The Theory of Numbers by R. D. Carmichael

(4 User reviews)   2886
By Charlotte Girard Posted on Nov 15, 2025
In Category - Philosophy
Carmichael, R. D. (Robert Daniel), 1879-1967 Carmichael, R. D. (Robert Daniel), 1879-1967
English
Ever wonder what makes numbers tick? I just finished 'The Theory of Numbers' by R.D. Carmichael, and it's not your average math book. Forget dry equations—this is a guided tour through the hidden patterns and secrets of whole numbers. Carmichael writes with a teacher's clarity, showing how questions about prime numbers, divisibility, and ancient puzzles are actually thrilling intellectual adventures. It's like he's handing you a key to a locked room full of fascinating problems. If you've ever been curious about the 'why' behind the math you learned in school, this classic is your perfect starting point. It’s surprisingly approachable and utterly absorbing.
Share

Read "The Theory of Numbers by R. D. Carmichael" Online

This book is available in the public domain. Start reading the digital edition below.

START READING FULL BOOK
Instant Access    Mobile Friendly

Book Preview

A short preview of the book’s content is shown below to give you an idea of its style and themes.

Including a Vindication of the Traditional Reading of 1 Timothy III. 16. By John William Burgon, B.D. Dean of Chichester. “Little children,—Keep yourselves from idols.”—1 John v. 21. Dover Publications, Inc. New York 1971 CONTENTS Dedication. Preface. Article I. The New Greek Text. Article II. The New English Version. Article III. Westcott And Hort’s New Textual Theory. Letter To Bishop Ellicott, In Reply To His Pamphlet. Appendix Of Sacred Codices. Index I, of Texts of Scripture,—quoted, discussed, or only referred to in this volume. Index II, of Fathers. Index III, Persons, Places, and Subjects. Footnotes [Transcriber’s Note: This book contains much Greek text, which will not be well-rendered in plain text versions of this E-book. Also, there is much use of Greek characters with a vertical bar across the tops of the letters to indicate abbreviations; because the coding system used in this e-book does not have such an “overline”, they are rendered here with underlines. It also contains some text in Syriac, which is written right-to-left; for the sake of different transcription methods, it is transcribed here in both right-to-left and left-to-rights, so that regardless of the medium of this E-book, one or the other should be readable.] The following is PREBENDARY SCRIVENER’S recently published estimate of the System on which DRS. WESTCOTT AND HORT have constructed their “_Revised Greek Text of the New Testament_” (1881).—That System, the Chairman of the Revising Body (BISHOP ELLICOTT) has entirely adopted (see below, pp. 391 to 397), and made the basis of his Defence of THE REVISERS and their “_New Greek Text._” (1.) “There is little hope for the stability of their imposing structure, if _its foundations have been laid on the sandy ground of ingenious conjecture_. And, since barely the smallest vestige of historical evidence has ever been alleged in support of the views of these accomplished Editors, their teaching must either be received as intuitively true, or _dismissed from our consideration as precarious and even visionary_.” (2.) “DR. HORT’S System _is entirely destitute of historical foundation_.” (3.) “We are compelled to repeat as emphatically as ever our strong conviction that the Hypothesis to whose proof he has devoted so many laborious years, _is destitute not only of historical foundation, but of all probability, resulting from the internal goodness of the Text which its adoption would force upon us_.” (4.) “ ‘We cannot doubt’ (says DR. HORT) ‘that S. Luke xxiii. 34 comes from an extraneous source.’ [_Notes_, p. 68.]—_Nor can we, on our part, doubt_,” (rejoins DR. SCRIVENER,) “_that the System which entails such consequences is hopelessly self-condemned_.” SCRIVENER’S “Plain Introduction,” &c. [ed. 1883]: pp. 531, 537, 542, 604. DEDICATION. To The Right Hon. Viscount Cranbrook, G.C.S.I., &c., &c., &c. MY DEAR LORD CRANBROOK, _Allow me the gratification of dedicating the present Volume to yourself; but for whom—(I reserve the explanation for another day)—it would never have been written._ _This is not, (as you will perceive at a glance,) the Treatise which a few years ago I told you I had in hand; and which, but for the present hindrance, might by this time have been completed. It has however_ grown out _of that other work in the manner explained at the beginning of my Preface. Moreover it contains not a few specimens of the argumentation of which the work in question, when at last it sees the light, will be discovered to be full._ _My one object has been to defeat the mischievous attempt which was made in 1881 to thrust upon this Church and Realm a Revision of the Sacred Text, which—recommended though it be by eminent names—I...

This is a limited preview. Download the book to read the full content.

R.D. Carmichael's The Theory of Numbers isn't a novel with a plot, but it absolutely has a story to tell. It's the story of integers—the whole numbers 1, 2, 3, and so on. The book walks you through their fundamental properties, exploring concepts like prime numbers, divisibility rules, and congruences (a clever way of looking at remainders). Think of it as learning the grammar of the number universe. Carmichael builds from simple ideas to more complex ones, tackling famous puzzles and theorems along the way. You'll see how mathematicians ask questions about these basic building blocks and slowly uncover the elegant, sometimes mysterious, rules that govern them.

Why You Should Read It

This book changed how I see numbers. Carmichael doesn't just state facts; he shows you the thought process. You feel like you're solving puzzles alongside him. The clarity is remarkable—he makes abstract ideas feel concrete and manageable. It’s not about rote calculation; it’s about understanding the 'why' behind the patterns. Reading it gives you a real sense of discovery, like you're peeking behind the curtain of mathematics. It’s intellectually satisfying in a way that few books are.

Final Verdict

Perfect for curious readers, hobbyist mathematicians, or anyone who enjoyed math but wants to see its more playful, conceptual side. It's also a fantastic resource for students looking for a clear, foundational text. If you like logic puzzles, brain teasers, or just understanding how things work, you'll find a lot to love here. It’s a classic for a reason: it makes a beautiful subject genuinely accessible.



ℹ️ License Information

This book is widely considered to be in the public domain. You do not need permission to reproduce this work.

Joseph Wright
10 months ago

This is one of those stories where it manages to explain difficult concepts in plain English. Absolutely essential reading.

Elizabeth Rodriguez
5 months ago

Perfect.

Aiden Jackson
1 year ago

The fonts used are very comfortable for long reading sessions.

Carol Brown
3 months ago

High quality edition, very readable.

4
4 out of 5 (4 User reviews )

Add a Review

Your Rating *
There are no comments for this eBook.
You must log in to post a comment.
Log in


Related eBooks