On the study and difficulties of mathematics by Augustus De Morgan

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By Charlotte Girard Posted on Nov 15, 2025
In Category - Adventure
De Morgan, Augustus, 1806-1871 De Morgan, Augustus, 1806-1871
English
Ever wondered why math feels like a secret language only some people speak? Augustus De Morgan wrote this book in 1831 to answer that exact question. It's not a math textbook—it's a backstage pass to how mathematicians think. He takes the ideas that trip people up (like why negative times negative equals positive) and explains the 'why' behind the rules. It's like having a patient, brilliant friend walk you through the tricky parts of arithmetic and algebra, showing you the logic instead of just handing you formulas. If you've ever been frustrated by math, this book feels like someone finally explaining the joke.
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SHAKESPEARE, WITH INTRODUCTORY MATTER ON POETRY, THE DRAMA, AND THE STAGE. Definition Of Poetry. Poetry is not the proper antithesis to prose, but to science. Poetry is opposed to science, and prose to metre. The proper and immediate object of science is the acquirement, or communication, of truth; the proper and immediate object of poetry is the communication of immediate pleasure. This definition is useful; but as it would include novels and other works of fiction, which yet we do not call poems, there must be some additional character by which poetry is not only divided from opposites, but likewise distinguished from disparate, though similar, modes of composition. Now how is this to be effected? In animated prose, the beauties of nature, and the passions and accidents of human nature, are often expressed in that natural language which the contemplation of them would suggest to a pure and benevolent mind; yet still neither we nor the writers call such a work a poem, though no work could deserve that name which did not include all this, together with something else. What is this? It is that pleasurable emotion, that peculiar state and degree of excitement, which arises in the poet himself in the act of composition;—and in order to understand this, we must combine a more than ordinary sympathy with the objects, emotions, or incidents contemplated by the poet, consequent on a more than common sensibility, with a more than ordinary activity of the mind in respect of the fancy and the imagination. Hence is produced a more vivid reflection of the truths of nature and of the human heart, united with a constant activity modifying and correcting these truths by that sort of pleasurable emotion, which the exertion of all our faculties gives in a certain degree; but which can only be felt in perfection under the full play of those powers of mind, which are spontaneous rather than voluntary, and in which the effort required bears no proportion to the activity enjoyed. This is the state which permits the production of a highly pleasurable whole, of which each part shall also communicate for itself a distinct and conscious pleasure; and hence arises the definition, which I trust is now intelligible, that poetry, or rather a poem, is a species of composition, opposed to science, as having intellectual pleasure for its object, and as attaining its end by the use of language natural to us in a state of excitement,—but distinguished from other species of composition, not excluded by the former criterion, by permitting a pleasure from the whole consistent with a consciousness of pleasure from the component parts;—and the perfection of which is, to communicate from each part the greatest immediate pleasure compatible with the largest sum of pleasure on the whole. This, of course, will vary with the different modes of poetry;—and that splendour of particular lines, which would be worthy of admiration in an impassioned elegy, or a short indignant satire, would be a blemish and proof of vile taste in a tragedy or an epic poem. It is remarkable, by the way, that Milton in three incidental words has implied all which for the purposes of more distinct apprehension, which at first must be slow-paced in order to be distinct, I have endeavoured to develope in a precise and strictly adequate definition. Speaking of poetry, he says, as in a parenthesis, “which is simple, sensuous, passionate.” How awful is the power of words!—fearful often in their consequences when merely felt, not understood; but most awful when both felt and understood!—Had these three words only been...

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Forget everything you think you know about old math books. On the Study and Difficulties of Mathematics isn't a dry collection of problems. It's a conversation. Augustus De Morgan, a famous 19th-century mathematician, noticed that students often memorized rules without understanding them. So, he sat down and wrote this guide to the logic behind the numbers.

The Story

There isn't a plot in the traditional sense. Instead, the 'story' is the journey of understanding. De Morgan starts with the very basics of arithmetic and builds up to algebra. He focuses entirely on the points where learners typically get stuck. Why do we use the rules of signs? What does dividing by a fraction actually mean? He breaks down these mental blocks step-by-step, using clear language and everyday examples to build a solid foundation of sense, not just memorization.

Why You Should Read It

This book is a revelation for anyone who thinks they're 'bad at math.' De Morgan argues that the difficulty isn't in you, but in how the subject is often taught. Reading it feels incredibly validating. He treats the reader's confusion with respect and dismantles it with brilliant clarity. You finish a chapter not just knowing a rule, but believing it, because you've seen the reasoning laid bare. It builds confidence from the ground up.

Final Verdict

Perfect for curious adults, parents helping kids with homework, or students who want to truly grasp the 'why' behind their math classes. It's also a fascinating historical look at education. While some examples use old British currency, the core ideas are timeless. If you want to make peace with mathematics and finally see the logic in its language, this 19th-century teacher is still one of the best guides you can find.



🔖 Public Domain Notice

The copyright for this book has expired, making it public property. It is available for public use and education.

Lucas Johnson
10 months ago

Great read!

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4 out of 5 (1 User reviews )

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