Mathematics, as a science commenced when first someone, probably a Greek, proved propositions about any things or about some things, without specification of definite particular things. … Perhaps it required the introduction of the arabic numerals, by which the use of letters as standing for definite numbers has been completely discarded in mathematics, in order to suggest to mathematicians the technical convenience of the use of letters for the ideas of any number and some number.

As an aside, I note two specious claims:

1. Stuff fitting the name “mathematics” surely predates the Greeks, and Whitehead’s characterization of the first mathematical activities seem to bear the unmistakable mark of logicist’s bias.
2. There are still letters used to refer to some definite numbers, e.g., \( e \).

… the enormous importance of good notation. By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race. (39)

Writing inscription is an intellectual prosthetic. It is so in the shallower, more obvious sense that it can be used to extend memory by recording information externally, and in innumerable deeper senses:

• Notation organizes, concentrates, accelerates thought
• The logic of inscriptions is reinscribed in our thought, amplifying reflectivity
• The externalization and objectification of concepts forces a dialectical process that refines and sharpens understanding
• The communication of thought through beings causes world and consciousnessness to interpenetrate, weaving together community at the limiting points of alterity. (Nancy’s “Literary Communism”).

…by the aid of symbolism we can make transitions in reasoning almost mechanically by the eye, which otherwise would call in to play the higher faculties of the brain.

It is a profoundly erroneous truism, repeated by all ….