Not A Simple Equation: Mathematics Translation as a Language of its Own

Mathematics translation presents a unique set of linguistic challenges. These challenges differ from those confronted by academic translators in other subjects because language and linguistic structures in mathematics are unlike those in everyday use. Essentially, mathematics is a language of its own.

Understanding the patterns common to mathematics and differentiating them from other academic subjects is critical to the success of mathematics and scientific translation. One such mathematical pattern that math translators should be aware of is the use of multiple semiotic systems. Mathematics employs the use of several meaning-making systems -- including graphs, diagrams, oral language, written language and symbols. Meaning in mathematics is created by combining these different semiotic systems. Mathematical representation is all about how these different systems interact and how they may be manipulated.

Another mathematical pattern relates to verbal constructs; these may include dense and long noun phrases that name and describe quantifiable yet abstract head nouns (e.g. the volume of a rectangular prism that has sides of 12, 15 and 18cm), adjectives that classify and precede the noun (e.g. the volume of), and qualifiers that follow the noun (e.g. that can be divided by three and itself). These noun phrases are central to the construction of complex meaning relationships because they refer to relational processes.

These relational processes are constructed with clauses that use the verbs to have and to be; these may present grammatical challenges in languages in which verbs are constructed by identity and attribution. For example, in Spanish, the verb has different forms and relates to different meaning relationships. Figuring out the meaning of these relational constructions can pose a challenge to an academic translator.

Since academic translation, among these multiple semiotic systems, presents significant linguistic challenges in mathematical translation, translators must have a broad understanding of these issues, beyond familiarity with specialized terminology, vocabulary and everyday informal use of language.

Mathematics uses language to serve new functions

It assigns new meanings to everyday words. For example, the word product has an entirely different meaning in mathematics than in other contexts. Mathematics also uses symbols to represent concepts which may be difficult to express in ordinary language or that go beyond what can be expressed in ordinary language. In addition, conjunctions in mathematics have technical meanings. For example, therefore, when and if are used in very specific ways to create complex connections between clauses.

Construction of knowledge in mathematics is different from other academic subjects. Moreover, implicit logical relationships between objects exist, so proofs may not always be spelled out explicitly. Mathematics also makes unique use of word combinations and modes of argument. Understanding the distinction between the description of mathematical knowledge and other academic knowledge is key to a successful translation.

Since math is a language of its own and makes use of symbols and language in its own way, coherent mathematical reading is a translation process in and of itself. The presence of natural language in mathematics, however, cannot be ignored; it indicates an interplay between mathematical language and natural language used to conceptualize mathematical theories, define and explain terms, translate calculations and explain the implications of proofs.

While it is unlikely that mathematics could do without natural language, it is considerably limited. For instance, the word prime in English has many meanings, but only one of those is applicable in math.

The Scientific Translator’s Cognitive Language

A study conducted by Van Rinsveld, Schiltz, Brunner, Landerl and Ugen found that when posed with questions of general knowledge, bilingual people responded differently depending on the language in which the questions were asked. This suggests that the language of translation may affect translation outcome.

Van Rinsveld, Dricot, Guillaume, Rossion, and Schiltz established that even highly proficient bilinguals have a variety of mathematical problem-solving processes taking place in their minds that are dependent on the language in which they are thinking. This confirms that language indeed plays a vital role in mathematical problem-solving. It also suggests that academic translators require mathematics-specific knowledge in both the source and target languages since a mental mathematical process is taking place separately in each language.

In a different study conducted on bilinguals, Venkatraman, Siong, Chee, and Ansari discovered that mathematical calculations are more precise when performed in the language in which mathematics had been taught. This suggests that mathematics translation is influenced by the language in which the translator learned mathematics; the best mathematics translators would then be those whose math education was in both source and target languages.

Key Points for Scientific Translation

The information and studies presented above have important implications for academic translators, because they highlight that:

• Knowledge of vocabulary, technical terms, and everyday grammar alone is insufficient for precise mathematics translation.

• Since mathematics is a language of its own, simply reading it is a translation process in itself.

• Mathematical skills involve complex verbal and linguistic processes that exceed the translation skills required by other academic subjects.

• The language in which a translator thinks affects the precision of the resultant mathematics translation.

• The language in which the translator was taught mathematics impacts the precision of the mathematics translation.

• Scientific translators require math-specific knowledge in the language in which they are working.

• There is very little leeway in mathematics translation for creative thinking and artistic license.

• Natural language is considerably limited when used in mathematics.