In patriotic duty bound, the Cambridge of Newton adhered to Newton's fluxions, to Newton's geometry, to the very text of Newton's Principia; in my own Tripos in 1881 we were expected to know any lemma in that great work by its number alone, as if it were one of the commandments or the 100th Psalm.
.... Finally, in the earlier section of the Tripos Examinations (officially described as "qualifying for honours", commonly known as "the three days"), there was a rigid rule against the explicit use of a differential coefficient and of an integration-process: we might substitute x+h for x and subtract, dodging onwards to the satisfaction of the examiner; we might use a Newton curve, if we could devise it, to effect a quadrature; but never might we use d/dx or the ∫-sign of integration which were taboo.
A R Forsyth, Old Tripos Days at Cambridge, The Mathematical Gazette, Vol 19, No 234, July1935 (at JSTOR, unfortunately)
3 comments:
The Internet Archive has two collections of old Tripos papers. The one from 1878 has questions on Newton here—I presume these Newton questions were the only ones where the d/dx notation was forbidden as the setters use it in other sections. The one from 1919 shows that the examiners had, by then, lightened up enough to draw a few diagrams for the examinees.
Anyone who is interested in what it was like to do the old mathematical Tripos in its last days can read 'A Mathematical Education' in JE Littlewood's A Mathematician's Miscellany. (The whole book is great; I pretty much read the print off a library copy of the second edition that was issued under the title Littlewood's Miscellany). Littlewood was one of the people responsible for sweeping away the strict order of merit (Senior Wrangers and so on) on the grounds that it had all become a daft horse-race based on tricksy questions with little connection to real maths.
It was similar when I did Mathematical Olympiad Training in 1980: they gave us the impression that the use of calculus or even analytic geometry was a form of cheating.
Andrew!!!! No!!!!!!!!
Funnily enough, I had a friend who was very good at math whose schoolteachers gave him a hard time for his bad handwriting and atrocious spelling; at some point he solved a physics problem using calculus, which they were not supposed to know, and was told off.
All I can say is, I only WISH the people who notionally represent my business interests were cheating by using calculus.
Steve - I'll bet the Staatsbibliothek has a copy of Littlewood. I'll see if I can get my hands on it.
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