In the Concise Guide to Numerical Algorithmics: The Foundations and Spirit of Scientific Computing, John Lawrence Nazareth in his discussion why number zero was such an important achievement for field of mathematics, goes to quote Whitehead to fully enlighten the reader on the philosophy of mathematics:
For our present purposes, however, the history of the notation is a detail. The interesting point to notice is the admirable illustration which this numeral system affords of the importance of a 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.
Whitehead doubles down on this statement, by asserting the following (emphasis as in original):
… by the aid of symbolism, we can make transitions in reasoning almost mechanical by the eye, which otherwise would call into play the higher faculties of the brain.
It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking. Operations of thought are like cavalry charges in a battle—they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
Let that sink in.