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Archive for March 22nd, 2009

Giving credit

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V. I. Arnold, On teaching mathematics:

What is a group? Algebraists teach that this is supposedly a set with two operations that satisfy a load of easily-forgettable axioms. This definition provokes a natural protest: why would any sensible person need such pairs of operations? […]

What is a smooth manifold? In a recent American book I read that PoincarĂ© was not acquainted with this (introduced by himself) notion and that the “modern” definition was only given by Veblen in the late 1920s: a manifold is a topological space which satisfies a long series of axioms.

For what sins must students try and find their way through all these twists and turns? Actually, in PoincarĂ©’s Analysis Situs there is an absolutely clear definition of a smooth manifold which is much more useful than the “abstract” one.

(Interesting talk, do read.)

Meanwhile…

Bill Poser at the Language Log:

Sir William Jones is incorrectly viewed as the discoverer of the Indo-European language family and founder of modern historical linguistics […]

The second and more important point is that Jones cannot be considered the founder of modern historical linguistics because he did not use the comparative method, the crucial innovation that distinguishes modern historical linguistics from its predecessors.

Sigh. Let’s not forget people who actually caused us to perceive the world differently, and leave it to pedantic types to define who invented what.


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Written by S

Sun, 2009-03-22 at 23:05:50