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 - Philosophy
De Morgan, Augustus, 1806-1871 De Morgan, Augustus, 1806-1871
English
Ever feel like math is a secret language you're not meant to understand? Augustus De Morgan, a 19th-century math professor, felt your pain and decided to do something about it. This book isn't a math textbook. It's a friendly, often funny, guide written by someone who genuinely wanted to clear up the confusion. He tackles the exact points where students get stuck—why negative times negative is positive, the weirdness of infinity, the logic behind algebra—and explains them in plain language. It’s like having a patient, brilliant grandpa sit you down and finally tell you how the magic trick works. If you've ever been curious about the 'why' behind the numbers, this is your backstage pass.
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The second and third autographs have William written above Shakspere. Who but an illiterate person would sign his name thus? In the last two signatures (being told perhaps that his name ought to be written on one line) he puts William before Shakspere; but the fourth William reads Willin. See now how differently each letter is formed in the name Shakspere, beginning with the initial: Did anybody ever write the first letter of his name so differently? After four attempts to form a capital S he succeeds tolerably well the fifth time. The second S, though of singular shape, appears to have been a customary one as early as 1598. (See examples of that year below.) Shakspere’s first attempt to form the crooked letter is a failure, but the second passably good. So again in 1616, when he has a different form to copy, his first attempt is futile, the second is passable, and the third quite successful. But in attempting the next letter he makes it worse every time: With the letter a he is more successful, making it legible three times out of five: [5] But the attempt to form a k is a signal failure: With the long s he succeeds best the first time, and worst the second and third: The letter p is legible the first time, but grows worse and worse to the last: It seems as if in the first attempt to sign his name in 1613 he thought it was complete when he made it end with sp e; but being reminded that it lacked a letter or two he undertook to add one by putting an a over the e thus: The next time, which was probably the same day,(1) he seems to have written his name Shaksper, though the terminal letters are uncertain: The third time he gets it more like Shakspoze: The deed to Shakspere and two other trustees is dated March 10 and signed Henry Walker. The mortgage from Shakspere and the other trustees is dated March 11. But for some unaccountable reason a duplicate verbatim copy of the deed from Henry Walker is signed by William Shakspere. This duplicate is in the Library of the city of London; the mortgage is in the British Museum. The duplicate deed we suspect was signed after the mortgage. Hence the improvement in the autograph; it was probably Shakspere’s second attempt to write. Compare it with the third. [6] The fourth time he seems to have tried to disguise the termination with awkward flourishes, making the letters totally illegible: Finally, he omits the flourishes and comes nearer legibility, but still it is impossible to tell whether he meant to write _ear, ere, or eare_: And now let the reader mark, that notwithstanding the orthodox spelling of the name from 1593 to 1616, and indeed up to the present time, was and is Shakespeare, there is no e in the first syllable and no a in the last, although some have imagined the letter a to exist in the last part of the final autograph. We have said that these signatures are all that. Shakspere is known to have written; we ought to add that he prefixed to the last one the following scrawl: For a long time we puzzled over this. Could it be an attempt to write “25th of March,” the day of the execution of the will? At last we read the following in Hallowell-Phillipps’s Shakspere: “It may be observed that the words By me, which, the autograph excepted, are the only ones in the poet’s handwriting known to...

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Forget dry equations and endless drills. On the Study and Difficulties of Mathematics is a different beast. Written in 1831, it’s a series of essays where De Morgan, a renowned teacher, directly addresses the common hurdles students face. He doesn't just present rules; he walks you through the mental stumbling blocks, the confusing concepts, and the historical reasons why math is taught the way it is.

The Story

There's no plot in the traditional sense. Instead, think of it as a guided tour through the tricky parts of arithmetic, algebra, and the beginnings of calculus. De Morgan acts as your tour guide, pointing out the potholes (like the concept of 'nothing' in arithmetic) and explaining why the road was built that way. He discusses the proper use of symbols, the meaning of negative numbers, and the foundations of mathematical reasoning. The 'story' is the reader's own journey from confusion to clarity.

Why You Should Read It

What's amazing is how modern it feels. De Morgan had a gift for spotting the exact moment a student's eyes glaze over. His explanations are logical, patient, and surprisingly conversational. You get the sense of a great teacher who is frustrated with bad teaching. Reading it demystifies math. It shows that the difficulties aren't your fault—they're built into the subject, and smart people have been working to smooth them out for centuries. It builds confidence.

Final Verdict

This book is perfect for a curious adult who wants a second chance with math, a student feeling lost in their current class, or anyone who enjoys seeing how a great mind explains complex ideas. It’s not a quick reference or a problem solver; it’s a philosophy of understanding. If you want to think about math differently, give De Morgan a few hours of your time. You'll come away feeling like you're in on the secret.



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