog post by Don Ringe.

Example
Referring to a car as "wheels".
Example
Naming a mathematical structure by its underlying set. This happens very commonly. This is also a
case of suppression of parameters.
Example
Naming an equivalence class by a member of the class. Note that this is not an example of suppres-
sion of parameters.

Names from other languages
In English, many technical names are borrowed from other languages, mostly Latin and Greek. Al-
so, mathematicians from many countries are mentioned in mathematical discourse, commonly to give
them credit for theorems or to use their names for a type of mathematical object. Problems for the stu-
dent arise:
 The name may not suggest its meaning.
 The student may not know how to pronounce the name.
 The name of an object may use a foreign plural.
 Names borrowed from languages that do not use the English alphabet may be transliterated in
different ways.

No suggestion of the meaning
English is unusual among major languages in the number of technical words borrowed from other
languages instead of being made up from native roots. We have some, listed under suggestive names.
But how can you tell from looking at them what “parabola” or “homomorphism” mean? This applies to
concepts named after people, too: The fact that “Hausdorff” is German for a village near an estate doesn’t
tell me what a Hausdorff space is.
The English word “carnivore” (from Latin roots) can be translated as “Fleischfresser” in German; to a
German speaker, that word means literally “meat eater”. So a question such as “What does a carnivore
eat” translates into something like, “What does a meat-eater eat?”
Chinese is another language that forms words in that way: see the discussion of “diagonal” in Julia
Lan Dai’s blog. (I stole the carnivore example from her blog, too.)
The result is that many technical words in English do not suggest their meaning at all to a reader not
familiar with the subject. Of course, in the case of “carnivore” if you know Latin, French or Spanish you
are likely to guess the meaning, but it is nevertheless true that English has a kind of elitist stratum of
technical words that provide little or no clue to their meaning – and Chinese and German do not, at least
not so much.
This is a problem in all technical fields, not just in math.

Pronunciation
In English-speaking countries until the early twentieth century, the practice was to pronounce a name
from another language as if it were English, following the rules of English pronunciation.
During the twentieth century, it gradually became an         The older practice of pronunciation is explained by
history: In 1100 AD, the rules of pronunciation of
almost universal attitude among educated people in the             English, German and French, in particular, were
USA to stigmatize pronunciations of words from com-                remarkably similar. Over the centuries, the sound
systems changed, and Englishmen, for example,
mon European languages that are not approximately like             changed their pronunciation of "Lagrange" so that the
the pronunciation in the language they came from. For              second syllable rhymes with "range", whereas the
French changed it so that the second vowel is nasa-
example, today many mathematicians pronounce "La-                  lized (and the "n" is not otherwise pronounced) and
grange" the French way, and others, including (in my               rhymes with the "a" in "father".
limited observation) most engineers, pronounce it as if it
were an English word, so that the second syllable rhymes with "range". I have heard people who used the
second pronunciation corrected by people who used the first (this happened to me when I was a graduate
student), but never the reverse when Americans are involved.
This shift did not affect the most commonly-used words. We still pronounce “Euclid” as “you-clid”
and “parabola” with the second syllable rhyming with “dab”.
Forty years ago nearly all Ph.D. students had to show mastery in reading math in two foreign lan-
guages; this included pronunciation, although that was not emphasized. Today the language require-
ments in the USA are much weaker, and younger educated
Americans are generally weak in foreign languages. As a re-
sult, graduate students pronounce foreign names in a variety of
ways, some of which attract ridicule from older mathemati-
cians. (Example: the possibly apocryphal graduate student at a
blackboard who came to the last step of a long proof and an-
nounced, "Viola!", much to the hilarity of his listeners.)
Abstractmath.org comes to the
rescue of put-down students!                German spelling and pronunciation
Well, at least a little bit.                      The German letters "ä", "ö" and "ü" may also be spelled
"ae", "oe" and "ue" respectively. The letters "ä", "ö" and "ü" are
alphabetized in German documents as if they were spelled
"ae", "oe" and "ue". It is far better to spell "Möbius" as "Moebius" than to spell it "Mobius".
The letter "ö" represents a vowel that does not exist in English; it is roughly the vowel sound in
"fed" spoken with pursed lips. It is sometimes incorrectly pronounced like the vowel in "code" or else the
vowel in "herd". Similar remarks apply to "ü", which is "ee" with pursed lips. The letter "ä" may be pro-
nounced like the vowel in "raid".
The German letter "ß" may be spelled "ss" and often is by Swiss Germans. Thus Karl Weierstrass
spelled his last name "Weierstraß". Students sometimes confuse the letter "ß" with "f" or "r". In English
language documents it is probably better to use "ss" than "ß".
Another pronunciation problem concerns the combinations "ie" and "ei". The first is pronounced like
the vowel in "reed" and the second like the vowel in "ride". Thus "Riemann" is pronounced REE-mon.

Transliterations from Cyrillic
The name of the Russian mathematician most commonly spelled "Chebyshev" in English is also
spelled Chebyshov, Chebishev, Chebysheff, Tschebischeff, Tschebyshev, Tschebyscheff and Tschebys-
chef. (Also Tschebyschew in papers written in German.) The correct spelling of his name is                      ,
since he was Russian and the Russian language uses the Cyrillic alphabet. The only spelling in the list
above that could be said to have some official sanction is “Chebyshev”, which is used by the Library of
Congress.
In spite of the fact that most of the transliterations show the last vowel to be an "e", the name in Rus-
sian is pronounced approximately "chebby-SHOFF", accent on the last syllable. Now, that is a ridiculous
situation, and it is the transliterators who are ridiculous, not Russian spelling, which in spite of that pecu-
liarity about the Cyrillic letter “e” is much more nearly phonetic than English spelling.

Plurals
Many authors form the plural of certain technical words using endings from the language from which
the words originated. Students may get these wrong, and may sometimes meet with ridicule for doing s o.

Plurals ending in a vowel
Here are some of the common mathematical terms with vowel plurals.
singular       plural
automat    automa
on        ta
polyhedr polyhe
on        dra
focus          foci
locus          loci
formula
formula
e
   Linguists have noted that such plurals seem to be processed differently from s-plurals. In
particular, when used as adjectives, most nouns appear in the singular, but vowel-plural nouns
appear in the plural: Compare "automata theory" with "group theory". No one says groups
theory. I used to say “automaton theory” but people looked at me funny.
   The plurals that end in a (of Greek and Latin neuter nouns) are often not recognized as plurals
and are therefore used as singulars. That is how “data” became singular. This does not seem
to happen with my students with the -i plurals and the -ae plurals.
   In the written literature, the -ae plural appears to be dying, but the -a and -i plurals are hanging
on. The commonest -ae plural is "formulae"; other feminine Latin nouns such as "parabola" are
usually used with the English plural. In the 1990-1995 issues of six American mathematics
journals, I found 829 occurrences of "formulas" and 260 occurrences of "formulae", in contrast
with 17 occurrences of "parabolas" and and no occurrences of "parabolae". (There were only
three occurrences of "parabolae" after 1918.) In contrast, there were 107 occurrences of
"polyhedra" and only 14 of "polyhedrons".

Plurals in s with modified roots
sing
plural
ular
matri        matric
x            es

simpl     simpli
ex           ces

verte        vertice
x            s

Students recognize these as plurals but produce new singulars for the words as back formations. For
example, one hears "matricee" and "verticee" as the singular for "matrix" and "vertex". I have also heard
"vertec".

Remark
It is not unfair to say that some scholars insist on using foreign plurals as a form of one-upmanship.
Students and young professors need to be aware of these plurals in their own self interest.
It appears to me that ridicule and put-down for using standard English plurals instead of foreign
plurals, and for mispronouncing foreign names, is much less common than it was thirty years ago.
However, I am assured by students that it still happens.

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