Let there be no mistake about it. Many of the pictures that now routinely appear in print are no more than pictorial aids to reasoning, graphical sketches intended to suggest or persuade rather than convince.
This is a far cry from the prevailing orthodoxy of only a few decades ago. It has always been a widespread practice, enjoyed by most working mathematicians in the privacy of the study, to use pictorial images of one kind or another to aid in understanding and to prompt discovery. The very same pictures rarely appeared in the final polished manuscript. The canons of scientific writing required formal exposition, often obscuring what was, upon a time, simple and clear. Indeed, although pictorial reasoning in mathematics may have prevailed up to the middle of the 19th century, it fell from favor by the beginning of the 20th century, when lessons then learned showed that pictures might ...
