# Prepositions in mathematics

I’m preparing talks on modular forms for a meeting in Peru sponsored by CIMPA, and they have to be in Spanish.  The basic vocabulary is not a problem, but it’s always hard to guess the foreign equivalents of English prepositions as used in mathematics.  My technique has been to throw  guesses out onto Google until one comes up right, and this is how I discovered the amazing series of high school textbooks by Aurelio Baldor.   That’s Al-Khwarizmi on the cover of his Algebra book, first published in 1941, reprinted in 1983 and 1997.  According to the Wikipedia page for Baldor’s Algebra,

El texto de Baldor es el libro más consultado en escuelas y colegios de Latinoamérica. El Álgebra de Baldor tiene 5.790 puntos en total. (19 puntos en cada ejercicio en promedio)

which means that it’s the book most frequently used in Latin American schools.  And the exercises are worth a total of 5790 points, 19 per exercise on average, which go a long way toward explaining why it may well be the most detested book in Latin America.   The exercises are brutally repetitious.  For example, there are 40 polynomials to simplify on pp. 21-22.  Here’s exercise 37:

But the pictures are great, like this one on p. 46,

and the historical material goes well beyond anything I’ve seen in an algebra textbook outside Latin America.

There are also Baldor textbooks on geometry and arithmetic.  Look:  the Cro-Magnon had arithmetic too:

There is no Wikipedia page in any language other than Spanish!  There is an English Wikipedia page about its Cuban author, who apparently had good relations with the revolutionary leader Camilo Cienfuegos, but not with Raúl Castro; when Cienfuegos died, Baldor left the country at age 54, finally winding up as a high school math teacher in Jersey City and Hoboken before retiring to Miami.

Anyway, if you need to know what preposition to use when you write “we change the sign when we subtract (-4)” in Spanish (note:  no preposition in English), that’s the best place to look.

The lesson is that even in simple algebra the meaning changes when translated from one language to another.  This is completely lost when it is translated into a uniform formal language.  And I think that’s not such a good thing.