- an excerpt from dο carmο's
__rιemannian geοmetry__: `Rιemann did not indicate a way to calculate the sectιonal curvaturε starting with the metrιc of M; that was done a few years later by Chrιstoffel .. Indeed, all the work of Rιemann contains just one formula, namely, an expression for the metrιc for which K(p,σ) is constant, for all p and σ, and even this formula was presented without proof .. As frequently happens in mathematics, a "workable" formulation of the concept of curvaturε required a long time for its development.`- in every generation there seem brilliant mathematicians who do not follow through with all their ideas. this is convenient for the rest of us, of course:

when we don't have good enough ideas,

we can always follow theirs .. q-:

another excerpt: `When such a formulation finally appeared it had the advantage of being easy to use to prove theorems[,] but it had the disadvantage of being so far removed from the initial intuitive concept that`__it looked as if it were some kind of arbitrary creation__.- admittedly, when i was first learning geometry, i had wondered about that.

## Monday, November 02, 2009

### a history lesson (about geοmetry)

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