How to Read Mathematics

"Know Thyself

Texts are written with a specific audience in mind. Make sure that you are the intended audience, or be willing to do what it takes to become the intended audience.

T.S.Eliot's

A Song for Simeon:

Lord, the Roman hyacinths are blooming in bowls and
The winter sun creeps by the snow hills;
The stubborn season has made stand.
My life is light, waiting for the death wind,
Like a feather on the back of my hand.
Dust in sunlight and memory in corners
Wait for the wind that chills towards the dead land.

For example, Eliot's poem pretty much assumes that its readers are going to either know who Simeon was or be willing to find out. It also assumes that its reader will be somewhat experienced in reading poetry and/or is willing to work to gain such experience. He assumes that they will either know or investigate the allusions here. This goes beyond the 'knowledge' issues in claim 1. For example, why are the hyacinths 'Roman'? Why is that important?

Elliot assumes that the reader will read slowly and pay attention to the images: he juxtaposes dust and memory, relates old age to winter, compares waiting for death with a feather on the back of the hand, etc. He assumes that the reader will recognize this as poetry; in a way, he's assuming that the reader is familiar with a whole poetic tradition. The reader is supposed to notice that alternate lines rhyme, but that the others do not, and so on.

Most of all, he assumes that the reader will read not only with the mind, but also with the emotions and the imagination, allowing the images to summon up this old man, tired of life but hanging on, waiting expectantly for some crucial event, for something to happen.

Most math books are written with assumptions about the audience: that they know certain things, that they have a certain level of 'mathematical maturity', etc. Before you start to read, make sure you know what the author expects you to know"