Daily Archives: August 14, 2008

I tried to make up my own problem along the lines of this problem, but wanting it to be slightly different. 

Let . Show that exactly. 

Coming up with your own problems is so much harder than solving problems. 

(If you need help, see the solution to the problem linked above. The general method I used for solving this problem is the same method I used for creating this problem.)

I want to share with you an article I found on ArXiv written by mathematician Steven Krantz for mathematicians on mathematics in the larger university context. [Paper on ArXiv; or get it here.] It’s a good read for mathematicians, yes. It makes a convincing charge that the isolationist tendency of mathematics (specifically the individuals, the departments, and the profession) can’t remain so. But it’s also a really good read for high school math teachers who want to know what professional mathematicians do, how they think. 

Abstract: We consider the question of how mathematicians view themselves and how non-mathematicians view us. What is our role in society? Is it effective? Is it rewarding? How could it be improved? This paper will be part of a forthcoming volume on this circle of questions. 

A choice excerpt to get you interested:

When we meet someone at a cocktail party and say, “I am a mathematician,” we expect to be snubbed, or perhaps greeted with a witty rejoinder like, “I was never any good in math.” Or, “I was good at math until we got to that stuff with the letters—like algebra.”  

When I meet a brain surgeon I never say, “I was never any good at brain surgery. Those lobotomies always got me down.” When I meet a proctologist, I am never tempted to say, “I was never any good at . . . .” Why do we mathematicians elicit such foolish behavior from people? 

Krantz first came on my radar when I was writing a research paper on rhetoric in Wolfram’s A New Kind of Science. To this day, I have not forgotten his review of that book: the most vicious piece of academic writing I’ve come across. Ever. Krantz knows how to pack a wallop, with rhetorical aplomb. (Plus, I agree with almost everything Krantz had to say damning Wolfram’s book.)

I was browsing old math journals a few days ago and got caught up in looking at puzzles/challenging problems sent in by professors to The Mathematical Gazette (the original publication of the Mathematical Association). 

I got engaged in battle with a problem from it’s first year of publication (No. 1, Vol. 7, April 1896 – if you have JSTOR access, see the original problem here). The journal stated that it was a question “from recent Entrance Scholarship papers at Oxford and Cambridge.”

I think it’s a darn good problem, so take a stab at it. I’ll type my solution to it below the fold, but maybe you’ll get a better one? (I went down two wrong roads before I came up with this one…)

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