Sunday, March 14, 2010

David S. Richeson - Euler's Gem

Read from-to: Feb 19, 2010  - Mar 14, 2010 (24 days).

Liked:'s math, what's not to like?

Didn't like: al final se pone un poco denso y pierde un poco las ayudas visuales (que es entendible, hablando de n-dimensiones no sirven de mucho, pero hay algunas que no son tan triviales de entender con la poca explicación que da).

Overall: nice book =D.

Get it here.

Notes & Quotes:
"Mathematical folklore says that he [Euler] could write mathematics papers while bouncing a baby on his knee, and that he could compose a treatise between the first and second calls to dinner" (p.16)

"Later he [Pythagoras] settled in the Greek city of Croton in what is now southern Italy" (p.37).

Italia? Interesting...
"I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted, so as to leave to others the pleasure of discovery" - Rene Descartes (quoted in p.81).

Riiiiiiiight jaja.
There is a oft-repeated quip that "objects in mathematics are named after the first person after Euler to discover them" (p.86)

Jaja THAT's fame.

La prueba de Legendre [JAJAJA la caricatura en wikipedia =P] de la fórmula de Euler, en el capítulo 10 (pp.87-99)... wow. Beautiful. Too long to transcribe though.
G. H. Hardy wrote "Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess gambit; a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game" (p.123).

"Ok, you win, it is false. But HA! That means it's true! IN YOUR FACE!"
Any knot can be obtained as the boundary of an orientable surface with one boundary component (p.185).

Mathematicians work in a store that makes and sells tools. Occasionally they take special orders from their scientific customers, but most of the day they toil away making elegant tools, the uses for which have not yet been invented. Scientists visit this tool shop and browse the shelves in hopes that one of the tools fits their needs (p.201).

Nice description.
Poincaré had a restless curiosity that kept him moving from topic to topic. He would attack a new area of mathematics, make an indelible mark, then move on the the next. A contemporary called him "a conqueror, not a colonist" (p.212).

Otra buena descripción.

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