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Last edited 3/10/2008 10:52:00 AM

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.

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), or "connected subspace" (of a topological space).

Suggestive names cause problems.  See semantic contamination. 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? 

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?”  (And do they do it in Grant’s tomb?)   Similarly the word for “plane” (ebene) looks like “flat”.

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.

This is a problem in all technical fields, not just in math.

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  and .  Punctuation marks are used, too:  Bracket, comma category.

Synecdoche

A synecdoche is a name of part of something that is used as a name for the whole thing.

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 suppression of parameters.

Names from other languages

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. Three problems for the student arise: Lack of suggestiveness, pronunciation and variant spellings.

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? 

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?”  (And do they do it in Grant’s tomb?)   Similarly the word for “plane” (ebene) looks like “flat”.

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.

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 almost universal attitude among educated people in the USA to stigmatize pronunciations of words from common European languages that are not approximately like the pronunciation in the language they came from. For example, today many mathematicians pronounce "Lagrange" the French way, and others, including (in my 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 languages; this included pronunciation, although that was not emphasized. Today the language requirements in the USA are much weaker, and educated Americans are generally weak in foreign languages. As a result, graduate students pronounce foreign names in a variety of ways, some of which attract ridicule from older mathematicians. (Example: the possibly apocryphal graduate student at a blackboard who came to the last step of a long proof and announced, "Viola!", much to the hilarity of his listeners.)

German spelling and pronunciation

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 pronounced like the vowel in "fed".

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 Tschebyschef. (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 Russian is pronounced approximately "chebby-SHOFF", accent on the last syllable.

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 so.

Plurals ending in a vowel

Here are some of the common mathematical terms with vowel plurals.

¨     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".

¨     The plurals that end in a (of Greek and Latin neuter nouns) are often not recognized as plurals and are therefore used as singulars. 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

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.