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More math illiteracy August 20, 2009

Posted by lumixedia in General, math education, number theory.
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Just for fun, here’s a rather pointless anecdote.

My third-grade teacher decided to have a fun, hands-on activity to teach our class about primes. Now I have a low opinion of all fun, hands-on activities (give me a good, proper whiteboard lecture any day, and if you’re incapable of doing so you should really just work on improving your teaching skills before making me pay attention to you, and yes, this was my opinion even when I was very, very young) but that’s not the point of this post. (more…)

Another math illiteracy moment August 15, 2009

Posted by lumixedia in General, history of mathematics, math education, number theory.
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I was recently informed that the Goldbach conjecture is popularly known in China as the “1+1=2” conjecture. As in, “every positive even number can be written as the sum of two primes. For example, 1+1=2.” [Edit–I was told this by a Chinese person who might nevertheless not be representative of how this nickname is understood–see comments.]

When I mentioned that this nickname is not in fact accurate, the person who so informed me got rather annoyed with my pointless pedantry. Why shouldn’t 1 be prime? Why not define a “prime” to be a positive integer with at most two distinct divisors, rather than a positive integer with exactly two distinct divisors? Clearly the “1+1=2” conjecture sounds way cooler than the “2+2=4” conjecture to a layman, and we are talking about popular mathematics here, so why not?

Okay, I guess it might not be immediately obvious why current notation is preferable. Maybe. From a certain perspective. It is also admittedly true, according to Wikipedia, that 1 was indeed widely considered to be prime by mathematicians up to a few hundred years ago. Fine. So let’s temporarily redefine “prime” to mean a positive integer with at most two distinct divisors, and see if it’s acceptable today. (more…)

A random math illiteracy moment August 9, 2009

Posted by lumixedia in combinatorics, General.
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I can’t figure out how, but this memory from policy debate camp a couple years back just floated into my head and this seems like the appropriate place to recount it.

This was back when the topic for the upcoming year was Resolved: The United States federal government should substantially increase its public health assistance to Sub-Saharan Africa. For readers not familiar with policy debate, policy teams generally come up with a single plan which falls under the scope of the resolution and research it in great depth throughout the year. A plan for this resolution might look something like “The United States federal government should substantially increase funding for treatment of AIDS in Zimbabwe”. In each round, the affirmative team presents their plan and the negative team attacks it.

Besides directly arguing that the plan is a bad idea, the negative team can also argue that the plan doesn’t actually fit the resolution by some interpretation of the resolution. This is known as a topicality argument and might go something like “Your plan to treat AIDS in Zimbabwe is non-topical because the resolution implies that the increased public health assistance should go to all of Africa, not just a small subset such as a single country”. This particular example is the subsets topicality argument. (more…)