Extract : A Short History of Mathematical Notation by Robyn Arianrhod

Robyn Arianrhod is a writer and mathematician (she is Adjunct Research Fellow in the School of Mathematical Sciences, Monash University).
Her first book, Einstein’s Heroes: Imagining the world through the language of mathematics, was published by UQP in 2003. It has since been published in the UK and the US, and has been translated into French, Japanese, Korean and Turkish. It was shortlisted for the Age Non-Fiction Book of the Year and the Victorian Premier’s Prize for a first book of history.

It is easy to forget, with our four centuries of post-Cartesian hindsight, that for thousands of years arithmetic and algebra were done rhetorically or geometrically, without the benefit of our familiar x’s and y’s, our pluses, minuses, square root signs, indices, and other symbols. These symbols make algebraic processes so transparent, so universal, and so easily generalized that mathematical thought becomes simpler and more economical.

This simplicity is possible because mathematical symbols can « evoke subliminal, sharpy, focused perceptions and connections », as Joseph Mazur puts it his entertaining and insightful new book. « Just as with the symbolism in music and poetry, these mathematical symbols might also transfer metaphorical thoughts capable of such tranferences as words on a page. In a reading an algebraic expression, the experienced mathematical mind leaps through similarity short neuro transmitter lag times.

Thinking about the history of mathematics in terms of the history of symbolic mathematical notation offers an interesting perspective on the dramatic increase in mathematical progress from the seventeenth century onwards. It also makes us wonder how ancient mathematicians made as much progress as they did without an internalized, subconscious symbolic language to aid their thinking. Enlightening Symbols offers food for thought on both these themes : the history of mathematics and symbolic cognition.

References : A. Einstein, The foundation of the general theory of relativity, Einstein’s paper was originally published in German in Annalen der Physik,49 (1916).

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