The Mechanism of Mind

Descartes’s invention of co-ordinates made possible the development of analytical geometry. Newton and Leibniz independently discovered the calculus, but Newton’s notation was so very cumbersome compared to that of Leibniz, that those who followed Leibniz made much more progress. This is surprising when one realizes that the basic principles were the same in each case and only the notation was different.

The development of mathematics was held up for a long time by the cumbersome notation of the Greeks and then the Romans. The Roman system was good for adding, subtracting and tallying, but very awkward for multiplication or division. Then came the Arabic system, with its emphasis on the position of a symbol as well as its shape. Then there was the invention of the zero, which has had an immense usefulness in the development of mathematics. The invention of the decimal notation again made things easier.