The Language of Mathematics: Telling Mathematical Tales

by Prof Bill Barton, University of Auckland, NZ

Abstract:
This seminar presents some of the ideas from my recent book 
"The Language of Mathematics: Telling Mathematical Tales". 
It begins by examining how different languages express mathematical 
ideas-it turns out that mathematics is expressed grammatically in 
very different ways. In flights of fancy, these grammatical differences 
are expanded into mathematical worlds that are different from mathematics 
as we know it. The picture of mathematics that emerges is of a subject 
that is much more contingent, relative, and subject to human experience 
than is usually accepted. I demonstrate the congruence between mathematics 
as we know it and the English language in comparison with other languages.
The second part of the talk further illustrates the conjunction between 
mathematical and language development, building on Devlin's concept of 
the Mathematical Gene. I thereby present alternative answers to conventional 
questions about mathematics: where it comes from, how it develops, what it 
does and what it means. 
Finally, these playful ideas imply some serious reconsideration of 
mathematics education practices, in particular our use of minority 
languages and the role of abstraction in young children's education.