Ultima Thule

In ancient times the northernmost region of the habitable world - hence, any distant, unknown or mysterious land.

Thursday, May 11, 2006

Algebra and Its Enemies

By Aussiegirl

How can you not read an article that begins with this delicious title? And then goes on to inform us that Richard Cohen looks back on typing class as the acme of his high school scholastic career! This article helps you realize how much we take all this knowledge for granted, and aren't awed, as we should be, by the genius of those scientists and mathematicians who went all by themselves into the intellectual void and came back with ideas and theories that miraculously enough work in the real world. From the article: The remarkable thing is not that it took humanity so long to learn how to do this stuff, but that we can do it at all.
For all of you who wish to add to what you remember from high school algebra class, here's the link to Wikipedia's article on the subject. The illustration that accompanies this post is an imagined portrait of Hypatia, referred to in the article thus: The brutal death of the female mathematician-philosopher Hypatia in 415 at the hands of a religious mob marked the twilight of math in the declining Roman Empire. (Here's the Wikipedia article on Hypatia. Wikipedia gives various theories as to the reason for her horrendous death at the hands of a mob, one of them being that she was considered to be a witch. Surely the fact that she was a brilliant woman, and not just a "witch", was a key factor in the mob's decision to kill her.)

TCS Daily - Algebra and Its Enemies

Algebra and Its Enemies
By Kenneth Silber

Early this year, Washington Post op-ed columnist Richard Cohen weighed in on a subject about which he, by his own admission, knew nothing. The subject was algebra, and Cohen's column took the form of advice to a young woman who had dropped out of high school after failing in that subject. Cohen advised the ex-student and the public at large that algebra's importance was overblown -- and that he, Cohen, "had never once used it and never once even rued" that he could not use it. [....]

"Most of math" Cohen explained, "can now be done by a computer or a calculator," and moreover it is a "lie" that algebra teaches reasoning. "Writing is the highest form of reasoning," Cohen affirmed, stating that the most valuable class he himself had taken in high school was ... typing.

Cohen's dismissal of a central branch of mathematics got some negative attention from science bloggers. Biologist P.Z. Myers castigated Cohen for complacency and arrogance in advising a young woman to throw away career options and intellectual tools; Myers also noted that the people who design calculators, among many others, need to know algebra. [....]

Stdents (and pundits) who find algebra hard might consider how difficult such math must have been for the people who actually pioneered it. That story is told in a new book, Unknown Quantity: A Real and Imaginary History of Algebra, by John Derbyshire (Joseph Henry Press). Derbyshire, who wrote a previous book on math, Prime Obsession, and is a frequent contributor to National Review, gives an absorbing account of algebra over the millennia, from its rudimentary origins in ancient Mesopotamia and Egypt to its cutting-edge applications in 21st-century physics.

An interesting feature of this history is just how slow progress often was. Babylonians in the 2nd millennium BCE worked out algebraic word problems on cuneiform tablets, and the ancient Greeks handled similar problems with a geometrical approach, but it was only at the time of Diophantus, who lived in Alexandria in roughly the 3rd century CE, that anyone used letter symbols to keep track of unknowns in equations. The brutal death of the female mathematician-philosopher Hypatia in 415 at the hands of a religious mob marked the twilight of math in the declining Roman Empire. [....]

Such tortuous history, as Derbyshire points out, suggests that symbolic algebra, with its high level of abstraction, does not exactly come naturally to people. He finds this a bit depressing but also inspiring. No thanks to some pundits, though.


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