This edition of Wisdom From Our Elders comes exactly a year and a half after my last such post. (Clearly this blog has some productivity issues.)

Prof. Larsen: My advisor used to say that one should never do matrix calculations in public.

Commentary:

Matrix calculations are not the most elegant way of proving things in algebra, as they involve a lot of repetitive arithmetic. There is also a deeper mathematical reason: using matrices requires a choice of "coordinates" for whatever object is being studied, and it's often preferable to approach the object more generally, without tying it down to specific coordinates.

However, it's another general fact in mathematics that the insight needed to write a proof often can only come from doing arithmetic until you spot the pattern. Hence, this came a few moments after that first bit of wisdom:

Prof. Larsen: I'm sure that he himself did extensive matrix calculations in private.
-- posted at 10:34 PM | 3 comments

The Vienna Vegetable Orchestra

(Thanks to the IU recorder players. I'd like to see any of you call the recorder a silly instrument now.)
-- posted at 11:31 PM | 1 comments

It's much more of a logic puzzle than a mathematical one, but it does have some graph-theoretical uses.
-- posted at 9:51 AM | 0 comments

A Contribution to the Mathematical Theory of Big Game Hunting
The American Mathematical Monthly, Aug.-Sep. 1938

Besides mathematical ideas, the article includes methods from theoretical and experimental physics. If you don't have access to JSTOR (which I should mention is an incredibly useful resource), you can find many variations on the original through Google.
-- posted at 9:58 AM | 2 comments

... Star Wars was released.

Here is a report on one of the most important filming locations, and an interesting place in its own right. Star Wars, like other popular works of science fiction and fantasy, is appealing since it has both very familiar and very alien elements; the fact that "Tatooine" is actually an out-of-the-way corner of Earth illustrates this.
-- posted at 4:01 AM | 0 comments

As I am sure you know, Boris Yeltsin passed away earlier this week. This morning there was news of another death in Moscow: cellist and conductor Mstislav Rostropovich. Here he is playing the beginning of Dvořák's cello concerto (I encourage you to watch the rest).
-- posted at 5:39 PM | 1 comments

One of the greatest mathematical geniuses of all time, Leonhard Euler, was born 300 years ago today.

To me, the main lesson to be taken from his life is that of dedication to one's work. From his early 30s onward his eyesight steadily deteriorated, to the point of near-total blindness; this appears to have had little or no effect on his abilities. He continued to produce insightful results until the end of his life; though I have been unable to confirm this elsewhere, I have heard one professor claim that Euler's output actually increased as he went blind. Perhaps some of this can be attributed to his raw mental capacity and incredible memory, but these qualities would have been useless he truly loved his subject.
-- posted at 2:58 AM | 0 comments