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Posted 24
June 2009
THE LANGUAGES OF
MATH
Mathematics in the English-speaking world is communicated using two languages:
¨ Mathematical English is a special form of English.
· It uses ordinary
words with special meanings.
· Some of its structural words (“if”, “or”) have
different meanings from those of ordinary English.
· It is both written and spoken.
· Other languages also have special mathematical forms.
¨ The symbolic language of math
is a distinct, special-purpose language.
· It has its own symbols and rules that are rather
different from spoken languages.
· It is not a dialect of English.
· It is largely a written language. Simple expressions can be pronounced, but
complicated expressions may only be pointed to or referred to.
· It is used by all
mathematicians, not just those who write math in
English.
Math in writing and in lectures involve both mathematical English and the symbolic language embedded in each other and referring back and forth to each other.
Contents
The languages
of math are covered in three chapters, each with several parts. Some things are not covered; see notes.
Glossary: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Grammar of the symbolic
language
Displayed symbolic
expressions
Preconditions and postconditions
Speaking math
Links
¨ Gyre&Gimble, a blog about math and language by Charles Wells
¨ Earliest Known Uses of Some of the Words of
Mathematics, by Jeff Miller
¨ The Handbook of Mathematical Discourse, by Charles Wells
¨
The history of mathematical symbols, by Douglas
Weaver
¨
The language and grammar
of mathematics, by Timothy Gowers
¨
Mathematical
notation: past and future, by Stephen Wolfram
¨
On the communication of
mathematical reasoning, by Atish Bagchi and Charles Wells.
¨ Varieties of mathematical prose,
by Atish Bagchi and Charles Wells
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References
Barton, Bill (2009), The Language of Mathematics: Telling Mathematical Tales. Springer.
Bullock, J. O.
(1994), ‘Literacy in the language of mathematics’. American Mathematical Monthly, volume
101, pages 735743.
de Bruijn, N. G.
(1994), ‘The mathematical vernacular, a language for mathematics with
typed sets’. In Selected Papers on
Automath, Nederpelt, R. P., J. H. Geuvers, and R. C. de Vrijer,
editors, volume 133 of Studies in
Logic and the Foundations of Mathematics, pages 865 935.
Epp, S. S.
(1999), ‘The language of quantification in mathematics instruction’. In Developing Mathematical Reasoning in Grades
K-12. Stiff, L. V., editor
(1999), NCTM Publications. Pages 188197.
Gillman, L.
(1987), Writing Mathematics
Well. Mathematical Association of
Higham, N. J. (1993), Handbook of Writing for the Mathematical Sciences. Society for Industrial and Applied Mathematics.
Knuth, D. E., T.
Larrabee, and P. M. Roberts (1989), Mathematical Writing, volume 14 of MAA Notes. Mathematical Association of
Krantz, S. G.
(1997), A Primer of
Mathematical Writing. American Mathematical Society.
O'Halloran, K. L. (2005), Mathematical Discourse: Language, Symbolism
And Visual Images. Continuum International Publishing Group.
Schwartzman, S.
(1994), The Words of
Mathematics. American Mathematical Society.
Schweiger, F. (1994b), ‘Mathematics is a language’. In Selected Lectures from the 7th International Congress on Mathematical Education, Robitaille, D. F., D. H. Wheeler, and C. Kieran, editors. Sainte-Foy: Presses de l’Université Laval.
Steenrod, N. E., P. R. Halmos, M. M. Schiffer, and J. A.
Dieudonné (1975), How to Write Mathematics.
American Mathematical Society.
Stiff, L. V., editor (1999), Developing Mathematical Reasoning in Grades K-12. NCTM Publications.
Notes
¨ Math communication also uses pictures, graphs and diagrams, which abstractmath.org doesn’t discuss. The book by O’Halloran goes into considerable detail about the way pictures and math language refer to each other.
¨ We also don’t cover the history and etymology of mathematical notation. See the book by Schwartzmann and the links to Miller, Weaver and Wolfram.