The authors open by noting how familiar the numerals are to modern readers, yet how recent their general acceptance in European commerce actually is—only the last four centuries. They stress that the system of place value struggled for nearly a thousand years before displacing Roman notation. The preface declares no theory to exploit, aiming instead to weigh testimony and set forth reasonable conclusions from available evidence.

This editorial note focuses on the authors' choices in diction, dialogue, and description, particularly how they handle manuscript evidence, numeral forms, and the tension between scholarly caution and narrative momentum.

Preface as Methodological Statement

Smith and Karpinski use the preface to establish a restrained, evidence-based approach. They write that they have “had no theory to exploit” and have “weighed the testimony” to reach reasonable conclusions. This diction signals a deliberate departure from earlier historians who, in their view, let speculation outrun documentation. The phrasing “set forth the general problem of the origin and development” frames the work as an open inquiry rather than a closed argument. The authors also address multiple audiences—mathematician, student of civilization, teacher, business man—by noting that each may find a different kind of interest. This rhetorical move broadens the work’s appeal while maintaining scholarly tone.

Numeral Forms as Evidence of Change

The authors devote considerable space to tracing the physical shapes of numerals across manuscripts and early printed books. They observe that “fashion played a leading part until printing was invented,” which then tended to fix forms. For each digit from 1 to 8, they list variant shapes with source citations. For example, “four” is singled out as a key test for dating and localizing a manuscript: “one of the first tests as to the age of a manuscript on arithmetic, and the place where it was written, is the examination of this numeral.” They note that the Florentine manuscript of Leonard of Pisa uses a distinct form, and that early printed books generally used a closed-top “4” while the open-top writing form is “purely modern.” Such granular description shows how paleographic detail can reveal historical transmission.

Mixed Numerals and Monumental Evidence

The authors present examples of transitional usage, such as a 1470 book with pages numbered by hand using a mixture of Roman and Hindu numerals. They also discuss disputed monumental inscriptions: a gravestone at Katharein supposedly dated 1007, and one at Biebrich of 1299, but they note that only later examples—Pforzheim 1371 and Ulm 1388—are certain. The Wells Cathedral numerals assigned to the thirteenth century are “undoubtedly considerably later.” This careful sifting of epigraphic evidence illustrates the authors’ method: they do not simply report claims but assess reliability. The inclusion of a table of early manuscript forms (from the twelfth to fifteenth centuries) further grounds the discussion in visual data.

The Role of Printing in Standardization

Smith and Karpinski argue that printing fixed numeral forms that had previously varied widely. They note that even in printing, complete uniformity was not achieved: “it is often difficult for a foreigner to distinguish between the 3 and 5 of the French types.” They also remark on the use of “i” for “one” in early printed books, possibly to save types, and “z” for “two,” so that “12” appeared as “iz.” These observations tie typographical economy to the evolution of numeral shapes. The authors further compare manuscript forms with printed ones, showing that certain digits (like “six” and “eight”) changed little, while others (like “four” and “seven”) assumed their present erect forms only after the fifteenth century.

Readers interested in the material culture of mathematics will find this work a meticulous compilation of primary sources. The authors’ reluctance to overclaim—their insistence on weighing testimony rather than advancing a thesis—makes the book a reliable reference for the early history of numeral forms. Pay attention to the footnotes and tables, which contain the evidentiary backbone of the argument.