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Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots

We cannot usually hear the voice of the namers of the remote past but we can of more recent ones. Naming is not just the business of the original namer. Others have to adopt the term and keep it going. Every time a word is used there is an opportunity to re-name it. Yet terms do get replaced. The origins story of bootstrap is exceptionally tidy. In its short history bootstrap has not been subject to significant semantic drift.


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Of course further investigation of bootstrap might uncover earlier uses in pre-publication writing and in recorded conversations and possibly even show that other terms were tried and discarded. As well as going back to before the date of publication it is possible to go forwards and notice that the term is not used in exactly the same way now as it was in A historian writing in or even now would be interested in both the backward and forward stories.

As translation into English has been so important building up the English mathematical lexicon see below it is interesting to see how bootstrap has gone from English into other languages. It is a very tricky word and an obvious expedient—in the short run at least—is to take the word or the phrase bootstrap method into the language: ALGEBRA is a remnant of such a phrase. English has often operated in this way, borrowing wholesale from Latin , French and Greek. The translations of bootstrap method given in t he ISI Multilingual Glossary illustrate a variety of more permanent arrangements.

In the translations the essence of the original joke—you can't pull yourself up by your own bootstraps—is retained but the accidentals are lost. English writers of the Late Middle Ages and Renaissance had the same options when they translated Latin words. See Graddol Because of the idiom in which it is embedded, bootstrap is an especially tricky word but translation is always tricky. Of course the translator is just one more person who makes choices: choices were made by the person who originally coined the term and the people who sanctioned its use by adopting it.

For another famous mistranslation see SINE. Words have come into English as singletons and also when an entire work—a book or an article—has been translated. It is mentioned in over entries in the OED although not all of these involve mathematical words and not all are first uses. Some other translations appear repeatedly in Earliest Uses. The problems of finding the right word for topological concepts in different languages is discussed by. Translation is of such cultural and commercial significance that it has given rise to an academic subject, Translation Studies. The following books give an idea of the range of the subject, although neither discusses mathematics.

Modern translators of old texts face different and very difficult problems. Three hundred years ago when Bernoulli wrote his Ars Conjectandi the i. Sylla prefaces her translation by describing the problem of choosing the right words. English M athematical words. English as a language of mathematics presents a paradox. The explanation is that. The historical development of a specialised branch of language, such as mathematical language, belongs to the history of mathematics and to the history of language.

There are many works on these subjects but very few on their intersection. The Wikipedia: History of the English language is a useful summary. Works on the history of mathematical words in English are described below. The history of mathematics in the English-speaking lands is relevant and so is the history of mathematics education there.

Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots

There appear to be no specialised studies of the former, for the latter I refer to Howson. The MacTutor series on the history of mathematical education is also useful. The following table gives some information on the origins of a few of the words in use today. A table like this would work for other Western European languages but for Chinese, say, a complete reconstruction would be required. When and whence for some English mathematical words.

Latin Greek BC. Sanskrit Arabic French German From this table of English words it is striking. The colour coding indicates the significant other language of the age. Simplifying heroically. In the beginning the main centre was in Italy but later the action moved north and west. In the beginning most of the French literature was produced in France but later French was adopted as an international language.

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See Katz Part IV. However when Poland was reconstuted after the First World War Polish mathematicians chose French as their international language: see the journal Fundamenta Mathematicae.

Latin melted away. There is a large body of native English speakers doing mathematics and English is more dominant internationally than French and German were in the past. The Latin, French, German and English have been at different times international or in a smaller world world languages. M athematics in English: behind the table. Before Before —off the table. There was not much demand for English mathematical words.

By the middle of the C14 French was no longer an official language in England but it remained important because ideas from the rest of the world generally came through France. By the C14 English was the language of lowland Scotland.

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With the Reformation of the C16 Latin ceased to be the language of religion. Scholars wrote in Latin but a market developed for mathematical works in English—especially after the introduction of printing. Many words were borrowed from Greek and Latin. Towards the end of the period a brilliant group of mathematicians appeared of whom the best known is Newton. In this period—for the first time—important original work appears in English. Mathematics in English is not the same as mathematics done by the English for Scottish and Irish mathematicians also wrote in English and the British Empire took English all over the world.

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Mathematical Words, Words of Mathematics

In the early part of this period the most important mathematical work in the European tradition was being done on the Continent of Europe. Before the C20 the only mathematicians who wrote in English lived in English-speaking countries.


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Today English is used by anybody anywhere. I have been referring to English mathematical words without questioning the notion of Englishness. Linguists are familiar with the varieties of English around the world and their differences in vocabulary, spelling, pronunciation, etc. D ifferences in the mathematical languages of the varieties of English seem trivial.

American English and British English are the two most important national forms and Earliest Uses entries indicate some differences. Math and Maths. When everyday words are given a mathematical sense some of the zest is lost if the word is not an everyday one in the other variety; in British English the word JACKKNIFE is not an everyday word and has currency only as a technical term in Statistics.

A difference in pronunciation mathematicians will notice is that of the Greek letters Beta, Zeta, etc. Old English. Of course, these four languages are not the only ones that are reflected in modern English but mathematical terms originating in, say, Arabic e. The small number of loan-words from a particular language may bear little relation to the extent of mathematics developed in that language; see e.

The order in which the languages are presented may seem strange but it reflects the rough order in which mathematical words from those languages first came directly into English. There appear to be no works specialising in mathematical terms but several treat the foreign origins of English words in general use: at the scholarly end there is Serjeantson and at the popular end there is Metcalf.

Lurquin works in the opposite direction from the source language s.

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Shipley and Watkins consider the place of English in the Indo-European language family. The Wikipedia articles show how English has borrowed extensively from Arabic, Russian and Italian but not many mathematical words are included.