# MacTutor History of Mathematics archive

February 28, 2009 12:47 PM Subscribe

The MacTutor History of Mathematics archive is an astounding collection of historical material on mathematics, especially biographies. (Previously: 1 2 3 4.)

*You may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.*

I loved this quote by William Clifford.

posted by francesca too at 5:26 PM on February 28, 2009

Boy, that quote from William Clifford is about the falsest thing I've ever heard said about math.

posted by escabeche at 5:56 PM on February 28, 2009

posted by escabeche at 5:56 PM on February 28, 2009

Right. I defy anyone to turn Homological Algebra into good english with sound common sense, though it is enormously useful in extremely disparate places. For me, algebra steps in when we get to the boundary of what common sense can handle. Like, say, figuring out what happens when you take the prism of a four-dimensional simplex.* If we could do it all by common sense and wit alone, there would be no use for mathematics.

* - The four-dimensional simplex is the next thing in the sequence [point, interval, triangle, tetrahedron,...]; it's prism is that thing stretched out along an interval in a fifth dimension. The prism of a triangle looks like, well, a prism. Question: How many five-simplices can you cut up the prism of a four-simplex into? Now, prove it. Good luck without developing some algebra to describe the objects involved...

posted by kaibutsu at 6:45 PM on February 28, 2009

* - The four-dimensional simplex is the next thing in the sequence [point, interval, triangle, tetrahedron,...]; it's prism is that thing stretched out along an interval in a fifth dimension. The prism of a triangle looks like, well, a prism. Question: How many five-simplices can you cut up the prism of a four-simplex into? Now, prove it. Good luck without developing some algebra to describe the objects involved...

posted by kaibutsu at 6:45 PM on February 28, 2009

I guess Clifford was talking about non-homological algebra, since he died in 1879.

The quote resonated with me because that is the way I usually understand algebraic equations, by verbalizing them.

posted by francesca too at 7:25 PM on February 28, 2009

The quote resonated with me because that is the way I usually understand algebraic equations, by verbalizing them.

posted by francesca too at 7:25 PM on February 28, 2009

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posted by LSK at 2:14 PM on February 28, 2009