Monday, November 02, 2009

a history lesson (about geοmetry)

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.

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