The Theory of Numbers by R. D. Carmichael

(5 User reviews)   2449
Carmichael, R. D. (Robert Daniel), 1879-1967 Carmichael, R. D. (Robert Daniel), 1879-1967
English
Hey, have you ever looked at a clock, a calendar, or even a sunflower and wondered if there was a hidden pattern? That's the world of number theory, and Carmichael's classic book is your guide. It's not about dry calculations—it's about uncovering the surprising rules that govern the most basic building blocks of our universe. Think of it as detective work for your brain, where the clues are prime numbers, divisibility, and ancient puzzles. If you've ever been curious about why math feels so elegant and mysterious, this is where that feeling comes from.
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affected, nevertheless, an high Contempt for this,—their Native. I listened with silent Indignation, and determined to contribute my Mite towards giving such unattentive, uninformed Youths, a more adequate Idea of this Kingdom, under its ancient and under its present happy Establishment. The common Accidents of Time must lead them by better Authority to clearer Knowledge: In the mean while, I profess my Obligations to them, as they have given me this Opportunity of declaring my Regard to my Country in general, and the particular Attachments that ever bind me, in the strictest Sense of Fidelity and Esteem, to a Friend so worthy as You have been to, Sir, Your very obliged, and Most obedient Servant. ESSAY. In a Nation, where almost every Gentleman is better acquainted, and more conversant, with the Nature and Circumstances of other Countries than those of his own, the Publication of such Hints as may somewhat contribute to remove so odd an Inattention, and induce those far better qualified to render a Subject so interesting some Justice, will not, I hope, be deemed an Impertinence; in one especially who, by this Essay, however feeble, hath nothing beside the Honour and Advantage of _Ireland_ in View, a Kingdom whereof he is, without Vanity, proud of being a Native. As the Story of Savages and Barbarians can contain nothing instructive, or entertaining, the _Antemilesian_ Inhabitants of this Land having been mostly such, and all surviving Accounts of them almost totally overcast with Fable, we are therefore, in treating of the antient _Scotia_, or modern _Ireland_, to refer principally to three distinguished æras, whereof the _first_ is, its being peopled by an _Iberian_ or _Spanish_ Colony: The _second_, truly glorious, the Arrival of St. _Patrick_, in his most salutary Mission: The _third_ and last, its Cession to _Henry_ the Second, King of _England_, (the first of the Royal Race of _Plantagenet_) partly from a pretended Title of _Adrian_ the Fourth, Pope of _Rome_; partly from the restless and insatiable Desires of _Henry_; _more_ from the manifold Infirmities of the then reigning _Irish_ Chiefs—but above all, from the peculiarly adverse Fate of _Roderick_, the last of our Kings. The assiduous, exact, and candid Author of the _Dissertations_,(1) lately published, on the Origin, Government, Letters, Sciences, Religion, Manners and Customs of the antient Inhabitants of this Country, hath put all those Matters in so clear and happy, and, at the same Time, in so strong a Light, by the Powers of various foreign Testimonies, of undeniable Authenticity, coincident with our own, that scarce any Thing new can be offered on the same Subject. It may, however, in general be observed, that _Milesius_, a _Spanish_ Prince, so far back as the Reign of _Solomon_ (instigated by Necessity, or induced by Ambition) with a considerable Number of Associates and Followers, landed from the Western Parts of _Spain_, on the Southern Coasts of this Island, where it is probable they met little, or but faint Opposition, from wild and undisciplined Inhabitants. Those People, from their early Knowledge of the _Phœnician_ Arts and Letters, imported such Rudiments of Government and Learning, as those primitive Times admitted; a Truth visible from the Similarity or rather Identity of the _Phœnician_ and _Scotic_ Alphabet. This antient Colony quietly settled here, remote from the Storms and Revolutions of the greater World, and secured by Situation from its hostile Incursions, there is no Doubt but the Cultivation of Religion, Philosophy, Politicks, Poetry, and Musick, became the chief Objects of popular Study and Application: The Spirit of Ambition in succeeding Ages, with its unhappy concomitant Train of Sedition, Faction, and Violence,...

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Let's be clear: this isn't a novel with a plot. The Theory of Numbers is an exploration. It systematically introduces you to the fundamental ideas of number theory—the study of integers and their properties. You start with the basics like divisibility and prime numbers. Then, Carmichael walks you through concepts like congruences (a fancy way of talking about remainders), Diophantine equations (finding whole-number solutions), and quadratic residues. It builds a framework for understanding how numbers behave, piece by logical piece.

Why You Should Read It

I'll be honest, this is an older book, and the writing is formal by today's standards. But there's a magic in its clarity and directness. Carmichael doesn't waste words. He shows you the beautiful, logical structure behind numbers. Reading it feels like being let in on a secret language that describes the world. It’s satisfying to follow his reasoning and suddenly 'get' a concept that has puzzled people for centuries. It makes you feel smarter, in the best possible way.

Final Verdict

This book is perfect for a specific reader: the curious amateur, the student looking for a clear foundational text, or anyone who enjoys logic puzzles and wants to understand the 'why' behind the math. It's not a light read, but it's a rewarding one. If you have some basic algebra under your belt and a patient mind ready for a challenge, Carmichael's classic will open a door to a fascinating intellectual world.



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William Torres
1 year ago

From the very first page, the flow of the text seems very fluid. Definitely a 5-star read.

Ashley Lee
6 months ago

I came across this while browsing and the clarity of the writing makes this accessible. I couldn't put it down.

Linda Young
10 months ago

Helped me clear up some confusion on the topic.

Michael Walker
1 year ago

Helped me clear up some confusion on the topic.

Jessica Walker
1 month ago

Without a doubt, the narrative structure is incredibly compelling. A true masterpiece.

5
5 out of 5 (5 User reviews )

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