Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.
Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.
A rich and fascinating account of one of music history's most ancient, varied, and distinctive instruments From its origins in animal horn instruments in classical antiquity to the emergence of the modern horn in the seventeenth century, the horn appears wherever and whenever humans have made music. Its haunting, timeless presence endures in jazz and film music, as well as orchestral settings, to this day. In this welcome addition to the Yale Musical Instrument Series, Renato Meucci and Gabriele Rocchetti trace the origins of the modern horn in all its variety. From its emergence in Turin and its development of political and diplomatic functions across European courts, to the revolutionary invention of valves, the horn has presented in innumerable guises and forms. Aided by musical examples and newly discovered sources, Meucci and Rocchetti's book offers a comprehensive account of an instrument whose history is as complex and fascinating as its music.
Cats have very distinctive personalities, and every new kitten deserves a name to match its looks and character. Prince might be the perfect name for a pussycat of regal appearanceï¿1/2though Yogi would be a better fit for a comical cat who always gets into mischief. Those two plus 998 additional names fill this entertaining and informative little book, written to inspire soon-to-be cat owners. Theyï¿1/2ll find names to match not only their kittenï¿1/2s personality, but also to reflect their own tastes and interests, all names presented in alphabetical order. And while trying to decide on that perfect feline nameï¿1/2whether it be Pinocchio or Picasso, Hercules or Hamletï¿1/2cat owners can delight over the dozens of enchanting, comical, and endearing color photos of kittens at rest and at play.
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