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Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a^2 - b^2 but was floored because the examiner unkindly asked for the factors of p^2 - q^2.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Introducing the History of Mathematics: An Italian Experience Using Original Documents
Pythagorean Theorem (English)
Dematte, Adriano, "Introducing the History of Mathematics: An Italian Experience Using Original Documents," Loci (August 2008), DOI: 10.4169/loci002856
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