# Seeking Comprehensive References on the History of Scientific Notation

I am on a quest to uncover the rich tapestry of history surrounding scientific notation as a way of expressing numbers. Specifically, I'm interested in scholarly books, peer-reviewed articles, and historical documents that delve into:

• The scientific context and historical era during which scientific notation was first conceptualized and utilized.
• The key scientists and mathematicians who played pivotal roles in the development and refinement of scientific notation.
• The reasons for the widespread adoption and enduring popularity of scientific notation in the scientific community. My research so far, including a review of the available Wikipedia content, has not yielded the depth of information I require. I would greatly appreciate any leads on academic or historical sources that provide a thorough analysis of these points.
• You may want to clarify what you mean by "scientific notation". Nov 20 at 14:44

First (mathematical) use of the term cited by the OED: F.L. Griffin, An experiment in correlating freshman mathematics, MAA Monthly (1915), p. 328. Griffin later published a book, Introduction to Mathematical Analysis (1921), pp. 190f. His purpose in his article and book is the improvement of teaching. He also states that the notation is "common in scientific work" (1915), which seems the basis for calling it "scientific notation." One advantage: "This avoids operations with long rows of zeros or decimal places." (1921) He also argues that familiarity with the notation will aid the student's learning and appreciation of logarithms.

The broader notion that a scientific notation might allow the reduction of solving problems to symbolic operations, such as Vieta's algebra notation did for solving problems in numbers (see @Katz's answer), grew in the 19th century. By the late 19th century and on into the 20th, you find people arguing for and proposing scientific notations for phonetics, music, color, and the scientific teaching of English. At least one of these projects led to something still in use, namely the IPA.

The OP may be the first person interested in a comprehensive history of scientific notation. As a representation of numbers, I do not know of a work that examines the use of the notation "so common in scientific work" prior to 1915, according to Griffin. I know a random instance or two. Airy's Numerical Lunar Theory (1886) has some tables in which the entries are integers to be multiplied by a "unit" at the head of the column that is a power of ten. This is not the present-day convention for scientific notation, but it is similar. As far as the history after Griffin, I suspect scientific notation evolved due to the need for convenient forms of input/output for computers. I realize the OP is not looking to start research into the question, but assuming the basic research has not been done, I offer these "waypoints" in the hope they are helpful.

• In the context of the provided text, OED refers to ordinary exponential notation or standard form, which is a way of writing very large or very small numbers in a more compact and concise form. This notation is commonly used in scientific and engineering fields to represent numerical values that would be difficult or impractical to express in standard decimal form. Nov 19 at 19:20
• @HumbertoJoséBortolossi That is correct. Nov 19 at 19:29

Vieta (Viète) is the original creator of algebraic notation. Fermat in particular benefited from Vieta's innovations and always adhered to his formalism. Descartes developed a system of notation closer to what we use today. You may want to consult the helpful recent book

Mazur, Joseph. Enlightening symbols. A short history of mathematical notation and its hidden powers. Princeton University Press, Princeton, NJ, 2014. xxiv+285 pp. ISBN: 978-0-691-15463-3

• I think OP is asking about notation like $5E3=5\times10^3$. Did you realize that? Nov 19 at 15:42
• @J.W.Tanner, No, not at all. I did wonder why the question seems so broad. Nov 20 at 11:22
• If it is any consolation @MikhailKatz I had no idea either that the OP meant that. Nov 20 at 14:40
• Those with this confusion should approve the current edit of the question that clarifies it. Nov 23 at 10:23
• @mdewey, ehat does OP mean? me? Nov 24 at 11:34