Every human being who is capable of learning how to speak a language is also capable of acquiring not just simple but deep mathematical skills, says ICTP's new mathematics group head Le Dung Trang.

Culture of Mathematics

Research on brain function and behaviour has highlighted the central role of language in all human activities.
Language is indispensable both for comprehending what is happening around us and for learning new ideas. Put another way, without language it is difficult to understand and to learn.
Research, moreover, also has shown that language is a cornerstone of culture: That the language we speak has a great bearing on who we are--precisely because it serves as a major force driving the socialisation process.
If language is culture-bound, mathematics has long been viewed as a culture-free, universal source of knowledge and understanding.
Yet language at its core evolves around a set of rules and codes that parallel the rules and codes framing mathematics. For this reason, I would contend that language capability is a deep and complex reflection of mathematical capability and that both, in turn, are 'naturally' present in all human beings.
I use the word 'naturally' in a broad sense and not as a concept that language stems only from genetic predisposition. Because of the close ties between language and mathematics, I have concluded that every human being who is capable of learning how to speak a language (that means virtually everyone) is also capable of acquiring not just simple but deep mathematical skills. After all, the logic and abstract understanding embodied in language--translating sounds, images, ideas and facts--into a common base of understanding represents the very principles of mathematics as well. Language skills, however, do not translate easily into mathematical skills. As many math-challenged people will readily admit, mastering mathematics is not easy.

If these common strains between language and mathematics are true, then they raise serious questions about our abiding beliefs in the culture-free universality of mathematics, particularly the creation of mathematics. Perhaps it is not by chance that the Greeks invented geometry or that the Arabs invented algebra.
Instead of concluding that mathematics--and, by implication, science--progresses on the shoulders of individual geniuses, we should consider the fact that progress is driven, in part, by differences in cultures that enable gifted individuals within these cultures to explore and shed light on unanswered mathematical problems from different perspectives.
These differences may be comparable to those we find in musical expression among various cultures. Everyone follows the same scales and notes but the sound of the music--and the pleasure we derive from such sounds--varies enormously. And so do the compositions of a culture's most gifted musicians.
Today we continue to find differences in mathematical interest depending on the culture involved. French-born mathematicians, for example, have a preference for large systems, particularly those related to algebra and geometry. US-born mathematicians lean towards topology, most notably low dimensional topology. Italian mathematicians often concentrate on geometry, especially algebraic geometry, while Japanese mathematicians have displayed keen interest in mathematical formulae and combinatorial mathematics.
What are we to make of these diverse preferences for the study of mathematics? We still do not know enough about the relationship between genetics and nurturing to determine whether these differences are simply intriguing facts without explanation or a reflection of something deeply revealing about the essence of mathematics and culture.
No one would claim that language is disconnected from culture. It may now be time to consider that the same is true of mathematics.

Le Dung Trang
Head, ICTP Mathematics Group

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