Comments on: Lies My Abstract Algebra Teacher Told Me http://www.arsmathematica.net/archives/2005/06/16/lies-my-abstract-algebra-teacher-told-me/ Dedicated to the mathematical arts. Fri, 05 Dec 2008 13:34:48 +0000 http://wordpress.org/?v=2.5.1 By: Walt http://www.arsmathematica.net/archives/2005/06/16/lies-my-abstract-algebra-teacher-told-me/#comment-36 Walt Mon, 20 Jun 2005 22:23:06 +0000 http://www.arsmathematica.net/?p=60#comment-36 That theory fits the first one, but not the other two. I think I succumbed to a more general temptation: to assume that the examples you haven't seen are like the ones you have. That theory fits the first one, but not the other two. I think I succumbed to a more general temptation: to assume that the examples you haven’t seen are like the ones you have.

]]> By: Marc Hamann http://www.arsmathematica.net/archives/2005/06/16/lies-my-abstract-algebra-teacher-told-me/#comment-34 Marc Hamann Fri, 17 Jun 2005 13:34:59 +0000 http://www.arsmathematica.net/?p=60#comment-34 I wonder if you aren't describing a more general phenomenon in mathematical education: the tyranny of numbers. Our pre-university education teaches us that mathematics is about numbers, and as we go on to learn about more abstract math, we cling to the notion that the abstractions are abstractions of numbers. So what we tend to remember is properties of algebra that make for useful tricks with numbers. Once we break free of this tyrrany of numbers, we start to study algebraic abstractions as interesting constructions in their own right, and lo and behold, sometimes they don't act very much like numbers, or have properties that are fascinating on their own, but are not very interesting when translated into plain old numbers. But that's when we start to really "do math'. ;-) I wonder if you aren’t describing a more general phenomenon in mathematical education: the tyranny of numbers.

Our pre-university education teaches us that mathematics is about numbers, and as we go on to learn about more abstract math, we cling to the notion that the abstractions are abstractions of numbers.

So what we tend to remember is properties of algebra that make for useful tricks with numbers.

Once we break free of this tyrrany of numbers, we start to study algebraic abstractions as interesting constructions in their own right, and lo and behold, sometimes they don’t act very much like numbers, or have properties that are fascinating on their own, but are not very interesting when translated into plain old numbers.

But that’s when we start to really “do math’. ;-)

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