A History of Mathematical Notations (Dover Books on Mathematics) by Florian Cajori (PDF)

Description

This classic study notes the first appearance of a mathematical symbol and its origin, the competition it encountered, its spread among writers in different countries, its rise to popularity, its eventual decline or ultimate survival. The author’s coverage of obsolete notations — and what we can learn from them — is as comprehensive as those which have survived and still enjoy favor. Originally published in 1929 in a two-volume edition, this monumental work is presented here in one volume.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a true gold-mine of information on origins of mathematical notations. Whenever I want to innovate in notations, I want to know how and why the traditional notation was chosen. This book tells me that. Then I can think about whether my new notation fits its purpose better than the old one.In my opinion, the importance of notations is very much underestimated. Anyone who has spent a lot of time reading old mathematics literature, going back hundreds of years or more, knows that the principal difficulty with reading old texts is the lack of good notation to express the ideas. Even books written 50 years ago are often painfully difficult to read because of their ill-chosen notations. Some subjects have surged forward when notations have improved, while others have languished due to the difficulty of expressing ideas in poor notations. When you upgrade old notations to new requirements, I think it’s important to understand their history first.Another way to think of the importance of notations is that they give meaning to symbols in the same way definitions give meaning to words and phrases. But definitions serve to highlight the concepts which are most important in a mathematical topic. We define concepts because they are of enduring importance. And notations likewise highlight the most important concepts. But since a mathematical formula is a kind of picture, it is interpreted more by pictorial perception than linguistic perception. In other words, formulas are more like diagrams than text. We take (or should take) a great interest in the history of concepts. So we should also take a great interest in the history of notations!The only drawback of this book is the page numbering because it is “two volumes in one”. The index for volume I is on pages 433-451 of Volume 1, in the middle of the book! So you really have to keep a permanent book-mark there for index look-up. Many times I have looked up things in the Volume 2 index at the back of the book, forgetting about the separate Volume 1 index.As far as I know, this is the only encyclopedic history of mathematical notations. Many books do give a few snippets of history about notations here and there. But this book is quite comprehensive and authoritative, up until the early 20th century anyway.

⭐I love math and like history. What could be better than a history of math book? Not this book. Remember that professor that you had in college with the monotone voice that drones on forever and ever? He must have written this book. I’m sure it has fantastic insight, but I can’t stay awake long enough to find it.

⭐A thorough review of mathematical notations, I know of no other tome that covers this material in the depth that this book uses. However, there are three improvements that come readily to mind.1) This book is stodgy, written in a high scholarly style of the late 1920’s. This is not surprising since it _was_ written as a scholarly book in the late 1920’s. Still, one could hope for a more accessible reading style. 2) The book is dated, written in the late 1920’s. Again, not surprising, but one could hope for a supplement that would cover the mostly minor changes in notation that have occurred since then. 3) The book arranges the material only by the area of mathematics used. When a given symbol has been used in another sense, the book often but not always covers the other uses of the symbol in question. It would be nice if coverage by symbol were consistently available for _all_ symbols.In summary, a good book if you need the information, but one I would not recommend for casual reading in the area of mathematics.

⭐This book is very interesting and it was just what I was looking for. (I was working on a project over the history of algebraic expressions) The book contains images that come from primary sources and it is well written.

⭐Mathematical notation is important, because it allows for precision, I begin with this because I received the book today, and have not begun to read it, but…..but….the table of contents and index in this edition are completely useless. By page 16 the entries in the ToC don’t match, and since this edition is 2 volumes bound as one, the index lists entries by page # as if it were one volume, but volume 2, which begins after pg 451, begins again at page 1. Precision people, precision. These facts may not influence my enjoyment of the text if i read it linearly, but unless I create my own index, it’s useless as a reference book.

⭐A good reference on specific issues; I would not recommend that it be read cover-to-cover unless you’re a complete nerd.

⭐This book is so awesome. Nobody ever thinks about the history of mathematical notation!

⭐Recommend for anyone with an interest in mathematics. I have found a deeper appreciation for the methods of communicating mathematical ideas and thoughts. The ability to progress deeper into mathematics, and discover new, more powerful ways to do mathematics can be limited by the notation one uses. One realizes that math is a language that is evolving, which in turn can allow greater ease of expression.

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